{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":45413,"title":"Characterize fluid flow in a pipe as to laminar or turbulent","description":"In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.\r\n\r\nHence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, *Re*. For a fluid flowing inside a circular pipe, *Re* is computed as follows:\r\n\r\n Re = D x v x rho / mu\r\n where:\r\n D = inside diameter of the pipe [m]\r\n v = mean flow velocity [m/s]\r\n rho = fluid density [kg/m^3]\r\n mu = fluid viscosity [Pa.s] or [kg/m/s]\r\n \r\nNote: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease. \r\n\r\nWe can then adopt the following rule: If *Re* \u003c 2300, the flow is laminar; if *Re* \u003e 2900, the flow is turbulent; otherwise, the flow is in transition. \r\n\r\nWrite a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of |D|, |v|, |rho|, and |mu| in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.\r\n\r\nSee sample test cases:\r\n\r\n \u003e\u003e flow_pattern([0.02 0.1 1000 8.9e-4])\r\nans =\r\n 'LAMINAR'\r\n\u003e\u003e flow_pattern([0.02 0.5 1000 8.9e-4])\r\nans =\r\n 'TURBULENT'\r\n\u003e\u003e flow_pattern([0.02 0.1 1200 8.9e-4])\r\nans =\r\n 'TRANSITION'\r\n \r\n","description_html":"\u003cp\u003eIn fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.\u003c/p\u003e\u003cp\u003eHence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, \u003cb\u003eRe\u003c/b\u003e. For a fluid flowing inside a circular pipe, \u003cb\u003eRe\u003c/b\u003e is computed as follows:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eRe = D x v x rho / mu\r\n where:\r\n D = inside diameter of the pipe [m]\r\n v = mean flow velocity [m/s]\r\n rho = fluid density [kg/m^3]\r\n mu = fluid viscosity [Pa.s] or [kg/m/s]\r\n\u003c/pre\u003e\u003cp\u003eNote: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.\u003c/p\u003e\u003cp\u003eWe can then adopt the following rule: If \u003cb\u003eRe\u003c/b\u003e \u0026lt; 2300, the flow is laminar; if \u003cb\u003eRe\u003c/b\u003e \u0026gt; 2900, the flow is turbulent; otherwise, the flow is in transition.\u003c/p\u003e\u003cp\u003eWrite a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of \u003ctt\u003eD\u003c/tt\u003e, \u003ctt\u003ev\u003c/tt\u003e, \u003ctt\u003erho\u003c/tt\u003e, and \u003ctt\u003emu\u003c/tt\u003e in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.\u003c/p\u003e\u003cp\u003eSee sample test cases:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; flow_pattern([0.02 0.1 1000 8.9e-4])\r\nans =\r\n 'LAMINAR'\r\n\u0026gt;\u0026gt; flow_pattern([0.02 0.5 1000 8.9e-4])\r\nans =\r\n 'TURBULENT'\r\n\u0026gt;\u0026gt; flow_pattern([0.02 0.1 1200 8.9e-4])\r\nans =\r\n 'TRANSITION'\r\n\u003c/pre\u003e","function_template":"function y = flow_pattern(x)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(isequal(flow_pattern([0.025 0.089 986.29 0.00087]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.095 976.11 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.124 1089.38 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.095 1069.84 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.148 1004.66 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.082 922.17 0.00078]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.084 1063.42 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.127 924.05 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.083 1014.92 0.00087]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.117 1080.37 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.100 1077.98 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.103 1014.85 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.020 0.120 1001.35 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.021 0.086 946.85 0.00074]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.089 910.72 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.067 1082.44 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.070 1053.44 0.00071]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.066 957.29 0.00084]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.101 1044.27 0.00089]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.125 981.46 0.00075]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.072 1068.48 0.00083]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.129 993.82 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.149 1053.99 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.110 1050.57 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.057 1093.71 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.090 921.41 0.00084]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.128 1013.32 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.144 1074.29 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.097 1065.76 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.040 0.078 914.57 0.00085]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.142 965.40 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.096 1064.15 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.121 946.99 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.133 1099.07 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.143 1037.53 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.113 972.65 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.097 1000.68 0.00088]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.084 1014.83 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.108 1075.67 0.00071]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.029 0.058 1012.65 0.00081]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.073 