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.

IT IS THE SAME AS MANHATTAN TOURIST PROBLEM!!!!

Dynamic programming

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