Problem 1457. USC Spring 2013 ACM: Walking on Thin Ice

Created by Richard Zapor

Solve Later

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This Challenge is to solve the <a href = "http://contest.usc.edu/index.php/Spring13/Home">USC Spring 2013 ACM Contest</a> Problem E, Walking on Thin Ice.The Rooster is crossing to the other side of the frozen river. Minimize his distance traveled on thin ice given a river width (w) and polygons(polycell) that denote non-thin ice regions. Start anywhere on the x-axis(y=0) and finish by reaching y=w.Input:w=120polycell={[0 10 0 90 50 50 100 90 100 10] [0 110 100 110 50 70]};Output: 35.6174The only USC competition solver(45 minutes): <a href = "http://contest.usc.edu/index.php/Spring13/Home?action=download&upname=thinice.zhengcao.cpp.txt">Cao's C solution</a>Theory:Traveling Salesman Optimum Route. (Matlab one line while)Create Interconnect MatrixCalculate Route/Distances between Good-Ice using Polygon to Polygon distance function.Polygon to Polygon minimum distance uses minimum Point to Line Segment function.Related Challenges:1) <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1446-minimum-distance-point-to-segment">Minimum Distance Point to Segment</a>2) <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1452-minimum-distance-between-two-n-sided-polygons">Minimum Distance between Polygons</a>

This Challenge is to solve the <http://contest.usc.edu/index.php/Spring13/Home USC Spring 2013 ACM Contest> Problem E, Walking on Thin Ice.

The Rooster is crossing to the other side of the frozen river. Minimize his distance traveled on thin ice given a river width (w) and polygons(polycell) that denote non-thin ice regions. Start anywhere on the x-axis(y=0) and finish by reaching y=w.

*Input:*

w=120

polycell={[0 10 0 90 50 50 100 90 100 10] [0 110 100 110 50 70]};

*Output:* 35.6174

The only USC competition solver(45 minutes): <http://contest.usc.edu/index.php/Spring13/Home?action=download&upname=thinice.zhengcao.cpp.txt Cao's C solution>

*Theory:*

Traveling Salesman Optimum Route. (Matlab one line while)

Create Interconnect Matrix

Calculate Route/Distances between Good-Ice using Polygon to Polygon distance function.

Polygon to Polygon minimum distance uses minimum Point to Line Segment function.

*Related Challenges:*

1) <http://www.mathworks.com/matlabcentral/cody/problems/1446-minimum-distance-point-to-segment Minimum Distance Point to Segment>

2) <http://www.mathworks.com/matlabcentral/cody/problems/1452-minimum-distance-between-two-n-sided-polygons Minimum Distance between Polygons>

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Problem 1457. USC Spring 2013 ACM: Walking on Thin Ice

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