LeetCode – Refresh – Minimum Path Sum

转载于 2015-03-21 07:50:00 发布 · 76 阅读

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原文链接：http://www.cnblogs.com/shuashuashua/p/4355107.html

本文介绍了一种使用一维动态规划解决二维网格中寻找从起点到终点的最小路径和问题的方法。通过初始化一维数组记录每一步达到当前点的最小路径和，并逐步更新数组来解决问题。

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Simple DP, but notes:

1. initialize the array not only for dp[i] += dp[i-1], but also dp[i] += dp[i-1] + grid[i][0];

2. Clear that we are using one dimensional vector to record the sum.

 1 class Solution {
 2 public:
 3     int minPathSum(vector<vector<int> > &grid) {
 4         if (grid.size() == 0) return 0;
 5         int n = grid.size(), m = grid[0].size();
 6         vector<int> dp(n, 0);
 7         dp[0] = grid[0][0];
 8         for (int i = 1; i < n; i++) dp[i] = dp[i-1] + grid[i][0];
 9         for (int i = 1; i < m; i++) {
10             for (int j = 0; j < n; j++) {
11                 if (j == 0) dp[j] += grid[j][i];
12                 else dp[j] = min(dp[j], dp[j-1]) + grid[j][i];
13             }
14         }
15         return dp[n-1];
16     }
17 };