LeetCode 64 Minimum Path Sum--In C++

思路：

用动态规划的话，速度是最快的。

状态迁移方程：mat[i][j] = (mat[i][j + 1]<mat[i + 1][j] ? mat[i][j + 1] : mat[i + 1][j]) + grid[i][j];

即要找到一个格子的下边和右边较小的值，在加上grid中给他的值，作为mat中这个位置的最终值。

int minPathSum(vector<vector<int>>& grid) {int m = grid.size();if (m == 0){return 0;}int n = grid[0].size();int** mat = new int*[m]();for (int i = 0; i < m; i++){mat[i] = new int[n]();}mat[m - 1][n - 1] = grid[m-1][n-1];for (int i = m - 1; i >= 0; i--){for (int j = n - 1; j >= 0; j--){if (i == m - 1 && j == n - 1){continue;}if (j == n - 1){mat[i][j] = mat[i + 1][j] + grid[i][j];//最底最右的边，等于自身值加前空的值}else if (i == m - 1){mat[i][j] = mat[i][j + 1] + grid[i][j];}else{mat[i][j] = (mat[i][j + 1]<mat[i + 1][j] ? mat[i][j + 1] : mat[i + 1][j]) + grid[i][j];}}}int result = mat[0][0];for (int i = 0; i < m; i++){delete[] mat[i];}delete[] mat;return result;}