Description

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.

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

Solution

DP

class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0) {
            return 0;
        }
        
        int m = grid.length;
        int n = grid[0].length;
        int[][] minPathSum = new int[m][n];
        
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                minPathSum[i][j] = grid[i][j];
                if (i > 0 && j > 0) {
                    minPathSum[i][j] += Math.min(minPathSum[i - 1][j], minPathSum[i][j - 1]);
                } else if (i > 0) {
                    minPathSum[i][j] += minPathSum[i - 1][j];
                } else if (j > 0) {
                    minPathSum[i][j] += minPathSum[i][j - 1];
                }
            }
        }
        
        return minPathSum[m - 1][n - 1];
    }
}