From cc3e99ab725be8d69d858f30e2b8c6c7032a2f97 Mon Sep 17 00:00:00 2001 From: ShusenTang Date: Mon, 6 Apr 2020 21:53:41 +0800 Subject: [PATCH] add 329. Longest Increasing Path in a Matrix :beer: --- README.md | 1 + ...29. Longest Increasing Path in a Matrix.md | 40 +++++++++++++++++++ 2 files changed, 41 insertions(+) create mode 100644 solutions/329. Longest Increasing Path in a Matrix.md diff --git a/README.md b/README.md index 1d42278..55e832a 100644 --- a/README.md +++ b/README.md @@ -235,6 +235,7 @@ My LeetCode solutions with Chinese explanation. 我的LeetCode中文题解。 | 324 |[Wiggle Sort II](https://leetcode.com/problems/wiggle-sort-ii/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/324.%20Wiggle%20Sort%20II.md)|Medium| | | 326 |[Power of Three](https://leetcode.com/problems/power-of-three)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/326.%20Power%20of%20Three.md)|Easy| | | 328 |[Odd Even Linked List](https://leetcode.com/problems/odd-even-linked-list/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/328.%20Odd%20Even%20Linked%20List.md)|Medium| | +| 329 |[Longest Increasing Path in a Matrix](https://leetcode.com/problems/longest-increasing-path-in-a-matrix/)|[C++](solutions/329.%20Longest%20Increasing%20Path%20in%20a%20Matrix.md)|Hard| | | 331 |[Verify Preorder Serialization of a Binary Tree](https://leetcode.com/problems/verify-preorder-serialization-of-a-binary-tree/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/331.%20Verify%20Preorder%20Serialization%20of%20a%20Binary%20Tree.md)|Medium| | | 332 |[Reconstruct Itinerary](https://leetcode.com/problems/reconstruct-itinerary/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/332.%20Reconstruct%20Itinerary.md)|Medium| | | 334 |[Increasing Triplet Subsequence](https://leetcode.com/problems/increasing-triplet-subsequence/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/334.%20Increasing%20Triplet%20Subsequence.md)|Medium| | diff --git a/solutions/329. Longest Increasing Path in a Matrix.md b/solutions/329. Longest Increasing Path in a Matrix.md new file mode 100644 index 0000000..c93169e --- /dev/null +++ b/solutions/329. Longest Increasing Path in a Matrix.md @@ -0,0 +1,40 @@ +# [329. Longest Increasing Path in a Matrix](https://leetcode.com/problems/longest-increasing-path-in-a-matrix/) + +# 思路 + +给定一个二维矩阵，求矩阵中最长的递增路径。我们可以从尝试从每个位置出发进行DFS，计算出以每个位置为起始的最长递增路径，最后返回最长即可。注意到DFS会存在大量重复，所以我们需要开辟一个二维记忆数组`cache`，`cache[i][j]`表示以位置ij为起始的最长递增路径长度，初始为0。当我们进行DFS时，如果发现`cache[i][j] > 0`，说明之前已经计算过了，无需再进行计算，直接返回`cache[i][j]`即可。 + +# C++ +``` C++ +class Solution { +private: + int m, n; + vector>cache; + int DFS(const vector>& matrix, int i, int j){ + if(cache[i][j] > 0) return cache[i][j]; + + int sub_res = 0; + if(i > 0 && matrix[i-1][j] > matrix[i][j]) sub_res = max(sub_res, DFS(matrix, i-1, j)); + if(j > 0 && matrix[i][j-1] > matrix[i][j]) sub_res = max(sub_res, DFS(matrix, i, j-1)); + if(i < m-1 && matrix[i+1][j] > matrix[i][j]) sub_res = max(sub_res, DFS(matrix, i+1, j)); + if(j < n-1 && matrix[i][j+1] > matrix[i][j]) sub_res = max(sub_res, DFS(matrix, i, j+1)); + + cache[i][j] = 1 + sub_res; + return cache[i][j]; + } +public: + int longestIncreasingPath(vector>& matrix) { + m = matrix.size(); + if(!m) return 0; + n = matrix[0].size(); + + cache = vector>(m, vector(n, 0)); + int res = 0; + for(int i = 0; i < m; i++) + for(int j = 0; j < n; j++) + res = max(res, DFS(matrix, i, j)); + + return res; + } +}; +``` \ No newline at end of file