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92 lines
2.3 KiB
Markdown
Executable File
92 lines
2.3 KiB
Markdown
Executable File
# [329. Longest Increasing Path in a Matrix](https://leetcode.com/problems/longest-increasing-path-in-a-matrix/)
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## 题目
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Given an integer matrix, find the length of the longest increasing path.
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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).
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**Example 1**:
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Input: nums =
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[
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[9,9,4],
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[6,6,8],
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[2,1,1]
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]
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Output: 4
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Explanation: The longest increasing path is [1, 2, 6, 9].
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**Example 2**:
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Input: nums =
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[
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[3,4,5],
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[3,2,6],
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[2,2,1]
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]
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Output: 4
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Explanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.
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## 题目大意
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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）。
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## 解题思路
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- 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。
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- 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。
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## 代码
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```go
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package leetcode
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import (
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"math"
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)
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func longestIncreasingPath(matrix [][]int) int {
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cache, res := make([][]int, len(matrix)), 0
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for i := 0; i < len(cache); i++ {
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cache[i] = make([]int, len(matrix[0]))
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}
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for i, v := range matrix {
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for j := range v {
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searchPath(matrix, cache, math.MinInt64, i, j)
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res = max(res, cache[i][j])
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}
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}
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return res
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}
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func isInIntBoard(board [][]int, x, y int) bool {
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return x >= 0 && x < len(board) && y >= 0 && y < len(board[0])
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}
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func searchPath(board, cache [][]int, lastNum, x, y int) int {
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if board[x][y] <= lastNum {
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return 0
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}
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if cache[x][y] > 0 {
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return cache[x][y]
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}
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count := 1
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for i := 0; i < 4; i++ {
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nx := x + dir[i][0]
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ny := y + dir[i][1]
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if isInIntBoard(board, nx, ny) {
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count = max(count, searchPath(board, cache, board[x][y], nx, ny)+1)
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}
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}
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cache[x][y] = count
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return count
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}
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``` |