<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:

    int longestIncreasingPathHelper(
        const vector<vector<int>>& matrix, 
        const int &height, 
        const int &width, 
        int currX, 
        int currY, 
        vector<bool> &used,
        //map<pair<int, int>, int> &pathLengthMap
        vector<int> &pathLengthMap
    ) 
    {
        if(used[currY*width+currX])
            return 0;

        //pair<int, int> d =make_pair(currY, currX);
        //if(pathLengthMap.find(d)!=pathLengthMap.end())
        //    return pathLengthMap[d];
        const int d=currY*width+currX;
        if(pathLengthMap[d]>=0)
            return pathLengthMap[d];
        
        const int &currValue = matrix[currY][currX];
        used[d] = true;
        int maxPathLen  = 0;

        //left
        if(currX-1>=0 && matrix[currY][currX-1]>currValue)
        {
            int pathLen = longestIncreasingPathHelper(matrix,height, width, currX-1, currY, used, pathLengthMap);
            maxPathLen = max(pathLen, maxPathLen);
        }

        //right
        if(currX+1<width && matrix[currY][currX+1]>currValue)
        {
            int pathLen = longestIncreasingPathHelper(matrix,height, width, currX+1, currY, used, pathLengthMap);
            maxPathLen = max(pathLen, maxPathLen);
        }

        //top
        if(currY-1>=0 && matrix[currY-1][currX]>currValue)
        {
            int pathLen = longestIncreasingPathHelper(matrix,height, width, currX, currY-1, used, pathLengthMap);
            maxPathLen = max(pathLen, maxPathLen);
        }

        //bottom
        if(currY+1<height && matrix[currY+1][currX]>currValue)
        {
            int pathLen = longestIncreasingPathHelper(matrix,height, width, currX, currY+1, used, pathLengthMap);
            maxPathLen = max(pathLen, maxPathLen);
        }

        used[currY*width+currX] = false;

        pathLengthMap[d] = 1 + maxPathLen;

        return 1 + maxPathLen;
    }

    //O(W*H*log(W*H)) each cell calculated once, space O(W*H) if map is used
    int longestIncreasingPath(vector<vector<int>>& matrix) {

        int height = matrix.size();
        if(height==0)
            return 0;

        int width = matrix[0].size();
        vector<bool> used(width*height, false);
        vector<int> pathLengthMap(width*height, -1);
        //map<pair<int, int>, int> pathLengthMap;


        int longestPath = 0;
        for(int y=0; y<height; y++)
        {
            for(int x=0; x<width; x++)
            {
                int currPath = longestIncreasingPathHelper(matrix,height, width, x, y, used, pathLengthMap);
                longestPath = max(longestPath,currPath);      
                //cout<<"Longest "<<longestPath<<endl<<endl;
            }
        }

        return longestPath;        
    }
};
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