{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":1908,"title":"Equilibrium","description":"Is this tower of blocks going to fall?\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium02.jpg\u003e\u003e\r\n\r\n*Description*\r\n\r\nGiven a stacking configuration for a series of square blocks, your function should return _true_ if they are at equilibrium and _false_ otherwise. \r\n\r\nThe block configuration for N blocks is provided as a input vector *x* with N elements listing the _x-coordinates_ of the left-side of each block. The blocks are square with side equal to 1 (so the i-th block left side is at x(i) and its right side is at x(i)+1). The _y-coordinates_ of each block are determined implicitly by the order of the blocks, which are dropped \"tetris-style\" until they hit the floor or another block. \r\n\r\nAll blocks are identical (same dimensions and mass) and perfectly smooth (friction is to be disregarded).\r\n \r\nIntermediate positions may be unstable. You are only required to determine whether the final configuration is stable.\r\n\r\n*Examples*:\r\n\r\nExample (1) \r\n \r\n x = [0 0.4];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01a.jpg\u003e\u003e\r\n\r\nThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.4 1). This configuration is stable so your function should return _true_.\r\n\r\nExample (2) \r\n\r\n x = [0 0.6];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01b.jpg\u003e\u003e\r\n\r\nThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.6 1). This configuration is unstable (the second block will fall) so your function should return _false_.\r\n\r\nExample (3) \r\n\r\n x = [0 1.5 0.6];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01c.jpg\u003e\u003e\r\n\r\nThe three block bottom-left corner coordinates are (0,0) (1.5,0) and (0.6,1). This configuration is stable so your function should return _true_.\r\n\r\nExample (4) \r\n\r\n x = [0 .9 -.9 zeros(1,5)];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01d.jpg\u003e\u003e\r\n\r\nThis configuration is unstable, but note that if instead of five we add a few more blocks on top of this at the 0 position that will keep the tower from falling!\r\n\r\nExample (5) \r\n\r\nx = cumsum(fliplr(1./(1:8))/2);\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01e.jpg\u003e\u003e\r\n\r\nThis configuration is stable (see the \u003chttp://en.wikipedia.org/wiki/Block-stacking_problem classic optimal stacking solution\u003e) so your function should return _true_.\r\n\r\n*Display*\r\n\r\nIf you wish, you may display any given block configuration *x* using the code below:\r\n\r\n clf;\r\n y=[];\r\n for n=1:numel(x), y(n)=max([0 y(abs(x(1:n-1)-x(n))\u003c1)+1]); end\r\n h=arrayfun(@(x,y)patch(x+[0,1,1,0],y+[0,0,1,1],rand(1,3)),x,y);\r\n text(x+.5,y+.5,arrayfun(@num2str,1:numel(x),'uni',0),...\r\n 'horizontalalignment','center');\r\n\r\nVisit \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1910-block-canvas Block canvas\u003e for a related Cody problem.","description_html":"\u003cp\u003eIs this tower of blocks going to fall?\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium02.jpg\"\u003e\u003cp\u003e\u003cb\u003eDescription\u003c/b\u003e\u003c/p\u003e\u003cp\u003eGiven a stacking configuration for a series of square blocks, your function should return \u003ci\u003etrue\u003c/i\u003e if they are at equilibrium and \u003ci\u003efalse\u003c/i\u003e otherwise.\u003c/p\u003e\u003cp\u003eThe block configuration for N blocks is provided as a input vector \u003cb\u003ex\u003c/b\u003e with N elements listing the \u003ci\u003ex-coordinates\u003c/i\u003e of the left-side of each block. The blocks are square with side equal to 1 (so the i-th block left side is at x(i) and its right side is at x(i)+1). The \u003ci\u003ey-coordinates\u003c/i\u003e of each block are determined implicitly by the order of the blocks, which are dropped \"tetris-style\" until they hit the floor or another block.\u003c/p\u003e\u003cp\u003eAll blocks are identical (same dimensions and mass) and perfectly smooth (friction is to be disregarded).\u003c/p\u003e\u003cp\u003eIntermediate positions may be unstable. You are only required to determine whether the final configuration is stable.