# std::next_permutation and prev_permutation in C++

**std::next_permutation**

It is used to rearrange the elements in the range [first, last) into the next lexicographically greater permutation. A permutation is each one of the N! possible arrangements the elements can take (where N is the number of elements in the range). Different permutations can be ordered according to how they compare lexicographically to each other.The complexity of the code is O(n*n!) which also includes printing all the permutations.**Syntax: **

templatebool next_permutation (BidirectionalIterator first,BidirectionalIterator last);Parameters:first, last : Bidirectional iterators to the initial and final positions of the sequence. The range used is [first, last), which contains all the elements between first and last, including the element pointed by first but not the element pointed by last.return value:true :if the function could rearrange the object as a lexicographically greater permutation. Otherwise, the function returns false to indicate that the arrangementis not greater than the previous, but the lowest possible (sorted in ascending order).

**Application : **next_permutation is to find next lexicographically greater value for given array of values.

Examples:

Input : next permutation of 1 2 3 is Output : 1 3 2 Input : next permutation of 4 6 8 is Output : 4 8 6

## CPP

`// C++ program to illustrate` `// next_permutation example` `// this header file contains next_permutation function` `#include <algorithm>` `#include <iostream>` `using` `namespace` `std;` `int` `main()` `{` ` ` `int` `arr[] = { 1, 2, 3 };` ` ` `sort(arr, arr + 3);` ` ` `cout << ` `"The 3! possible permutations with 3 elements:\n"` `;` ` ` `do` `{` ` ` `cout << arr[0] << ` `" "` `<< arr[1] << ` `" "` `<< arr[2] << ` `"\n"` `;` ` ` `} ` `while` `(next_permutation(arr, arr + 3));` ` ` `cout << ` `"After loop: "` `<< arr[0] << ` `' '` ` ` `<< arr[1] << ` `' '` `<< arr[2] << ` `'\n'` `;` ` ` `return` `0;` `}` |

Output:

The 3! possible permutations with 3 elements: 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1 After loop: 1 2 3

**std::prev_permutation**

It is used to rearranges the elements in the range [first, last) into the previous lexicographically-ordered permutation. A permutation is each one of the N! possible arrangements the elements can take (where N is the number of elements in the range). Different permutations can be ordered according to how they compare lexicographically to each other.**Syntax : **

templatebool prev_permutation (BidirectionalIterator first,BidirectionalIterator last );parameters:first, last : Bidirectional iterators to the initial and final positions of the sequence. The range used is [first, last), which contains all the elements between first and last, including the element pointed by first but not the element pointed by last.return value:true :if the function could rearrange the object as a lexicographically smaller permutation. Otherwise, the function returns false to indicate that the arrangement is not less than the previous, but the largest possible (sorted in descending order).

**Application : **prev_permutation is to find previous lexicographically smaller value for given array of values.

Examples:

Input : prev permutation of 3 2 1 is Output : 3 1 2 Input : prev permutation of 8 6 4 is Output :8 4 6

## CPP

`// C++ program to illustrate` `// prev_permutation example` `// this header file contains prev_permutation function` `#include <algorithm>` `#include <iostream>` `using` `namespace` `std;` `int` `main()` `{` ` ` `int` `arr[] = { 1, 2, 3 };` ` ` `sort(arr, arr + 3);` ` ` `reverse(arr, arr + 3);` ` ` `cout << ` `"The 3! possible permutations with 3 elements:\n"` `;` ` ` `do` `{` ` ` `cout << arr[0] << ` `" "` `<< arr[1] << ` `" "` `<< arr[2] << ` `"\n"` `;` ` ` `} ` `while` `(prev_permutation(arr, arr + 3));` ` ` `cout << ` `"After loop: "` `<< arr[0] << ` `' '` `<< arr[1]` ` ` `<< ` `' '` `<< arr[2] << ` `'\n'` `;` ` ` `return` `0;` `}` |

Output:

The 3! possible permutations with 3 elements: 3 2 1 3 1 2 2 3 1 2 1 3 1 3 2 1 2 3 After loop: 3 2 1

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