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.

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

Solution:

  1. public class Solution {
  2.   public int minPathSum(int[][] grid) {
  3.     int n = grid.length, m = grid[0].length;
  5.     int[][] dp = new int[n][m];
  7.     dp[0][0] = grid[0][0];
  9.     // first row
  10.     for (int j = 1; j < m; j++)
  11.       dp[0][j] = grid[0][j] + dp[0][j - 1];
  13.     // first col
  14.     for (int i = 1; i < n; i++)
  15.       dp[i][0] = grid[i][0] + dp[i - 1][0];
  17.     for (int i = 1; i < n; i++) {
  18.       for (int j = 1; j < m; j++) {
  19.         dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
  20.       }
  21.     }
  23.     return dp[n - 1][m - 1];
  24.   }
  25. }