矩阵中最长连续递增子序列

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:

nums = [
[9,9,4],
[6,6,8],
[2,1,1]
]

 

Return 

4

The longest increasing path is 

[1, 2, 6, 9]

.

Example 2:

nums = [
[3,4,5],
[3,2,6],
[2,2,1]
]

 

Return 

4

The longest increasing path is 

[3, 4, 5, 6]

. Moving diagonally is not allowed.

int x_1[4] = { 1, -1, 0, 0 };
int y_1[4] = { 0, 0, -1, 1 };

int dfs(vector<vector<int>>& matrix,int rows,int cols,
int row, int col, vector<vector<int>>&dp)
{
if (dp[row][col])
return dp[row][col];
int maxDepth = 1;
for (int i = 0; i < 4; ++i)
{
int x = row + x_1[i];
int y = col + y_1[i];
if (x < 0 || y < 0 || x >= rows
|| y >= cols || matrix[x][y] <= matrix[row][col])
continue;
int len = dfs(matrix, rows, cols, x, y, dp) + 1;
if (maxDepth < len)
maxDepth = len;
}
dp[row][col] = maxDepth;
return maxDepth;
}

int longestIncreasingPath(vector<vector<int>>& matrix)
{
if (matrix.empty())
return 0;
int rows = matrix.size();
int cols = matrix[0].size();
vector<vector<int>> dp(rows, vector<int>(cols, 0));
int maxDepth = 1;
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < cols; ++j)
{
int tmp = dfs(matrix,rows,cols, i, j, dp);
if (maxDepth < tmp)
maxDepth = tmp;
}
}
return maxDepth;
}