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# next_permutation

Permutes the order of the elements
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### Key Facts

Gyroscopic Couple: The rate of change of angular momentum () = (In the limit).
• = Moment of Inertia.
• = Angular velocity
• = Angular velocity of precession.

Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.

## Definition

The next_permutation() algorithm is defined in the standard header <algorithm> and in the nonstandard backward-compatibility header <algo.h>.

## Interface

#include <algorithm>
template < class BidirectionalIterator >
bool next_permutation(
BidirectionalIterator first,
BidirectionalIterator last
);
template < class BidirectionalIterator, class BinaryPredicate >
bool next_permutation(
BidirectionalIterator first,
BidirectionalIterator last,
BinaryPredicate comp
);

Parameters:
Parameter Description
first A bidirectional iterator pointing to the position of the first element in the range to be permuted
last A bidirectional iterator pointing to the position one past the final element in the range to be permuted
comp User-defined predicate function object that defines the comparison criterion to be satisfied by successive elements in the ordering. A binary predicate takes two arguments and returns true when satisfied and false when not satisfied

## Description

Next_permutation function reorders the range [first, last) into the next permutation from the set of all permutations that are lexicographically ordered.

The first version uses operator< for comparison and the second uses the function object comp.

## Return Value

Returns true if there was a next permutation and has replaced the original ordering of the range,false otherwise.

## Complexity

The complexity is linear; performs at most (last - first) / 2 swaps.

### References

Example:
##### Example - next_permutation algorithm
Problem
The following example of code prints all three permutations of the string "aba" using next_permutation function.
Workings
#include <algorithm>
#include <string>
#include <iostream>
int main()
{
std::string s = "aba";
std::sort(s.begin(), s.end());
do {
std::cout << s << '\n';
} while(std::next_permutation(s.begin(), s.end()));

return 0;
}
Solution
Output:

aab
aba
baa
References