Minimum Path Sum

33% Accepted

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.

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

Tags Expand

• Dynamic Programming

思路

• 动态规划
• 注意二维matrix记得给边界赋好初值

public class Solution {
    /**
     * @param grid: a list of lists of integers.
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    public int minPathSum(int[][] grid) {
        // write your code here
        int m = grid.length;
        int n = grid[0].length;
        int[][] sum = new int[m][n];
        sum[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) {
            sum[i][0] = sum[i-1][0] + grid[i][0];
        }
        for (int i = 1; i < n; i++) {
            sum[0][i] = sum[0][i-1] + grid[0][i];
        }

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