Minimax Triangulation UVA

按照紫书上面的思路，注意三角形面积的计算运用到向量以及利用计算几何的相关知识判断多边形点的连线是否是多变形的对角线，具体实现见如下代码：

#include<iostream>#include<vector>#include<string>#include<set>#include<stack>#include<queue>#include<map>#include<algorithm>#include<cmath>#include<iomanip>#include<cstring>#include<sstream>#include<cstdio>#include<deque>using namespace std;int T;int n;double point[55][2];double dp[55][55];double area(int index1,int index2,int index3){double x1 = point[index1][0] - point[index3][0];double y1 = point[index1][1] - point[index3][1];double x2 = point[index2][0] - point[index3][0];double y2 = point[index2][1] - point[index3][1];return fabs((x1*y2-x2*y1)/2);}bool feasible(int i,int j,int k){double s = area(i, j, k);for (int ind = 0; ind < n; ind++){if (ind == i || ind == j || ind == k) continue;double test = area(i, k, ind) + area(j, k, ind) + area(i, j, ind);if (fabs(test - s) < 1e-6) return false;}return true;}int main(){cin >> T;while (T--){cin >> n;for (int i = 0; i < n; i++){cin >> point[i][0]>>point[i][1];}for (int i = n - 1; i >= 0; i--){for (int j = i+2; j < n; j++){dp[i][j] = 1e10;for (int k = i + 1; k < j; k++){if (feasible(i,j,k)){dp[i][j] = min(dp[i][j], max(max(dp[k][j],dp[i][k]), area(i, j, k)));}}}}cout<<fixed<<setprecision(1)<< dp[0][n - 1] << endl;}return 0;}