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# prev_permutation

Permutes the order of the element
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### Key Facts

Gyroscopic Couple: The rate of change of angular momentum ($\inline&space;\tau$) = $\inline&space;I\omega\Omega$ (In the limit).
• $\inline&space;I$ = Moment of Inertia.
• $\inline&space;\omega$ = Angular velocity
• $\inline&space;\Omega$ = 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 prev_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 prev_permutation(
BidirectionalIterator first,
BidirectionalIterator last
);
template < class BidirectionalIterator, class BinaryPredicate >
bool prev_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

Prev_permutation function reorders the range [first, last) into the previous 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 previous 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 - prev_permutation algorithm
Problem
The following code prints all six permutations of the string "abc" in reverse order using prev_permutation function.
Workings
#include <algorithm>
#include <string>
#include <iostream>
#include <functional>
int main()
{
std::string s="abc";
std::sort(s.begin(), s.end(), std::greater<char>());
do {
std::cout << s << ' ';
} while(std::prev_permutation(s.begin(), s.end()));
std::cout << '\n';
}
Solution
Output:

cba cab bca bac acb abc
References