## Introduction

In combinatorial mathematics and algorithm design, permutations play a pivotal role. They represent the rearrangement of elements in a sequence, offering insights into various problem-solving scenarios. Among these permutations, understanding the concept of the "next permutation" holds particular significance in algorithms and programming.

**What is the Next Permutation?**

The Next Permutation algorithm generates the lexicographically next greater permutation of a sequence. It rearranges the elements in the sequence into the next greater order, considering the dictionary or lexicographic ordering of the elements.

In simpler terms, given a sequence of elements, the Next Permutation algorithm rearranges these elements to produce the next permutation in lexicographic order. This is crucial in scenarios where permutations need to be generated systematically or when finding the next arrangement is essential for optimization or solving certain problems efficiently.

**Syntax**

The syntax for the Next Permutation algorithm in C++ is:

```
template <class BidirectionalIterator>
bool next_permutation (BidirectionalIterator first, BidirectionalIterator last);
```

The **next_permutation** function in C++ takes two iterators representing the range of elements to permute. It rearranges the elements in this range to their next lexicographically greater permutation if such a permutation exists. The function returns **true** if a next permutation was found, otherwise **false**.

**Parameters**

**first**: Iterator pointing to the beginning of the sequence or range of elements.**last**: Iterator pointing to the end of the sequence or range of elements.

The **first** and **last** parameters define the range of elements for which the next permutation needs to be computed. The **first** iterator points to the first element in the sequence, while the **last** iterator points to one position past the last element in the sequence. The range between **first** and **last** will be modified to contain the next lexicographically greater permutation if it exists.

**Return Value**

The **next_permutation** function returns a boolean value:

**true**if the function successfully finds the next lexicographically greater permutation.**false**if the current sequence is already the last permutation, and no next permutation exists.

The return value of **next_permutation** indicates whether a next permutation was found. If a next permutation exists, the function rearranges the elements and returns **true**. If the current permutation is already the last one in lexicographic order, the function leaves the elements unchanged and returns **false**.