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eExample (1)\u003c/p\u003e\u003cpre\u003e x = [0 0.4];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01a.jpg\"\u003e\u003cp\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.4 1). This configuration is stable so your function should return \u003ci\u003etrue\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eExample (2)\u003c/p\u003e\u003cpre\u003e x = [0 0.6];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01b.jpg\"\u003e\u003cp\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.6 1). This configuration is unstable (the second block will fall) so your function should return \u003ci\u003efalse\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eExample (3)\u003c/p\u003e\u003cpre\u003e x = [0 1.5 0.6];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01c.jpg\"\u003e\u003cp\u003eThe three block bottom-left corner coordinates are (0,0) (1.5,0) and (0.6,1). This configuration is stable so your function should return \u003ci\u003etrue\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eExample (4)\u003c/p\u003e\u003cpre\u003e x = [0 .9 -.9 zeros(1,5)];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01d.jpg\"\u003e\u003cp\u003eThis configuration is unstable, but note that if instead of five we add a few more blocks on top of this at the 0 position that will keep the tower from falling!\u003c/p\u003e\u003cp\u003eExample (5)\u003c/p\u003e\u003cp\u003ex = cumsum(fliplr(1./(1:8))/2);\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01e.jpg\"\u003e\u003cp\u003eThis configuration is stable (see the \u003ca href = \"http://en.wikipedia.org/wiki/Block-stacking_problem\"\u003eclassic optimal stacking solution\u003c/a\u003e) so your function should return \u003ci\u003etrue\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDisplay\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIf you wish, you may display any given block configuration \u003cb\u003ex\u003c/b\u003e using the code below:\u003c/p\u003e\u003cpre\u003e clf;\r\n y=[];\r\n for n=1:numel(x), y(n)=max([0 y(abs(x(1:n-1)-x(n))\u0026lt;1)+1]); end\r\n h=arrayfun(@(x,y)patch(x+[0,1,1,0],y+[0,0,1,1],rand(1,3)),x,y);\r\n text(x+.5,y+.5,arrayfun(@num2str,1:numel(x),'uni',0),...\r\n 'horizontalalignment','center');\u003c/pre\u003e\u003cp\u003eVisit \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1910-block-canvas\"\u003eBlock canvas\u003c/a\u003e for a related Cody problem.\u003c/p\u003e","function_template":"function y = equilibrium(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = [0 0.6];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [0 0.4];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [0 1.5 0.6];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = cumsum(fliplr(1./(1:16))/2);\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [1.5 2.5 1 0.25 5.5 3.5 -1.5 -0.25 -4 -1.75 6.25 -1.25 0.5 1 -0.5 4.75 -1.25 -1.5 0.5 1.5];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [-1.5 -0.25 -0.25 -1.75 1.75 -2 -5.25 2.25 0.75 -0 0.25 0 -1 -1.5 4.75 -1 4.75 -2.5 3.25 -1];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [1.25 -1.75 -0.75 2.75 -1.5 3.75 1.75 1.5 -0.25 -4 -0.5 -2 1.75 -3.5 -2 -3.75 0 -1.75 1.75 3.25 -1.5 -0.5 1.25 -2 1.5 3 -0.25 1.75 -0.5 2.75 0.5 -4.25 1.5 5.5 3 4.25 2.75 -0.75 0.5 3 3.5 3.25 1.75 1.5 3.25 2.5 5.5 -2 -3.75 -1 5 0.25 -3.75 5.5 1.75 2 1.75 0.5 -3.75 1.5 -0 2 0.5 0 -0.25 0.25 -9 1.75 -3.75 1.25 -3.75 -0 1.75 3.5 -3.75 3.75 -5.75 1.25 3.5 1.5 -2 2 -2.5 -1.5 3 1.75 -1.5 3.25 1.75 -1.5 1.25 -2.5 1.25 -4.25 3.25 -2.5 1.75 1.75 7.25 3.5];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [-0.5 1.5 3.5 0.5 -5.75 2 -1.5 0.25 -0.25 -3 -0.25 3 -3.5 -4.5 1.75 -0.25 0.75 3 0.25 -2.5 2.25 -0.25 1.75 -1.5 -5 -0 -0.5 -2 -0 4.75 -0 2 3.5 1.5 -2.25 3.5 -0.5 4.5 2.5 0.5 1.75 3.5 -0 -2.25 -0.25 -4.75 -2.5 -0.75 -6 2.75 -5 2.25 1 -2.25 -0.75 -0.25 -3.5 0.75 -0 -0.5 -0.5 -1.75 -2 -0.25 -0.25 5 -0.25 -0.75 -0.25 -5 -2 -0.25 -5.5 -5 -0.5 -2 1 -0.75 2 3.25 4.5 2.25 1.25 -0.25 -0.5 -0.25 -2.5 -5 2.25 -2 7.5 6.5 2.25 -0.25 -0.5 7.25 -2.5 1 -2.5 -4.75];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [0.1 0.1 -4.6 -0.4 -1.5 1.6 3 2.7 2.3 -2.7 0.1 -1.7 0 4.4 3.8 -0.4 -2 -0.6 3.3 2.5 -3 -1.7 3.1 2.7 2.7 3.1 -0.4 1.1 -0.2 -0.1 -0.3 2.7];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [0.1 0.1 -4.6 -0.4 -1.5 1.6 3 2.7 2.3 -2.7 0.1 -1.7 0 4.4 3.8 -0.4 -2 -0.6 3.3 2.5 -3 -1.7 3.1 2.7 2.7 3.1 -0.4 1.1 -0.2 -0.1 -0.3 2.7 -1.8 2.3];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [-3.5 2.6 -0.7 -1.1 -2.6 -2 0.8 -0.7 2.7 0.4 -5 3.7 -1.2 -1.3 2.8 0.8 -1.5 -1.8 0 -0 4.8 -1.4 -1.2 -1.5 1 0.2 2.6 1.7 1.6 -1.3 2.1 -1.5 -1.4 2 0.1 -0.1 -0.1 4.6 -3 -0.3 0.2 -1.9 -0 0.1 0 2.1 -1.7 -3.1 -0 0.2 -0.1 -0.5 4.7 -1.8 -0.1 -2.2];\r\nassert(isequal(equilibrium(x),false));\r\n\r\n%%\r\nx = [-2.5 2.6 -0.7 -1.1 -2.6 -2 0.8 -0.7 2.7 0.4 -5 3.7 -1.2 -1.3 2.8 0.8 -1.5 -1.8 0 -0 4.8 -1.4 -1.2 -1.5 1 0.2 2.6 1.7 1.6 -1.3 2.1 -1.5 -1.4 2 0.1 -0.1 -0.1 4.6 -3 -0.3 0.2 -1.9 -0 0.1 0 2.1 -1.7 -3.1 -0 0.2 -0.1 -0.5 4.7 -1.8 -0.1 -2.2];\r\nassert(isequal(equilibrium(x),true));\r\n\r\n%%\r\nx =[0 .9 -.9 zeros(1,8)];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx =[0 .9 -.9 zeros(1,6)];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = repmat([0 .7 -.7 0],1,2);\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = repmat([0 .6 -.6 0],1,2);\r\nassert(isequal(equilibrium(x),true))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-02T08:49:59.000Z","updated_at":"2013-10-08T00:22:34.000Z","published_at":"2013-10-02T09:44:07.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId4\",\"target\":\"/media/image4.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId5\",\"target\":\"/media/image5.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId6\",\"target\":\"/media/image6.JPEG\"}],\"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\u003eIs this tower of blocks going to fall?\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\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\u003eGiven a stacking configuration for a series of square blocks, your function should return\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\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they are at equilibrium 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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise.\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\u003eThe block configuration for N blocks is provided as a input vector\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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with N elements listing the\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\u003ex-coordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the left-side of each block. The blocks are square with side equal to 1 (so the i-th block left side is at x(i) and its right side is at x(i)+1). The\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\u003ey-coordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of each block are determined implicitly by the order of the blocks, which are dropped \\\"tetris-style\\\" until they hit the floor or another block.\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\u003eAll blocks are identical (same dimensions and mass) and perfectly smooth (friction is to be disregarded).\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\u003eIntermediate positions may be unstable. You are only required to determine whether the final configuration is stable.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (1)\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[ x = [0 0.4];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.4 1). This configuration is stable so your function should return\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\u003etrue\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (2)\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[ x = [0 0.6];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.6 1). This configuration is unstable (the second block will fall) so your function should return\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\u003efalse\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (3)\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[ x = [0 1.5 0.6];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThe three block bottom-left corner coordinates are (0,0) (1.5,0) and (0.6,1). This configuration is stable so your function should return\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\u003etrue\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (4)\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[ x = [0 .9 -.9 zeros(1,5)];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThis configuration is unstable, but note that if instead of five we add a few more blocks on top of this at the 0 position that will keep the tower from falling!