# 329. Longest Increasing Path in a Matrix

矩阵里找最长的递增路径，二维走格+ longest increasing => DP。DFS + memorization的方法很直观，dp\[i]\[j]存下(i, j)对应的最长路径，检查一下四周看加上它最长能有多远，每个元素只会遍历一次，时间复杂度O(MN)。递推DP有点tricky, 顺序遍历的话对(i, j)并不知道(i +1, j)和(i, j+1)的值。它的状态变化除了表面上的从四周跳转过来，实质上是倒着从数大到小跳过来，最大的值长度只能是1，第二大的值长度最多为2，依次类推。

```cpp
/*
 * @lc app=leetcode id=329 lang=cpp
 *
 * [329] Longest Increasing Path in a Matrix
 */
class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        const int M = matrix.size(), N = M == 0 ? 0 : matrix[0].size();
        if (M == 0 || N == 0) return 0;
        vector<vector<int>> m;
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                m.push_back({matrix[i][j], i, j});
            }
        }
        sort(m.begin(), m.end(), [](const auto &a, const auto &b) {
            return a[0] > b[0];
        });
        vector<vector<int>> dirs = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}};
        vector<vector<int>> dp(M, vector<int>(N, 1));
        int res = 0;
        for (const auto &e : m) {
            const int i = e[1], j = e[2];
            for (const auto &dir : dirs) {
                const int x = i + dir[0];
                const int y = j + dir[1];
                if (x >= 0 && x < M && y >= 0 && y < N && matrix[x][y] > matrix[i][j]) {
                    dp[i][j] = max(dp[i][j], dp[x][y] + 1);
                }
            }
            res = max(res, dp[i][j]);
        }
        return res;
    }
};


```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://hao-fu-1.gitbook.io/oj/dynamic_programming_i/zou-ge/329.-longest-increasing-path-in-a-matrix.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.