osancus / maximum-bipartite-matching

A straightforward implementation of the augmenting path algorithm for solving maximum bipartite matching in C++.

Simple Maximum Bipartite Matching

So, you may have just learned this or similar augmenting path proof for finding the maximum cardinality matching in a bipartite graph! This is pretty much the direct translation of that proof into an algorithm.

This is the augmenting path algorithm. Instead of converting it into a flow problem, this runs in O(VE) time and is probably the easiest thing you can code from scratch if you're doing ACM and can afford it.

We assume that you're working with an unweighted undirected graph.

Input Format

The first line of input contains 3 integers n, m and e ( 0 <= n, m, e <= 500) -- the number of vertices in partition A, the number of vertices in partition B and the number of edges respectively. The next e lines describe two vertices each. A vertex starts with a character 'A' or 'B' denoting its partition followed by a number [ 0, size of partition ).

Sample Input

5 5 10
A0 B0
A1 B0
A2 B0
A2 B1
A3 B1
B2 A3
A4 B2
B1 A4
B3 A4
B4 A4

Sample Output

This is one of a few possible outputs.

Size of maximum matching: 4
A0 B0
A2 B1
A3 B2
A4 B3