Minimum Path Sum

Description

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.

Notice
You can only move either down or right at any point in time.

Example

Link

Lintcode_ladder

Method

1. Dp, record min sum, considering the boundary
2. x

Example

1. 1

class Solution {
public:
    /**
     * @param grid: a list of lists of integers.
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    int minPathSum(vector<vector<int> > &grid) {
        // write your code here
        if (grid.empty()) {
           return 0;
        }
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>>& dp = grid;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (i == 0 && j == 0) {
                    continue;
                } else if (i == 0 && j != 0) {
                    dp[i][j] += dp[i][j-1];
                } else if (i != 0 && j == 0) {
                    dp[i][j] += dp[i-1][j];
                } else {
                    dp[i][j] += min(dp[i-1][j], dp[i][j-1]);
                }
            }
        }
        return dp[m-1][n-1];
    }
};

Similar problems

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Tags

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