# stable_sort

Category: algorithms | Component type: function

### Prototype

`Stable_sort` is an overloaded name; there are actually two `stable_sort` functions.

    template <class RandomAccessIterator>
    void stable_sort(RandomAccessIterator first, RandomAccessIterator last);

    template <class RandomAccessIterator, class StrictWeakOrdering>
    void stable_sort(RandomAccessIterator first, RandomAccessIterator last,
                     StrictWeakOrdering comp);

### Description

`Stable_sort` is much like `sort`: it sorts the elements in `[first, last)` into ascending order, meaning that if `i` and `j` are any two valid iterators in `[first, last)` such that `i` precedes `j`, then `*j` is not less than `*i`. `Stable_sort` differs from `sort` in two ways. First, `stable_sort` uses an algorithm that has different run-time complexity than `sort`. Second, as the name suggests, `stable_sort` is stable: it preserves the relative ordering of equivalent elements. That is, if `x` and `y` are elements in `[first, last)` such that `x` precedes `y`, and if the two elements are equivalent (neither `x < y` nor `y < x`) then a postcondition of `stable_sort` is that `x` still precedes `y`. [1]

The two versions of `stable_sort` 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:

- `RandomAccessIterator` is a model of Random Access Iterator.
- `RandomAccessIterator` is mutable.
- `RandomAccessIterator`'s value type is LessThan Comparable.
- The ordering relation on `RandomAccessIterator`'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:

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

### Preconditions

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

### Complexity

`Stable_sort` is an adaptive algorithm: it attempts to allocate a temporary memory buffer, and its run-time complexity depends on how much memory is available. Worst-case behavior (if no auxiliary memory is available) is `N (log N)^2` comparisons, where `N` is `last - first`, and best case (if a large enough auxiliary memory buffer is available) is `N (log N)`. [2]

### Example

Sort a sequence of characters, ignoring their case. Note that the relative order of characters that differ only by case is preserved.

    inline bool lt_nocase(char c1, char c2) { return tolower(c1) < tolower(c2); }

    int main()
    {
      char A[] = "fdBeACFDbEac";
      const int N = sizeof(A) - 1;
      stable_sort(A, A+N, lt_nocase);
      printf("%s\n", A);
      // The printed result is ""AaBbCcdDeEfF".
    }

### Notes

[1] Note that two elements may be equivalent without being equal. One standard example is sorting a sequence of names by last name: if two people have the same last name but different first names, then they are equivalent but not equal. This is why `stable_sort` is sometimes useful: if you are sorting a sequence of records that have several different fields, then you may want to sort it by one field without completely destroying the ordering that you previously obtained from sorting it by a different field. You might, for example, sort by first name and then do a stable sort by last name.

[2] `Stable_sort` uses the merge sort algorithm; see section 5.2.4 of Knuth. (D. E. Knuth, The Art of Computer Programming. Volume 3: Sorting and Searching. Addison-Wesley, 1975.)

### See also

`sort`, `partial_sort`, `partial_sort_copy`, `binary_search`, `lower_bound`, `upper_bound`, `less<T>`, StrictWeakOrdering, LessThan Comparable

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