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Breaks

Counts the number of breaks in a permutation.
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Interface

C++
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Break Count

 
intbreak_countintn
int*p )
Consider the permutation

A <em> break </em> is a pair of neighbors whose values differ by more than 1, i.e.

This function calculates the number of breaks in a permutation, using the following algorithm:
  • Starting with a permutation of order n.
  • We prepend an element labeled 0 and append an element labeled n + 1.
  • There are now n + 1 pairs of neighbors.
  • We now search for indices i \in \{0, 1, 2, \ldots, n\} such that the above
inequality stands.

The identity permutation has a break count of 0. The maximum break count is n + 1.

Example:

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

Output:

The number of breaks of the Sigma permutation: 3

References:

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

Parameters

nthe size of the permutation
pthe actual permutation stored as an array

Returns

the number of breaks found in the permutation

Authors

Lucian Bentea (August 2005)
Source Code

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