longest-increasing-path-in-a-matrix

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python3

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oraclesql

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cangjie

Algorithms

Given an <code>m x n</code> integers <code>matrix</code>, return the length of the longest increasing path in <code>matrix</code>.

From each cell, you can either move in four directions: left, right, up, or down. You may not move diagonally or move outside the boundary (i.e., wrap-around is not allowed).

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/05/grid1.jpg" style="width: 242px; height: 242px;" />
<pre>
Input: matrix = [[9,9,4],[6,6,8],[2,1,1]]
Output: 4
Explanation: The longest increasing path is <code>[1, 2, 6, 9]</code>.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/27/tmp-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
Input: matrix = [[3,4,5],[3,2,6],[2,2,1]]
Output: 4
Explanation: The longest increasing path is <code>[3, 4, 5, 6]</code>. Moving diagonally is not allowed.
</pre>

Example 3:

<pre>
Input: matrix = [[1]]
Output: 1
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= matrix[i][j] &lt;= 231 - 1</code></li>
</ul>

longestIncreasingPath

Longest Increasing Path in a Matrix

Number of Increasing Paths in a Grid

number-of-increasing-paths-in-a-grid

网格图中递增路径的数目

Depth-First Search

Breadth-First Search

Graph

Topological Sort

Memoization

Array

Dynamic Programming

Matrix

给定一个 <code>m x n</code> 整数矩阵 <code>matrix</code> ，找出其中 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）。

 

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/05/grid1.jpg" style="width: 242px; height: 242px;" />
<pre>
输入：matrix = [[9,9,4],[6,6,8],[2,1,1]]
输出：4 
解释：最长递增路径为 <code>[1, 2, 6, 9]</code>。</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/27/tmp-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
输入：matrix = [[3,4,5],[3,2,6],[2,2,1]]
输出：4 
解释：最长递增路径是 <code>[3, 4, 5, 6]</code>。注意不允许在对角线方向上移动。
</pre>

示例 3：

<pre>
输入：matrix = [[1]]
输出：1
</pre>

 

提示：

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 <= m, n <= 200</code></li>
	<li><code>0 <= matrix[i][j] <= 231 - 1</code></li>
</ul>