64. Minimum Path Sum

• Difficulty: Medium

• Topics: Array, Dynamic Programming

• Similar Questions:

  • Unique Paths

  • Dungeon Game

  • Cherry Pickup

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.

Solutions:

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        if (m == 0) return 0;
        int n = grid[0].size();
        if (n == 0) return 0;

        vector<vector<int>> dp(m, vector<int>(n, 0));

        dp[0][0] = grid[0][0];

        for (int i = 1; i < m; ++i) {
            dp[i][0] += grid[i][0] + dp[i-1][0];
        }

        for (int j = 1; j < n; ++j) {
            dp[0][j] += grid[0][j] + dp[0][j-1];
        }

        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1]);
            }
        }

        return dp[m-1][n-1];
    }
};