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