\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\u003eExample (5)\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\u003ex = cumsum(fliplr(1./(1:8))/2);\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThis configuration is stable (see the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Block-stacking_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eclassic optimal stacking solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) so your function should return\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\u003etrue\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDisplay\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\u003eIf you wish, you may display any given block configuration\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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e using the code below:\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[ clf;\\n y=[];\\n for n=1:numel(x), y(n)=max([0 y(abs(x(1:n-1)-x(n))\u003c1)+1]); end\\n h=arrayfun(@(x,y)patch(x+[0,1,1,0],y+[0,0,1,1],rand(1,3)),x,y);\\n text(x+.5,y+.5,arrayfun(@num2str,1:numel(x),'uni',0),...\\n 'horizontalalignment','center');]]\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\u003eVisit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1910-block-canvas\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBlock canvas\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for a related Cody problem.\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 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this tower of blocks going to fall?\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium02.jpg\u003e\u003e\r\n\r\n*Description*\r\n\r\nGiven a stacking configuration for a series of square blocks, your function should return _true_ if they are at equilibrium and _false_ otherwise. \r\n\r\nThe block configuration for N blocks is provided as a input vector *x* with N elements listing the _x-coordinates_ of the left-side of each block. The blocks are square with side equal to 1 (so the i-th block left side is at x(i) and its right side is at x(i)+1). The _y-coordinates_ of each block are determined implicitly by the order of the blocks, which are dropped \"tetris-style\" until they hit the floor or another block. \r\n\r\nAll blocks are identical (same dimensions and mass) and perfectly smooth (friction is to be disregarded).\r\n \r\nIntermediate positions may be unstable. You are only required to determine whether the final configuration is stable.\r\n\r\n*Examples*:\r\n\r\nExample (1) \r\n \r\n x = [0 0.4];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01a.jpg\u003e\u003e\r\n\r\nThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.4 1). This configuration is stable so your function should return _true_.\r\n\r\nExample (2) \r\n\r\n x = [0 0.6];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01b.jpg\u003e\u003e\r\n\r\nThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.6 1). This configuration is unstable (the second block will fall) so your function should return _false_.\r\n\r\nExample (3) \r\n\r\n x = [0 1.5 0.6];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01c.jpg\u003e\u003e\r\n\r\nThe three block bottom-left corner coordinates are (0,0) (1.5,0) and (0.6,1). This configuration is stable so your function should return _true_.\r\n\r\nExample (4) \r\n\r\n x = [0 .9 -.9 zeros(1,5)];\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01d.jpg\u003e\u003e\r\n\r\nThis configuration is unstable, but note that if instead of five we add a few more blocks on top of this at the 0 position that will keep the tower from falling!