Derangement Check

Verifies if a given permutation is a derangement.

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Interface
Derangement Check
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Interface

C++

Derangement Check

boolderangement_check(	int	`n`
	int*	`a`	)[inline]

This function checks whether a given permutation, given as an array of numbers in the range $\inline 1, 2, \ldots n$ , 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:

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

(2)

where $\inline \sigma$ 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

n	the size of the permutation
a	the actual permutation given as an array

Returns

true, if the permutation is a derangement, false otherwise

Authors

Lucian Bentea (August 2005)

Source Code

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