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There are also implementations of Hungarian algorithm that do not use graph theory.Rather, they just operate with cost matrix, making different transformation of it (see  for clear explanation).be a spanning subgraph of G (in other words, it includes all vertices from G).
Our goal is to complete all jobs minimizing total inputs, while assigning each worker to exactly one job and vice versa. Small example just to make things clearer: This problem is known as the assignment problem.
The assignment problem is a special case of the transportation problem, which in turn is a special case of the min-cost flow problem, so it can be solved using algorithms that solve the more general cases.
We’ll not touch these approaches, because it’s less practical for Top Coder needs.
As mentioned above, we are dealing with a bipartite graph.
In order to avoid this, on each step we can just modify the matching from the previous step, which only takes O(n2) operations.