Minimum Cost Polygon Triangulation

When nonintersecting diagonals are forming a triangle in a polygon, it is called the triangulation. Our task is to find a minimum cost of triangulation.

The cost of triangulation is the sum of the weights of its component triangles. We can find the weight of each triangle by adding their sides, in other words, the weight is the perimeter of the triangle.

Input and Output

Input:
The points of a polygon. {(0, 0), (1, 0), (2, 1), (1, 2), (0, 2)}
Output:
The total cost of the triangulation. Here the cost of the triangulation is 15.3006.

Algorithm

minCost(polygon, n)

Here cost() will be used to calculate the perimeter of a triangle.

Input: A set of points to make a polygon, and a number of points.

Output − Minimum cost for triangulation of a polygon.

Begin
   if n  val
               table[i, j] := val
      i := i + 1
      done
   done
   return table[0, n-1]
End

Example

#include 
#include 
#include 
#define MAX 1000000.0
using namespace std;

struct Point {
   int x, y;
};

double min(double x, double y) {
   return (x  val)
                  table[i][j] = val;    //update table data to minimum value
            }
         }
      }
   }  
   return  table[0][n-1];
}

int main() {
   Point points[] = {{0, 0}, {1, 0}, {2, 1}, {1, 2}, {0, 2}};
   int n = 5;
   cout 
Output
The minimumcost: 15.3006