Recently, I came across this problem: [ADABLOOM](https://www.spoj.com/problems/ADABLOOM/). In short, Given an array $A$ of length $n$, the problem requires us to find the number of maximum matching in which each matching $(i,j)$ satisfies $A_i < (A_i \oplus A_j) < A_j$ (XOR operator). ↵
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I found a solution [here](https://github.com/Coder-Boy1/SPOJ/blob/master/SPOJ%20ADABLOOM). They simply doubled the graph to make the left and right side and then find the maximum matching in the bipartite graph, and divide by $2$ to get the answer.↵
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I know that this algorithm won't work with general graph so I want to ask the proof of correctness of this algorithm and what properties that make this kind-of-general-matching problem solvable using this method. Thanks <3
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I found a solution [here](https://github.com/Coder-Boy1/SPOJ/blob/master/SPOJ%20ADABLOOM). They simply doubled the graph to make the left and right side and then find the maximum matching in the bipartite graph, and divide by $2$ to get the answer.↵
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I know that this algorithm won't work with general graph so I want to ask the proof of correctness of this algorithm and what properties that make this kind-of-general-matching problem solvable using this method. Thanks <3