\r\n\r\nExample (5) \r\n\r\nx = cumsum(fliplr(1./(1:8))/2);\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/equilibrium01e.jpg\u003e\u003e\r\n\r\nThis configuration is stable (see the \u003chttp://en.wikipedia.org/wiki/Block-stacking_problem classic optimal stacking solution\u003e) so your function should return _true_.\r\n\r\n*Display*\r\n\r\nIf you wish, you may display any given block configuration *x* using the code below:\r\n\r\n clf;\r\n y=[];\r\n for n=1:numel(x), y(n)=max([0 y(abs(x(1:n-1)-x(n))\u003c1)+1]); end\r\n h=arrayfun(@(x,y)patch(x+[0,1,1,0],y+[0,0,1,1],rand(1,3)),x,y);\r\n text(x+.5,y+.5,arrayfun(@num2str,1:numel(x),'uni',0),...\r\n 'horizontalalignment','center');\r\n\r\nVisit \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1910-block-canvas Block canvas\u003e for a related Cody problem.","description_html":"\u003cp\u003eIs this tower of blocks going to fall?\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium02.jpg\"\u003e\u003cp\u003e\u003cb\u003eDescription\u003c/b\u003e\u003c/p\u003e\u003cp\u003eGiven a stacking configuration for a series of square blocks, your function should return \u003ci\u003etrue\u003c/i\u003e if they are at equilibrium and \u003ci\u003efalse\u003c/i\u003e otherwise.\u003c/p\u003e\u003cp\u003eThe block configuration for N blocks is provided as a input vector \u003cb\u003ex\u003c/b\u003e with N elements listing the \u003ci\u003ex-coordinates\u003c/i\u003e of the left-side of each block. The blocks are square with side equal to 1 (so the i-th block left side is at x(i) and its right side is at x(i)+1). The \u003ci\u003ey-coordinates\u003c/i\u003e of each block are determined implicitly by the order of the blocks, which are dropped \"tetris-style\" until they hit the floor or another block.\u003c/p\u003e\u003cp\u003eAll blocks are identical (same dimensions and mass) and perfectly smooth (friction is to be disregarded).\u003c/p\u003e\u003cp\u003eIntermediate positions may be unstable. You are only required to determine whether the final configuration is stable.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eExample (1)\u003c/p\u003e\u003cpre\u003e x = [0 0.4];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01a.jpg\"\u003e\u003cp\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.4 1). This configuration is stable so your function should return \u003ci\u003etrue\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eExample (2)\u003c/p\u003e\u003cpre\u003e x = [0 0.6];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01b.jpg\"\u003e\u003cp\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.6 1). This configuration is unstable (the second block will fall) so your function should return \u003ci\u003efalse\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eExample (3)\u003c/p\u003e\u003cpre\u003e x = [0 1.5 0.6];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01c.jpg\"\u003e\u003cp\u003eThe three block bottom-left corner coordinates are (0,0) (1.5,0) and (0.6,1). This configuration is stable so your function should return \u003ci\u003etrue\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eExample (4)\u003c/p\u003e\u003cpre\u003e x = [0 .9 -.9 zeros(1,5)];\u003c/pre\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01d.jpg\"\u003e\u003cp\u003eThis configuration is unstable, but note that if instead of five we add a few more blocks on top of this at the 0 position that will keep the tower from falling!\u003c/p\u003e\u003cp\u003eExample (5)\u003c/p\u003e\u003cp\u003ex = cumsum(fliplr(1./(1:8))/2);\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/equilibrium01e.jpg\"\u003e\u003cp\u003eThis configuration is stable (see the \u003ca href = \"http://en.wikipedia.org/wiki/Block-stacking_problem\"\u003eclassic optimal stacking solution\u003c/a\u003e) so your function should return \u003ci\u003etrue\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDisplay\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIf you wish, you may display any given block configuration \u003cb\u003ex\u003c/b\u003e using the code below:\u003c/p\u003e\u003cpre\u003e clf;\r\n y=[];\r\n for n=1:numel(x), y(n)=max([0 y(abs(x(1:n-1)-x(n))\u0026lt;1)+1]); end\r\n h=arrayfun(@(x,y)patch(x+[0,1,1,0],y+[0,0,1,1],rand(1,3)),x,y);\r\n text(x+.5,y+.5,arrayfun(@num2str,1:numel(x),'uni',0),...