Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Notice: You can only move either down or right at any point in time.

Notes:

1. Coordinate DP

    public int minPathSum(int[][] grid) {
        // write your code here
        if (grid == null || grid.length == 0 || grid[0].length == 0) {
            return 0;
        }

        int m = grid.length;
        int n = grid[0].length;

        // state
        int[][] f = new int[m][n];

        // initialize
        f[0][0] = grid[0][0];
        for (int i = 1; i < m; ++i) {
            f[i][0] = f[i-1][0] + grid[i][0];
        }
        for (int i = 1; i < n; ++i) {
            f[0][i] = f[0][i-1] + grid[0][i];
        }

        // function
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                f[i][j] = Math.min(f[i-1][j], f[i][j-1]) + grid[i][j];
            }
        }

        // answer
        return f[m-1][n-1];
    }