Leetcode_64_Minimum Path Sum

[lihe]

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.

解题思路：

1. 设dp[i][j]是到达(i,j)时的最优解；
2. dp[i, j] = min(dp[i-1][j], dp[i][j-1]) + grid(i,j)

class Solution{
public:
    int minPathSum(std::vector<std::vector<int>> &grid){
        if(grid.size() == 0){
            return 0;
        }
        int row = grid.size();
        int column = grid[0].size();
        std::vector<std::vector<int>> dp(row, std::vector<int>(column, 0));

        dp[0][0] = grid[0][0];
        for(int i = 1; i < column; i++){
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        for(int i = 1; i < row; i++){
            dp[i][0] = dp[i - 1][0] + grid[i][0];
            for(int j = 1; j < column; j++){
                dp[i][j] = std::min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[row - 1][column - 1];
    }
};