\r\n 'horizontalalignment','center');\u003c/pre\u003e\u003cp\u003eVisit \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1910-block-canvas\"\u003eBlock canvas\u003c/a\u003e for a related Cody problem.\u003c/p\u003e","function_template":"function y = equilibrium(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = [0 0.6];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [0 0.4];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [0 1.5 0.6];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = cumsum(fliplr(1./(1:16))/2);\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [1.5 2.5 1 0.25 5.5 3.5 -1.5 -0.25 -4 -1.75 6.25 -1.25 0.5 1 -0.5 4.75 -1.25 -1.5 0.5 1.5];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [-1.5 -0.25 -0.25 -1.75 1.75 -2 -5.25 2.25 0.75 -0 0.25 0 -1 -1.5 4.75 -1 4.75 -2.5 3.25 -1];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [1.25 -1.75 -0.75 2.75 -1.5 3.75 1.75 1.5 -0.25 -4 -0.5 -2 1.75 -3.5 -2 -3.75 0 -1.75 1.75 3.25 -1.5 -0.5 1.25 -2 1.5 3 -0.25 1.75 -0.5 2.75 0.5 -4.25 1.5 5.5 3 4.25 2.75 -0.75 0.5 3 3.5 3.25 1.75 1.5 3.25 2.5 5.5 -2 -3.75 -1 5 0.25 -3.75 5.5 1.75 2 1.75 0.5 -3.75 1.5 -0 2 0.5 0 -0.25 0.25 -9 1.75 -3.75 1.25 -3.75 -0 1.75 3.5 -3.75 3.75 -5.75 1.25 3.5 1.5 -2 2 -2.5 -1.5 3 1.75 -1.5 3.25 1.75 -1.5 1.25 -2.5 1.25 -4.25 3.25 -2.5 1.75 1.75 7.25 3.5];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [-0.5 1.5 3.5 0.5 -5.75 2 -1.5 0.25 -0.25 -3 -0.25 3 -3.5 -4.5 1.75 -0.25 0.75 3 0.25 -2.5 2.25 -0.25 1.75 -1.5 -5 -0 -0.5 -2 -0 4.75 -0 2 3.5 1.5 -2.25 3.5 -0.5 4.5 2.5 0.5 1.75 3.5 -0 -2.25 -0.25 -4.75 -2.5 -0.75 -6 2.75 -5 2.25 1 -2.25 -0.75 -0.25 -3.5 0.75 -0 -0.5 -0.5 -1.75 -2 -0.25 -0.25 5 -0.25 -0.75 -0.25 -5 -2 -0.25 -5.5 -5 -0.5 -2 1 -0.75 2 3.25 4.5 2.25 1.25 -0.25 -0.5 -0.25 -2.5 -5 2.25 -2 7.5 6.5 2.25 -0.25 -0.5 7.25 -2.5 1 -2.5 -4.75];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [0.1 0.1 -4.6 -0.4 -1.5 1.6 3 2.7 2.3 -2.7 0.1 -1.7 0 4.4 3.8 -0.4 -2 -0.6 3.3 2.5 -3 -1.7 3.1 2.7 2.7 3.1 -0.4 1.1 -0.2 -0.1 -0.3 2.7];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx = [0.1 0.1 -4.6 -0.4 -1.5 1.6 3 2.7 2.3 -2.7 0.1 -1.7 0 4.4 3.8 -0.4 -2 -0.6 3.3 2.5 -3 -1.7 3.1 2.7 2.7 3.1 -0.4 1.1 -0.2 -0.1 -0.3 2.7 -1.8 2.3];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = [-3.5 2.6 -0.7 -1.1 -2.6 -2 0.8 -0.7 2.7 0.4 -5 3.7 -1.2 -1.3 2.8 0.8 -1.5 -1.8 0 -0 4.8 -1.4 -1.2 -1.5 1 0.2 2.6 1.7 1.6 -1.3 2.1 -1.5 -1.4 2 0.1 -0.1 -0.1 4.6 -3 -0.3 0.2 -1.9 -0 0.1 0 2.1 -1.7 -3.1 -0 0.2 -0.1 -0.5 4.7 -1.8 -0.1 -2.2];\r\nassert(isequal(equilibrium(x),false));\r\n\r\n%%\r\nx = [-2.5 2.6 -0.7 -1.1 -2.6 -2 0.8 -0.7 2.7 0.4 -5 3.7 -1.2 -1.3 2.8 0.8 -1.5 -1.8 0 -0 4.8 -1.4 -1.2 -1.5 1 0.2 2.6 1.7 1.6 -1.3 2.1 -1.5 -1.4 2 0.1 -0.1 -0.1 4.6 -3 -0.3 0.2 -1.9 -0 0.1 0 2.1 -1.7 -3.1 -0 0.2 -0.1 -0.5 4.7 -1.8 -0.1 -2.2];\r\nassert(isequal(equilibrium(x),true));\r\n\r\n%%\r\nx =[0 .9 -.9 zeros(1,8)];\r\nassert(isequal(equilibrium(x),true))\r\n\r\n%%\r\nx =[0 .9 -.9 zeros(1,6)];\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = repmat([0 .7 -.7 0],1,2);\r\nassert(isequal(equilibrium(x),false))\r\n\r\n%%\r\nx = repmat([0 .6 -.6 0],1,2);\r\nassert(isequal(equilibrium(x),true))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-02T08:49:59.000Z","updated_at":"2013-10-08T00:22:34.000Z","published_at":"2013-10-02T09:44:07.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId4\",\"target\":\"/media/image4.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId5\",\"target\":\"/media/image5.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId6\",\"target\":\"/media/image6.JPEG\"}],\"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\u003eIs this tower of blocks going to fall?\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\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\u003eGiven a stacking configuration for a series of square blocks, your function should return\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\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they are at equilibrium 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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise.