[alg.heap.operations.general]

# 26 Algorithms library [[algorithms]](./#algorithms)

## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#alg.heap.operations.general)

### 26.8.8 Heap operations [[alg.heap.operations]](alg.heap.operations#general)

#### 26.8.8.1 General [alg.heap.operations.general]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10877)

A random access range [a, b) is a[*heap with respect to comp and proj*](#def:heap_with_respect_to_comp_and_proj "26.8.8.1 General [alg.heap.operations.general]") for a comparator and projection comp and proj if its elements are organized such that:

- [(1.1)](#1.1)

  With N = b - a, for all i, 0<i<N, bool(invoke(comp, invoke(proj, a[⌊i−12⌋]), invoke(​proj, a[i]))) is false[.](#1.1.sentence-1)

- [(1.2)](#1.2)

  *a may be removed by pop_heap, or
 a new element added by push_heap,
 in O(logN) time[.](#1.2.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10894)

These properties make heaps useful as priority queues[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10897)

make_heap converts a range into a heap andsort_heap turns a heap into a sorted sequence[.](#3.sentence-1)