inverse

Calculates the inverse of the given permutation.

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Interface
Inverse
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Interface

C++

Inverse

std::vector<int>inverse(	int	`n`
	int*	`p`	)

The inverse of a permutation

$\sigma = \left( \begin{array}{cccc} 1 & 2 & \ldots & n \cr \sigma(1) & \sigma(2) & \ldots & \sigma(n) \end{array} \right)$

(2)

is a permutation $\inline \tau$ such that

$\sigma \circ \tau = \tau \circ \sigma = \left( \begin{array}{cccc} 1 & 2 & \ldots & n \cr 1 & 2 & \ldots & n \end{array} \right)$

(3)

where $\inline \sigma \circ \tau$ represents multiplication. This function searches for the permutation $\inline \tau$ with the property stated above and returns it as a C++ vector object.

References:

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

Example 1

#include <codecogs/maths/combinatorics/permutations/inverse.h>
#include <iostream>
int main()
{
  int sigma[5] = {5, 2, 1, 4, 3};
  std::vector<int> result = Maths::Combinatorics::Permutations::inverse(5, sigma);
  std::cout << "The inverse of the Sigma permutation is: ";
  std::cout << std::endl;
  for (int i = 0; i < 5; i++)
    std::cout << result[i] << " ";
  std::cout << std::endl;
  return 0;
}

Output:

The inverse of the Sigma permutation is:
3 2 5 4 1

Returns

the inverse of the given permutation p

Authors

Lucian Bentea (August 2005)

Source Code

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