1017.47 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.116 970.78 0.00077]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.145 959.64 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.124 1041.18 0.00084]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.020 0.087 1080.30 0.00076]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.080 925.00 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.148 1072.40 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.074 963.56 0.00090]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.125 1068.37 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.038 0.061 1049.02 0.00085]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.063 989.16 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.136 1035.54 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.146 913.34 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.098 1036.97 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.083 1076.17 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.146 930.58 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.059 990.88 0.00083]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.129 1042.54 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.146 1001.16 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.074 946.86 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.112 924.52 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.124 982.26 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.090 910.44 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.082 998.59 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.098 1008.00 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.056 1063.90 0.00085]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.140 1036.86 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.040 0.053 984.85 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.058 1032.03 0.00071]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.121 997.58 0.00082]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.115 976.13 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.076 948.26 0.00082]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.091 943.56 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.078 1023.08 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.142 976.96 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.061 931.76 0.00077]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.108 1017.24 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.051 1061.88 0.00082]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.077 951.62 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.055 933.85 0.00075]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.111 1064.74 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.121 1071.88 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.149 918.72 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.074 967.94 0.00074]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.145 978.92 0.00082]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.121 980.31 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.038 0.125 957.12 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.100 1022.14 0.00084]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.123 1077.46 0.00071]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.136 984.35 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.125 1096.20 0.00075]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.088 1000.05 0.00081]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.040 0.099 980.18 0.00090]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.117 1092.85 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.103 900.29 0.00088]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.080 1090.12 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.058 1016.44 0.00073]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.021 0.108 957.40 0.00077]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.136 969.58 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.071 1053.65 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version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For a fluid flowing inside a circular pipe,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is computed as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Re = D x v x rho / mu\\n where:\\n D = inside diameter of the pipe [m]\\n v = mean flow velocity [m/s]\\n rho = fluid density [kg/m^3]\\n mu = fluid viscosity [Pa.s] or [kg/m/s]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe can then adopt the following rule: If\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026lt; 2300, the flow is laminar; if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026gt; 2900, the flow is turbulent; otherwise, the flow is in transition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erho\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emu\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee sample test cases:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e flow_pattern([0.02 0.1 1000 8.9e-4])\\nans =\\n 'LAMINAR'\\n\u003e\u003e flow_pattern([0.02 0.5 1000 8.9e-4])\\nans =\\n 'TURBULENT'\\n\u003e\u003e flow_pattern([0.02 0.1 1200 8.9e-4])\\nans =\\n 'TRANSITION']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59721,"title":"finding vector pair with min angle between them","description":"given a matrix with more than one row , compare row vectors of the given matrix and find the pair with the minumum angle between them , \"without using the dot fucntion\" \r\nyou can find the angle