All Tracks Algorithms Dynamic Programming Problem

Perfect Matching
Tag(s):

Algorithms, Dynamic Programming, Hard

Problem
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Given a bipartite graph having $$N$$ vertices in each part and $$M$$ edges, find the number of perfect matchings in it modulo $$4$$.

Input format:
First line consists of a single integer $$T$$ denoting the number of test cases.
First line of each case consists of two space separated integers denoting $$N$$ and $$M$$.
Each of the following $$M$$ lines consists of two space separated integers $$u$$ and $$v$$, denoting that there is an edge between vertex numbered $$u$$ on the left side and vertex numbered $$v$$ on the right side. Vertices on each side are enumerated independently starting from $$0$$.

Output format:
For each test case, print a single number in a new line - number of perfect matchings modulo $$4$$

Constraints:
$$1 \le T \le 10$$
$$1 \le N \le 50$$
$$0 \le M \le N * N$$
$$0 \le u, v \le N-1$$

SAMPLE INPUT
1
2 4
1 0
0 1
0 0
1 1
SAMPLE OUTPUT
2
Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala 2.11.8, Swift, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

HackerEarth Collegiate Cup - Mirror Round

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