[LeetCode] 057: 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.

[Solution]

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        // empty
        if(grid.size() == 0 || grid[0].size() == 0)return 0;
        
        // initial
        int **dp = new int*[grid.size()];
        for(int i = 0; i < grid.size(); ++i){
            dp[i] = new int[grid[i].size()];
        }
        
        // dp
        for(int i = 0; i < grid.size(); ++i){
            for(int j = 0; j < grid[i].size(); ++j){
                if(i == 0 && j == 0){
                    dp[i][j] = grid[i][j];
                }
                else if(i == 0){
                    dp[i][j] = dp[i][j-1] + grid[i][j];
                }
                else if(j == 0){
                    dp[i][j] = dp[i-1][j] + grid[i][j];
                }
                else{
                    dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
                }
            }
        }
        return dp[grid.size()-1][grid[grid.size()-1].size()-1];
    }
};

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