# Leetcode 329 Solution

https://leetcode.com/problems/longest-increasing-path-in-a-matrix

## Solution

``````class Solution {
public:
int longestIncreasingPath(vector<vector<int>>& matrix, int m, int n, int i, int j, vector<vector<int>>& cache)
{
if (cache[i][j])
return cache[i][j];

int res = 1;
if (i > 0 && matrix[i][j] < matrix[i - 1][j])
res = max(res, longestIncreasingPath(matrix, m, n, i - 1, j, cache) + 1);

if (i < m - 1 && matrix[i][j] < matrix[i + 1][j])
res = max(res, longestIncreasingPath(matrix, m, n, i + 1, j, cache) + 1);

if (j > 0 && matrix[i][j] < matrix[i][j - 1])
res = max(res, longestIncreasingPath(matrix, m, n, i, j - 1, cache) + 1);

if (j < n - 1 && matrix[i][j] < matrix[i][j + 1])
res = max(res, longestIncreasingPath(matrix, m, n, i, j + 1, cache) + 1);

return cache[i][j] = res;
}

int longestIncreasingPath(vector<vector<int>>& matrix) {
int m = matrix.size();
if (m == 0)
return 0;
int n = matrix[0].size();

vector<vector<int>> cache(m, vector<int>(n, 0));

int max_path = 0;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
int res = longestIncreasingPath(matrix, m, n, i, j, cache);
max_path = max(res, max_path);
}
}

return max_path;
}
};
``````