This Challenge is to solve the 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): 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) Minimum Distance Point to Segment

2) Minimum Distance between Polygons