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# Breaks

Counts the number of breaks in a permutation.
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C++

## Break Count

 intbreak_count( int n 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 .
• There are now  pairs of neighbors.
• We now search for indices  such that the above
inequality stands.

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

## 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

 n the size of the permutation p the actual permutation stored as an array

### Returns

the number of breaks found in the permutation

### Authors

Lucian Bentea (August 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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