64. 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.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

public int minPathSum(int[][] grid) {
    int[][] dp = new int[grid.length][grid[0].length];
    dp[0][0] = grid[0][0];
    for(int i = 1; i < grid.length; i++) dp[i][0] += dp[i-1][0] + grid[i][0];
    for(int i = 1; i < grid[0].length; i++) dp[0][i] += dp[0][i-1] + grid[0][i];
    for(int i = 1; i < grid.length; i++) {
        for(int j = 1; j < grid[0].length; j++) {
            dp[i][j] = grid[i][j] + Math.min(dp[i-1][j], dp[i][j-1]);
        }
    }
    return dp[grid.length-1][grid[0].length-1];
}