This one is from leetcode: link

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]

]

**Solution**. We can treat each element in matrix as a node. For 2 adjacent nodes, if node1.value < node2.value. Then there is an edge from node1 to node2. In this way, we can transform the matrix to a graph. The problem changes to find the longest path in a directed graph.

In order to find the longest path in graph, each time, we delete the node which out-degree is zero. The number of iteration is the result. Below is a process to calculate the longest path for the graph. The result is 4.