64. Minimum Path Sum

https://leetcode.com/problems/minimum-path-sum/

Problem

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.

Solution

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        if (grid.empty()) return 0;
        for (int i = 1; i < grid.size(); ++i) grid[i][0] += grid[i - 1][0];
        for (int i = 1; i < grid[0].size(); ++i) grid[0][i] += grid[0][i - 1];
        
        for (int i = 1; i < grid.size(); ++i) {
            for (int j = 1; j < grid[0].size(); ++j) {
                grid[i][j] += min(grid[i - 1][j], grid[i][j - 1]);
            }
        }
        return grid.back().back();
    }
};

• #dp