\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\u003eThe block configuration for N blocks is provided as a input vector\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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with N elements listing the\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\u003ex-coordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the left-side of each block. The blocks are square with side equal to 1 (so the i-th block left side is at x(i) and its right side is at x(i)+1). The\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\u003ey-coordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of each block are determined implicitly by the order of the blocks, which are dropped \\\"tetris-style\\\" until they hit the floor or another block.\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\u003eAll blocks are identical (same dimensions and mass) and perfectly smooth (friction is to be disregarded).\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\u003eIntermediate positions may be unstable. You are only required to determine whether the final configuration is stable.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (1)\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[ x = [0 0.4];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.4 1). This configuration is stable so your function should return\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\u003etrue\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (2)\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[ x = [0 0.6];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThe first block bottom-left corner is at (0,0) and the second block falls on top of it, with its bottom-left corner at (0.6 1). This configuration is unstable (the second block will fall) so your function should return\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\u003efalse\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (3)\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[ x = [0 1.5 0.6];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThe three block bottom-left corner coordinates are (0,0) (1.5,0) and (0.6,1). This configuration is stable so your function should return\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\u003etrue\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample (4)\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[ x = [0 .9 -.9 zeros(1,5)];]]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThis configuration is unstable, but note that if instead of five we add a few more blocks on top of this at the 0 position that will keep the tower from falling!\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\u003eExample (5)\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\u003ex = cumsum(fliplr(1./(1:8))/2);\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eThis configuration is stable (see the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Block-stacking_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eclassic optimal stacking solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) so your function should return\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\u003etrue\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDisplay\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\u003eIf you wish, you may display any given block configuration\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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e using the code below:\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[ clf;\\n y=[];\\n for n=1:numel(x), y(n)=max([0 y(abs(x(1:n-1)-x(n))\u003c1)+1]); end\\n h=arrayfun(@(x,y)patch(x+[0,1,1,0],y+[0,0,1,1],rand(1,3)),x,y);\\n text(x+.5,y+.5,arrayfun(@num2str,1:numel(x),'uni',0),...\\n 'horizontalalignment','center');]]\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\u003eVisit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1910-block-canvas\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBlock canvas\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for a related Cody problem.\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 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