Depth First Search (DFS) marks all the vertices of a graph as visited. So for making DFS useful, some additional information can also be stored. For instance, the order in which the vertices are visited while running DFS.
Pre-visit and Post-visit numbers are the extra information that can be stored while running a DFS on a graph and which turns out to be really useful. Pre-visit number tells the time at which the node gets into the recursion stack and Post-visit number tells the time at which the node comes out from recursion stack of DFS.
The numbers written in brackets denote [Pre-visit number, Post-visit number].
Pre and Post numbers are widely used in graph algorithms. For example, they can be used to find out whether a particular node lies in the sub-tree of another node.
To find whether u lies in the sub-tree of v or not we just compare the pre and post number of u and v. If pre[u] > pre[v] and post[u] < post[v] then u lies in the sub-tree of v otherwise not. You can see above example for more clarification.
Pre-visit and Post-visit numbers can be found out by simple DFS. We will take two arrays one for storing pre numbers and one for post numbers and by taking a variable which will keep track of the time. The implementation of the same is given below:
Node 1 Pre number 1 Post number 12 Node 2 Pre number 2 Post number 11 Node 3 Pre number 4 Post number 9 Node 4 Pre number 3 Post number 10 Node 5 Pre number 5 Post number 8 Node 6 Pre number 6 Post number 7
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