CodeCogs

Verifies if a given permutation is a derangement.

Interface

#include <codecogs/maths/combinatorics/permutations/derangement_check.h>

using namespace Maths::Combinatorics::Permutations;

inline bool derangement_check(int n, int *a)

This function checks whether a given permutation, given as an array of numbers in the range $1, 2, \ldots n$ , is a derangement. A derangement of the integers 1 through n is a permutation of the integers such that the first value is not 1, the second is not 2, and so on. In more formal terms, the following condition stands:

$\sigma(i) \neq i, \quad \forall i = \overline{1, n}$

(1)

where $\sigma$ is the given permutation.

Example:

#include <codecogs/maths/combinatorics/permutations/derangement_check.h>
#include <iostream>
int main()
{
  int x[4] = {4, 3, 2, 1}, y[5] = {1, 3, 2, 5, 4};
  std::cout << Maths::Combinatorics::Permutations::derangement_check(4, x) << std::endl;
  std::cout << Maths::Combinatorics::Permutations::derangement_check(4, y) << std::endl;
  return 0;
}

Output:

1
0

References

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

Parameters

the size of the permutation

the actual permutation given as an array

Returns

true, if the permutation is a derangement, false otherwise

Derangement_Check