from the following formula\r\n θ = cos-1 [ (a. b) / (|a| |b|) ]\r\nthe product between the two vectors is the dot product \r\na⋅b=∑(ai​)*(bi) from i=1 to n​\r\nthe length of a vector is the square root of the sum of the squares of the components\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111px; transform-origin: 407px 111px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003egiven a matrix with more than one row , compare row vectors of the given matrix and find the pair with the minumum angle between them , \"without using the dot fucntion\" \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eyou can find the angle from the following formula\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e θ = cos-1 [ (a. b) / (|a| |b|) ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ethe product between the two vectors is the dot product \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e⋅\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e=\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e∑(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e​)*(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei) from i=1 to n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e​\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ethe length of a vector is the square root of the sum of the squares of the components\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v1 v2] = minAngle(mat)\r\n \r\nend","test_suite":"%%\r\nmat = [ 155 12 344 356\r\n 305 234 135 40\r\n 227 13 316 310\r\n 266 72 51 178\r\n 8 195 166 289];\r\nres1=[155 12 344 356];\r\nres2=[227 13 316 310];\r\n[v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n\r\n%%\r\nmat=[ 2 50 47\r\n 24 99 24\r\n 89 23 42\r\n 13 37 9\r\n 66 5 83\r\n 2 5 95\r\n 60 28 3\r\n 52 84 13\r\n 87 35 14\r\n 37 93 17\r\n 80 43 100\r\n 20 16 98\r\n 27 41 3\r\n 59 86 76\r\n 22 56 26\r\n 99 68 42\r\n 13 94 40];\r\n\r\n\r\n \r\n\r\n\r\n\r\n\r\n res1=[ 13 37 9];\r\n res2=[ 37 93 17];\r\n [v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n\r\n%%\r\nmat=[ 79 4 66 79 23\r\n 22 42 94 3 25\r\n 78 36 58 16 71\r\n 55 52 23 23 8\r\n 67 3 4 80 82\r\n 96 74 85 74 98];\r\n\r\n res1=[ 78 36 58 16 71];\r\n\r\n\r\n\r\n res2=[ 96 74 85 74 98];\r\n [v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n\r\n %%\r\n mat=[ 8 47 50 69\r\n 78 49 11 83\r\n 68 53 63 98\r\n 97 74 100 57\r\n 4 48 24 91\r\n 96 46 12 92\r\n 64 61 4 1\r\n 73 61 72 71\r\n 78 6 47 63\r\n 52 34 18 41\r\n 46 3 95 38\r\n 100 10 52 2\r\n 88 71 59 25\r\n 63 33 99 43\r\n 95 56 48 44\r\n 73 6 13 14\r\n 56 60 8 84\r\n 96 60 7 85\r\n 8 90 54 76\r\n 1 6 39 70\r\n 83 12 18 44\r\n 44 9 85 11\r\n 65 43 17 90\r\n 44 68 36 34\r\n 92 89 46 89\r\n 36 37 65 79\r\n 11 69 76 41\r\n 41 17 23 56\r\n 94 10 16 7\r\n 51 98 17 70\r\n 94 18 53 11\r\n 45 9 38 42\r\n 59 99 32 31\r\n 81 85 12 82\r\n 46 48 87 100\r\n 52 17 78 17\r\n 35 55 61 57\r\n 46 55 22 93\r\n 52 51 31 10\r\n 84 56 31 34\r\n 77 51 62 66\r\n 41 88 17 40\r\n 90 62 86 20\r\n 86 50 60 48\r\n 11 50 3 54\r\n 31 52 5 71\r\n 1 3 98 47\r\n 28 86 93 55\r\n 71 55 16 93\r\n 84 1 68 7\r\n 17 64 98 33\r\n 76 19 2 72\r\n 72 1 56 73\r\n 13 92 67 14\r\n 49 9 92 37\r\n 44 28 83 76\r\n 56 78 58 20\r\n 6 3 75 90\r\n 96 21 63 10\r\n 59 2 60 72\r\n 17 65 28 98\r\n 34 46 5 41\r\n 48 56 54 47\r\n 76 95 90 8\r\n 57 35 5 54\r\n 26 30 13 73\r\n 6 49 17 46\r\n 23 59 82 56\r\n 55 46 46 33\r\n 80 15 42 6\r\n 78 57 59 22\r\n 96 11 69 23\r\n 72 58 100 42\r\n 88 48 23 23\r\n 16 35 48 32\r\n 11 45 79 61\r\n 95 82 31 63\r\n 19 49 73 19\r\n 65 14 81 41\r\n 12 81 4 30\r\n 70 24 33 82\r\n 7 5 66 14\r\n 98 79 3 37\r\n 9 81 91 72\r\n 50 62 99 11\r\n 9 66 18 58\r\n 35 38 29 61\r\n 36 9 44 5\r\n 98 25 92 84\r\n 53 9 33 18\r\n 85 80 93 6\r\n 60 56 25 10\r\n 9 29 90 32\r\n 36 98 38 84\r\n 26 64 21 21\r\n 52 36 58 48\r\n 92 15 35 18\r\n 62 37 98 67\r\n 79 53 24 9\r\n 12 62 100 65\r\n 30 26 24 61\r\n 84 12 29 17];\r\n res1= [36 37 65 79];\r\n\r\n\r\n\r\n\r\n res2=[ 46 48 87 100];\r\n [v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":3838707,"edited_by":3838707,"edited_at":"2024-03-28T08:31:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-03-28T08:31:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-27T20:22:32.000Z","updated_at":"2026-01-06T16:39:24.000Z","published_at":"2024-03-27T20:23:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a matrix with more than one row , compare row vectors of the given matrix and find the pair with the minumum angle between them , \\\"without using the dot fucntion\\\" \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eyou can find the angle from the following formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e θ = cos-1 [ (a. b) / (|a| |b|) ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe product between the two vectors is the dot product \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e⋅\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e∑(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e​)*(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei) from i=1 to n\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e​\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe length of a vector is the square root of the sum of the squares of the components\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":45413,"title":"Characterize fluid flow in a pipe as to laminar or turbulent","description":"In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.