leetcode 064 Minimum Path Sum

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本文介绍了一个算法问题：在一个填充了非负数的m x n网格中，如何找到从左上角到右下角的路径，使得路径上的数字之和最小。只允许向右或向下移动。文章提供了一种解决方案，采用动态规划思想，通过一维数组进行状态压缩，从而降低了空间复杂度。

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.

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

		if(n == 0) return 0;

		m = grid[0].size();

		vector<int> cur(m, -1);

		//dp[i][j] = min(dp[i-1][j],dp[i][j-1])+mat[i][j];
		for(int i = 0; i < n; i++) {
			for(int j = 0; j < m; j++) {
				if(j>=1 && cur[j]!=-1) {
					cur[j] = min(cur[j-1], cur[j])+grid[i][j];
				} else if(j==0) {
					if(cur[j]==-1)
						cur[j] = grid[i][j];
					else
						cur[j] = cur[j]+grid[i][j];
				} else if(cur[j]==-1) {
					cur[j] = cur[j-1]+grid[i][j];
				}
			}
		}

		return cur[m-1];
    }
};