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website/content/ChapterFour/0329.Longest-Increasing-Path-in-a-Matrix.md

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+# [329. Longest Increasing Path in a Matrix](https://leetcode.com/problems/longest-increasing-path-in-a-matrix/)
+
+
+## 题目
+
+Given an integer matrix, find the length of the longest increasing path.
+
+From each cell, you can either move to four directions: left, right, up or down. You may NOT move diagonally or move outside of the boundary (i.e. wrap-around is not allowed).
+
+**Example 1**:
+
+    Input: nums = 
+    [
+      [9,9,4],
+      [6,6,8],
+      [2,1,1]
+    ] 
+    Output: 4 
+    Explanation: The longest increasing path is [1, 2, 6, 9].
+
+**Example 2**:
+
+    Input: nums = 
+    [
+      [3,4,5],
+      [3,2,6],
+      [2,2,1]
+    ] 
+    Output: 4 
+    Explanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.
+
+
+## 题目大意
+
+给定一个整数矩阵，找出最长递增路径的长度。对于每个单元格，你可以往上，下，左，右四个方向移动。 你不能在对角线方向上移动或移动到边界外（即不允许环绕）。
+
+
+## 解题思路
+
+
+- 给出一个矩阵，要求在这个矩阵中找到一个最长递增的路径。路径有上下左右 4 个方向。
+- 这一题解题思路很明显，用 DFS 即可。在提交完第一版以后会发现 TLE，因为题目给出了一个非常大的矩阵，搜索次数太多。所以需要用到记忆化，把曾经搜索过的最大长度缓存起来，增加了记忆化以后再次提交 AC。
+
+
+## 代码
+
+```go
+
+package leetcode
+
+import (
+	"math"
+)
+
+func longestIncreasingPath(matrix [][]int) int {
+	cache, res := make([][]int, len(matrix)), 0
+	for i := 0; i < len(cache); i++ {
+		cache[i] = make([]int, len(matrix[0]))
+	}
+	for i, v := range matrix {
+		for j := range v {
+			searchPath(matrix, cache, math.MinInt64, i, j)
+			res = max(res, cache[i][j])
+		}
+	}
+	return res
+}
+
+func isInIntBoard(board [][]int, x, y int) bool {
+	return x >= 0 && x < len(board) && y >= 0 && y < len(board[0])
+}
+
+func searchPath(board, cache [][]int, lastNum, x, y int) int {
+	if board[x][y] <= lastNum {
+		return 0
+	}
+	if cache[x][y] > 0 {
+		return cache[x][y]
+	}
+	count := 1
+	for i := 0; i < 4; i++ {
+		nx := x + dir[i][0]
+		ny := y + dir[i][1]
+		if isInIntBoard(board, nx, ny) {
+			count = max(count, searchPath(board, cache, board[x][y], nx, ny)+1)
+		}
+	}
+	cache[x][y] = count
+	return count
+}
+
+```