\r\n\r\nHence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, *Re*. For a fluid flowing inside a circular pipe, *Re* is computed as follows:\r\n\r\n Re = D x v x rho / mu\r\n where:\r\n D = inside diameter of the pipe [m]\r\n v = mean flow velocity [m/s]\r\n rho = fluid density [kg/m^3]\r\n mu = fluid viscosity [Pa.s] or [kg/m/s]\r\n \r\nNote: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease. \r\n\r\nWe can then adopt the following rule: If *Re* \u003c 2300, the flow is laminar; if *Re* \u003e 2900, the flow is turbulent; otherwise, the flow is in transition. \r\n\r\nWrite a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of |D|, |v|, |rho|, and |mu| in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.\r\n\r\nSee sample test cases:\r\n\r\n \u003e\u003e flow_pattern([0.02 0.1 1000 8.9e-4])\r\nans =\r\n 'LAMINAR'\r\n\u003e\u003e flow_pattern([0.02 0.5 1000 8.9e-4])\r\nans =\r\n 'TURBULENT'\r\n\u003e\u003e flow_pattern([0.02 0.1 1200 8.9e-4])\r\nans =\r\n 'TRANSITION'\r\n \r\n","description_html":"\u003cp\u003eIn fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.\u003c/p\u003e\u003cp\u003eHence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, \u003cb\u003eRe\u003c/b\u003e. For a fluid flowing inside a circular pipe, \u003cb\u003eRe\u003c/b\u003e is computed as follows:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eRe = D x v x rho / mu\r\n where:\r\n D = inside diameter of the pipe [m]\r\n v = mean flow velocity [m/s]\r\n rho = fluid density [kg/m^3]\r\n mu = fluid viscosity [Pa.s] or [kg/m/s]\r\n\u003c/pre\u003e\u003cp\u003eNote: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.\u003c/p\u003e\u003cp\u003eWe can then adopt the following rule: If \u003cb\u003eRe\u003c/b\u003e \u0026lt; 2300, the flow is laminar; if \u003cb\u003eRe\u003c/b\u003e \u0026gt; 2900, the flow is turbulent; otherwise, the flow is in transition.\u003c/p\u003e\u003cp\u003eWrite a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of \u003ctt\u003eD\u003c/tt\u003e, \u003ctt\u003ev\u003c/tt\u003e, \u003ctt\u003erho\u003c/tt\u003e, and \u003ctt\u003emu\u003c/tt\u003e in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.\u003c/p\u003e\u003cp\u003eSee sample test cases:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; flow_pattern([0.02 0.1 1000 8.9e-4])\r\nans =\r\n 'LAMINAR'\r\n\u0026gt;\u0026gt; flow_pattern([0.02 0.5 1000 8.9e-4])\r\nans =\r\n 'TURBULENT'\r\n\u0026gt;\u0026gt; flow_pattern([0.02 0.1 1200 8.9e-4])\r\nans =\r\n 'TRANSITION'\r\n\u003c/pre\u003e","function_template":"function y = flow_pattern(x)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(isequal(flow_pattern([0.025 0.089 986.29 0.00087]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.095 976.11 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.124 1089.38 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.095 1069.84 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.148 1004.66 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.082 922.17 0.00078]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.084 1063.42 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.127 924.05 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.083 1014.92 0.00087]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.117 1080.37 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.100 1077.98 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.103 1014.85 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.020 0.120 1001.35 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.021 0.086 946.85 0.00074]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.089 910.72 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.067 1082.44 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.070 1053.44 0.00071]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.066 957.29 0.00084]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.101 1044.27 0.00089]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.125 981.46 0.00075]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.072 1068.48 0.00083]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.129 993.82 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.149 1053.99 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.110 1050.57 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.057 1093.71 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.090 921.41 0.00084]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.128 1013.32 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.144 1074.29 0.00080]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.097 1065.76 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.040 0.078 914.57 0.00085]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.142 965.40 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.096 1064.15 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.121 946.99 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.133 1099.07 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.143 1037.53 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.113 972.65 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.097 1000.68 0.00088]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.084 1014.83 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.108 1075.67 0.00071]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.029 0.058 1012.65 0.00081]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.073 1017.47 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.116 970.78 0.00077]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.145 959.64 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.124 1041.18 0.00084]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.020 0.087 1080.30 0.00076]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.080 925.00 