// 1039. Minimum Score Triangulation of Polygon #include #include #include #include /* * given a convex n-sided polygon where each vertex has an integer value. you * are given an integer array 'values' where 'values[i]' is the value of the * i'th vertex (ie. clockwise order). you will triangulate the polygon into 'n - * 2' triangles. for each triangle, the value of that triangle is the product of * the values of its vertices and the total score of the triangulation is the * sum of these values over all 'n - 2' triangles in the triangulation. return * the smallest possible total score that you can achieve with some * triangulation of the polygon */ int minScoreTriangulation(int *values, int values_size) { int n = values_size, **dp = malloc(n * sizeof(int *)); for (int i = 0; i < n; i++) { dp[i] = malloc(n * sizeof(int)); dp[i][i] = 0; if (i + 1 < n) dp[i][i + 1] = 0; for (int j = i + 2; j < n; j++) dp[i][j] = INT_MAX / 3; } for (int len = 3; len <= n; len++) { for (int i = 0; i < n; i++) { int j = i + len - 1; if (j >= n) break; for (int k = i + 1; k < j; k++) dp[i][j] = fmin(dp[i][j], dp[i][k] + values[i] * values[k] * values[j] + dp[k][j]); } } int ans = dp[0][n - 1]; for (int i = 0; i < n; i++) free(dp[i]); free(dp); return ans; } int main() { int v1[] = {1, 2, 3}, v2[] = {3, 7, 4, 5}, v3[] = {1, 3, 1, 4, 1, 5}; printf("%d\n", minScoreTriangulation(v1, 3)); // expect: 6 printf("%d\n", minScoreTriangulation(v2, 4)); // expect: 144 printf("%d\n", minScoreTriangulation(v3, 6)); // expect: 13 }