leetcode 32: Minimum Path Sum

原创于 2013-01-11 08:45:50 发布 · 485 阅读

CC 4.0 BY-SA版权

本文介绍了一个m x n网格中寻找从左上角到右下角的路径问题，该路径上的数字之和最小。通过动态规划的方法实现了算法，并提供了详细的实现步骤及核心代码。

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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.

tips: 1 remember not every dynamic programming need d[m+1][n+1] like this one.

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