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.148 1072.40 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.027 0.074 963.56 0.00090]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.125 1068.37 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.038 0.061 1049.02 0.00085]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.063 989.16 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.136 1035.54 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.146 913.34 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.098 1036.97 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.083 1076.17 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.146 930.58 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.059 990.88 0.00083]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.129 1042.54 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.146 1001.16 0.00076]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.074 946.86 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.112 924.52 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.124 982.26 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.090 910.44 0.00081]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.035 0.082 998.59 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.098 1008.00 0.00074]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.056 1063.90 0.00085]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.140 1036.86 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.040 0.053 984.85 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.058 1032.03 0.00071]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.031 0.121 997.58 0.00082]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.115 976.13 0.00072]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.076 948.26 0.00082]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.091 943.56 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.078 1023.08 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.142 976.96 0.00073]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.061 931.76 0.00077]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.037 0.108 1017.24 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.051 1061.88 0.00082]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.077 951.62 0.00080]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.055 933.85 0.00075]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.111 1064.74 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.036 0.121 1071.88 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.149 918.72 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.024 0.074 967.94 0.00074]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.030 0.145 978.92 0.00082]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.032 0.121 980.31 0.00087]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.038 0.125 957.12 0.00086]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.100 1022.14 0.00084]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.123 1077.46 0.00071]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.023 0.136 984.35 0.00078]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.125 1096.20 0.00075]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.022 0.088 1000.05 0.00081]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.040 0.099 980.18 0.00090]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.025 0.117 1092.85 0.00083]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.103 900.29 0.00088]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.028 0.080 1090.12 0.00079]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.026 0.058 1016.44 0.00073]),'LAMINAR'))\r\n%%\r\nassert(isequal(flow_pattern([0.021 0.108 957.40 0.00077]),'TRANSITION'))\r\n%%\r\nassert(isequal(flow_pattern([0.034 0.136 969.58 0.00089]),'TURBULENT'))\r\n%%\r\nassert(isequal(flow_pattern([0.039 0.071 1053.65 0.00082]),'TURBULENT'))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":1,"created_by":255320,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":149,"test_suite_updated_at":"2020-04-01T01:14:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-01T00:39:41.000Z","updated_at":"2026-03-31T11:58:08.000Z","published_at":"2020-04-01T01:14:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For a fluid flowing inside a circular pipe,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is computed as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Re = D x v x rho / mu\\n where:\\n D = inside diameter of the pipe [m]\\n v = mean flow velocity [m/s]\\n rho = fluid density [kg/m^3]\\n mu = fluid viscosity [Pa.s] or [kg/m/s]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe can then adopt the following rule: If\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026lt; 2300, the flow is laminar; if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026gt; 2900, the flow is turbulent; otherwise, the flow is in transition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erho\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emu\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee sample test cases:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e flow_pattern([0.02 0.1 1000 8.9e-4])\\nans =\\n 'LAMINAR'\\n\u003e\u003e flow_pattern([0.02 0.5 1000 8.9e-4])\\nans =\\n 'TURBULENT'\\n\u003e\u003e flow_pattern([0.02 0.1 1200 8.9e-4])\\nans =\\n 'TRANSITION']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59721,"title":"finding vector pair with min angle between them","description":"given a matrix with more than one row , compare row vectors of the given matrix and find the