# prev_permutation

Category: algorithms | Component type: function

### Prototype

`Prev_permutation` is an overloaded name; there are actually two `prev_permutation` functions.

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

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

### Description

`Prev_permutation` transforms the range of elements `[first, last)` into the lexicographically next smaller 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 previous. If such a permutation exists, `prev_permutation` transforms `[first, last)` into that permutation and returns `true`. Otherwise it transforms `[first, last)` into the lexicographically greatest permutation [2] and returns `false`.

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

The two versions of `prev_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:

- `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:

- `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

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

      cout << "Initially:              ";
      copy(A, A+N, ostream_iterator<int>(cout, " "));
      cout << endl;

      prev_permutation(A, A+N);
      cout << "After prev_permutation: ";
      copy(A, A+N, ostream_iterator<int>(cout, " "));
      cout << endl;

      next_permutation(A, A+N);
      cout << "After next_permutation: ";
      copy(A, A+N, ostream_iterator<int>(cout, " "));
      cout << endl;
    }

### 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 greatest permutation is, by definition, sorted in nonascending order.

### See also

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

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