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cppdraft/alg/heap/operations/general.md

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+[alg.heap.operations.general]
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+# 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)