# next_permutation

Category: algorithms | Component type: function

### Prototype

`Next_permutation` is an overloaded name; there are actually two `next_permutation` functions.

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

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

### Description

`Next_permutation` transforms the range of elements `[first, last)` into the lexicographically next greater permutation of the elements. There is a finite number of distinct permutations (at most `N!` [1], where `N` is `last - first`), so, if the permutations are ordered by `lexicographical_compare`, there is an unambiguous definition of which permutation is lexicographically next. If such a permutation exists, `next_permutation` transforms `[first, last)` into that permutation and returns `true`. Otherwise it transforms `[first, last)` into the lexicographically smallest permutation [2] and returns `false`.

The postcondition is that the new permutation of elements is lexicographically greater than the old (as determined by `lexicographical_compare`) if and only if the return value is `true`.

The two versions of `next_permutation` differ in how they define whether one element is less than another. The first version compares objects using `operator<`, and the second compares objects using a function object `comp`.

### Definition

Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h.

### Requirements on types

For the first version, the one that takes two arguments:

- `BidirectionalIterator` is a model of Bidirectional Iterator.
- `BidirectionalIterator` is mutable.
- `BidirectionalIterator`'s value type is LessThan Comparable.
- The ordering relation on `BidirectionalIterator`'s value type is a strict weak ordering, as defined in the LessThan Comparable requirements.

For the second version, the one that takes three arguments:

- `BidirectionalIterator` is a model of Bidirectional Iterator.
- `BidirectionalIterator` is mutable.
- `StrictWeakOrdering` is a model of Strict Weak Ordering.
- `BidirectionalIterator`'s value type is convertible to `StrictWeakOrdering`'s argument type.

### Preconditions

- `[first, last)` is a valid range.

### Complexity

Linear. At most `(last - first) / 2` swaps.

### Example

This example uses `next_permutation` to implement the worst known deterministic sorting algorithm. Most sorting algorithms are `O(N log(N))`, and even bubble sort is only `O(N^2)`. This algorithm is actually `O(N!)`.

    template <class BidirectionalIterator>
    void snail_sort(BidirectionalIterator first, BidirectionalIterator last)
    {
      while (next_permutation(first, last)) {}
    }

    int main()
    {
      int A[] = {8, 3, 6, 1, 2, 5, 7, 4};
      const int N = sizeof(A) / sizeof(int);

      snail_sort(A, A+N);
      copy(A, A+N, ostream_iterator<int>(cout, "\n"));
    }

### Notes

[1] If all of the elements in `[first, last)` are distinct from each other, then there are exactly `N!` permutations. If some elements are the same as each other, though, then there are fewer. There are, for example, only three (`3!/2!`) permutations of the elements `1 1 2`.

[2] Note that the lexicographically smallest permutation is, by definition, sorted in nondecreasing order.

### See also

`prev_permutation`, `lexicographical_compare`, LessThan Comparable, Strict Weak Ordering, `sort`

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