pair with the minumum angle between them , \"without using the dot fucntion\" \r\nyou can find the angle from the following formula\r\n θ = cos-1 [ (a. b) / (|a| |b|) ]\r\nthe product between the two vectors is the dot product \r\na⋅b=∑(ai​)*(bi) from i=1 to n​\r\nthe length of a vector is the square root of the sum of the squares of the components\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111px; transform-origin: 407px 111px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003egiven a matrix with more than one row , compare row vectors of the given matrix and find the pair with the minumum angle between them , \"without using the dot fucntion\" \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eyou can find the angle from the following formula\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e θ = cos-1 [ (a. b) / (|a| |b|) ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ethe product between the two vectors is the dot product \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e⋅\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e=\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e∑(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e​)*(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ei) from i=1 to n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e​\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ethe length of a vector is the square root of the sum of the squares of the components\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v1 v2] = minAngle(mat)\r\n \r\nend","test_suite":"%%\r\nmat = [ 155 12 344 356\r\n 305 234 135 40\r\n 227 13 316 310\r\n 266 72 51 178\r\n 8 195 166 289];\r\nres1=[155 12 344 356];\r\nres2=[227 13 316 310];\r\n[v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n\r\n%%\r\nmat=[ 2 50 47\r\n 24 99 24\r\n 89 23 42\r\n 13 37 9\r\n 66 5 83\r\n 2 5 95\r\n 60 28 3\r\n 52 84 13\r\n 87 35 14\r\n 37 93 17\r\n 80 43 100\r\n 20 16 98\r\n 27 41 3\r\n 59 86 76\r\n 22 56 26\r\n 99 68 42\r\n 13 94 40];\r\n\r\n\r\n \r\n\r\n\r\n\r\n\r\n res1=[ 13 37 9];\r\n res2=[ 37 93 17];\r\n [v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n\r\n%%\r\nmat=[ 79 4 66 79 23\r\n 22 42 94 3 25\r\n 78 36 58 16 71\r\n 55 52 23 23 8\r\n 67 3 4 80 82\r\n 96 74 85 74 98];\r\n\r\n res1=[ 78 36 58 16 71];\r\n\r\n\r\n\r\n res2=[ 96 74 85 74 98];\r\n [v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n\r\n %%\r\n mat=[ 8 47 50 69\r\n 78 49 11 83\r\n 68 53 63 98\r\n 97 74 100 57\r\n 4 48 24 91\r\n 96 46 12 92\r\n 64 61 4 1\r\n 73 61 72 71\r\n 78 6 47 63\r\n 52 34 18 41\r\n 46 3 95 38\r\n 100 10 52 2\r\n 88 71 59 25\r\n 63 33 99 43\r\n 95 56 48 44\r\n 73 6 13 14\r\n 56 60 8 84\r\n 96 60 7 85\r\n 8 90 54 76\r\n 1 6 39 70\r\n 83 12 18 44\r\n 44 9 85 11\r\n 65 43 17 90\r\n 44 68 36 34\r\n 92 89 46 89\r\n 36 37 65 79\r\n 11 69 76 41\r\n 41 17 23 56\r\n 94 10 16 7\r\n 51 98 17 70\r\n 94 18 53 11\r\n 45 9 38 42\r\n 59 99 32 31\r\n 81 85 12 82\r\n 46 48 87 100\r\n 52 17 78 17\r\n 35 55 61 57\r\n 46 55 22 93\r\n 52 51 31 10\r\n 84 56 31 34\r\n 77 51 62 66\r\n 41 88 17 40\r\n 90 62 86 20\r\n 86 50 60 48\r\n 11 50 3 54\r\n 31 52 5 71\r\n 1 3 98 47\r\n 28 86 93 55\r\n 71 55 16 93\r\n 84 1 68 7\r\n 17 64 98 33\r\n 76 19 2 72\r\n 72 1 56 73\r\n 13 92 67 14\r\n 49 9 92 37\r\n 44 28 83 76\r\n 56 78 58 20\r\n 6 3 75 90\r\n 96 21 63 10\r\n 59 2 60 72\r\n 17 65 28 98\r\n 34 46 5 41\r\n 48 56 54 47\r\n 76 95 90 8\r\n 57 35 5 54\r\n 26 30 13 73\r\n 6 49 17 46\r\n 23 59 82 56\r\n 55 46 46 33\r\n 80 15 42 6\r\n 78 57 59 22\r\n 96 11 69 23\r\n 72 58 100 42\r\n 88 48 23 23\r\n 16 35 48 32\r\n 11 45 79 61\r\n 95 82 31 63\r\n 19 49 73 19\r\n 65 14 81 41\r\n 12 81 4 30\r\n 70 24 33 82\r\n 7 5 66 14\r\n 98 79 3 37\r\n 9 81 91 72\r\n 50 62 99 11\r\n 9 66 18 58\r\n 35 38 29 61\r\n 36 9 44 5\r\n 98 25 92 84\r\n 53 9 33 18\r\n 85 80 93 6\r\n 60 56 25 10\r\n 9 29 90 32\r\n 36 98 38 84\r\n 26 64 21 21\r\n 52 36 58 48\r\n 92 15 35 18\r\n 62 37 98 67\r\n 79 53 24 9\r\n 12 62 100 65\r\n 30 26 24 61\r\n 84 12 29 17];\r\n res1= [36 37 65 79];\r\n\r\n\r\n\r\n\r\n res2=[ 46 48 87 100];\r\n [v1 v2]=minAngle(mat);\r\nassert(isequal([v1 v2],[res1 res2]))\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":3838707,"edited_by":3838707,"edited_at":"2024-03-28T08:31:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-03-28T08:31:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-27T20:22:32.000Z","updated_at":"2026-01-06T16:39:24.000Z","published_at":"2024-03-27T20:23:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a matrix with more than one row , compare row vectors of the given matrix and find the pair with the minumum angle between them , \\\"without using the dot fucntion\\\" \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eyou can find the angle from the following formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e θ = cos-1 [ (a. b) / (|a| |b|) ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe product between the two vectors is the dot product \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e⋅\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e∑(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e​)*(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei) from i=1 to n\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e​\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe length of a vector is the square root of the sum of the squares of the components\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"if\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"if\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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