# 矩阵中的最长递增路径

<p>给定一个 <code>m x n</code> 整数矩阵 <code>matrix</code> ，找出其中 <strong>最长递增路径</strong> 的长度。</p>

<p>对于每个单元格，你可以往上，下，左，右四个方向移动。 你 <strong>不能</strong> 在 <strong>对角线</strong> 方向上移动或移动到 <strong>边界外</strong>（即不允许环绕）。</p>

<p> </p>

<p><strong>示例 1：</strong></p>
<img alt="" src="https://img-service.csdnimg.cn/img_convert/d436ea72ef06c6038b50f729e3e23740.jpeg" style="width: 242px; height: 242px;" />
<pre>
<strong>输入：</strong>matrix = [[9,9,4],[6,6,8],[2,1,1]]
<strong>输出：</strong>4 
<strong>解释：</strong>最长递增路径为 <code>[1, 2, 6, 9]</code>。</pre>

<p><strong>示例 2：</strong></p>
<img alt="" src="https://img-service.csdnimg.cn/img_convert/d467675b15c40a7cab7b64937f413672.jpeg" style="width: 253px; height: 253px;" />
<pre>
<strong>输入：</strong>matrix = [[3,4,5],[3,2,6],[2,2,1]]
<strong>输出：</strong>4 
<strong>解释：</strong>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>

<p><strong>示例 3：</strong></p>

<pre>
<strong>输入：</strong>matrix = [[1]]
<strong>输出：</strong>1
</pre>

<p> </p>

<p><strong>提示：</strong></p>

<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] <= 2<sup>31</sup> - 1</code></li>
</ul>


## template

```python

class Solution:
    def longestIncreasingPath(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: int
        """
        a = len(matrix)
        dic = {}
        nums_max = 1
        if a == 0:
            nums_max = 0
        else:
            b = len(matrix[0])
            for i in range(a):
                for j in range(b):
                    dic[(i,j)] = matrix[i][j]
            v =  dic.keys()
            nums1 = [[1 for i in range(b)] for j in range(a)]        
            dic = sorted(dic.items(),key = lambda x:x[1])
            for k in dic:
                i = k[0][0]
                j = k[0][1]
                if (i+1,j) in v and matrix[i+1][j]<matrix[i][j] and nums1[i][j]<nums1[i+1][j]+1:
                    nums1[i][j] = nums1[i+1][j] + 1
                if (i,j+1) in v and matrix[i][j+1]<matrix[i][j] and nums1[i][j]<nums1[i][j+1]+1:
                    nums1[i][j] = nums1[i][j+1] +1
                if (i-1,j) in v and matrix[i-1][j]<matrix[i][j] and nums1[i][j]<nums1[i-1][j]+1:
                    nums1[i][j] = nums1[i-1][j] +1
                if (i,j-1) in v and matrix[i][j-1]<matrix[i][j] and nums1[i][j]<nums1[i][j-1]+1:
                    nums1[i][j] = nums1[i][j-1] + 1    
                nums_max = max(nums_max,nums1[i][j])              
        return nums_max

```

## 答案

```python

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## 选项

### A

```python

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### B

```python

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### C

```python

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