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

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

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

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

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

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

class Solution {
public:
typedef map<pair<int,int>,vector<pair<int,int>>>GRAPH;
bool isvalid(vector<vector<int>>& matrix , int row , int col ,int item){
	if(row < 0 || row==matrix.size())return false;
	if(col < 0 || col==matrix[0].size())return false;
	if(matrix[row][col]<=item)return false;
	return true;
}
int longestIncreasingPath(vector<vector<int>>& matrix) {
	GRAPH G1;
	queue<pair<int,int>>q1;
	vector<vector<int>> indegree(matrix.size(),vector<int>(matrix[0].size()));
 for(int i=0; i<matrix.size(); i++){
 	for(int j=0; j<matrix[0].size(); j++){
 		if(isvalid(matrix,i+1,j,matrix[i][j]))G1[{i,j}].push_back({i+1,j});
 		if(isvalid(matrix,i-1,j,matrix[i][j]))G1[{i,j}].push_back({i-1,j});
 		if(isvalid(matrix,i,j+1,matrix[i][j]))G1[{i,j}].push_back({i,j+1});
 		if(isvalid(matrix,i,j-1,matrix[i][j]))G1[{i,j}].push_back({i,j-1});
	 }
 }	
 for(int i=0; i<matrix.size(); i++){
 	for(int j=0; j<matrix[0].size(); j++){
 		for(int c=0; c<G1[{i,j}].size(); c++)
 			indegree[G1[{i,j}][c].first][G1[{i,j}][c].second]++;
 	}
 }
 for(int i=0; i<matrix.size(); i++){
 	for(int j=0; j<matrix[0].size(); j++){
 		if(!indegree[i][j])q1.push({i,j});
 	}
 }
 int level=0,flag=0;
 while(!q1.empty()){
 	int sz=q1.size();
 	while(sz--){
 	int key1=q1.front().first;
 	int key2=q1.front().second;
	  	q1.pop();
 	for(int i=0; i<G1[{key1,key2}].size(); i++){
 		if(!--indegree[G1[{key1,key2}][i].first][G1[{key1,key2}][i].second]){
 			q1.push({G1[{key1,key2}][i].first,G1[{key1,key2}][i].second});
		 }
	 }
 }
 	 ++level ;
}
 return level;
}
};
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