I want to apply Dinic's algorithm with dynamic tree. But I find very few sources. especially about the dynamic tree. It would be great if there is a good source with detailed explains or some simple sources code which uses dynamic tree.
Any one come across something like that? Thanks in advance
The basic idea for improvement is avoiding premature pessimization in Dinic's algorithm. As opposed to preflow/push algorithms, Dinic's algorithm searches for paths in the residual flow graph. Once such a flow is addressed, instead of starting a new search, the modified algorithm deals with paths found in the previous search.
You can find here a very readable introduction for this, including an implementation of the data structure itself. here is a more detailed lecture. Finally, A Data Structure for Dynamic Trees (by Sleator and Tarjan) is the original paper focussing on the implementation of the data structure itself.