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.
// DFS Recursion + Memoization
int helper(const vector<vector<int> >& matrix, int i, int j, vector<vector<int> >& memo, const vector<vector<int> >& dirs) {
if (memo[i][j] != 0) return memo[i][j];
int cur = 1;
for (const vector<int>& dir : dirs) {
int x = i + dir[0], y = j + dir[1];
if (x < 0 || x >= matrix.size() || y < 0 || y >= matrix[0].size() || matrix[x][y] <= matrix[i][j]) continue;
int len = helper(matrix, x, y, memo, dirs) + 1;
cur = max(cur, len);
}
return memo[i][j] = cur;
}
int longestIncreasingPath(vector<vector<int>>& matrix) {
if (matrix.empty()) return 0;
int m = matrix.size(), n = matrix[0].size();
vector<vector<int> > dirs({{1, 0}, {-1, 0}, {0, 1}, {0, -1}}), memo(m, vector<int>(n));
int res = 1;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
res = max(res, helper(matrix, i, j, memo, dirs));
}
}
return res;
}