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This module provides a BinaryHeap adaptor that makes a binary heap out of any user-provided random-access range.
This module is a submodule of std.container.

Source: std/container/binaryheap.d

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
Steven Schveighoffer, Andrei Alexandrescu
struct BinaryHeap(Store, alias less = "a < b") if (isRandomAccessRange!Store || isRandomAccessRange!(typeof(Store.init[])));
Implements a binary heap container on top of a given random-access range type (usually T[]) or a random-access container type (usually Array!T). The documentation of BinaryHeap will refer to the underlying range or container as the store of the heap.
The binary heap induces structure over the underlying store such that accessing the largest element (by using the front property) is a Ο(1) operation and extracting it (by using the removeFront() method) is done fast in Ο(log n) time.

If less is the less-than operator, which is the default option, then BinaryHeap defines a so-called max-heap that optimizes extraction of the largest elements. To define a min-heap, instantiate BinaryHeap with "a > b" as its predicate.

Simply extracting elements from a BinaryHeap container is tantamount to lazily fetching elements of Store in descending order. Extracting elements from the BinaryHeap to completion leaves the underlying store sorted in ascending order but, again, yields elements in descending order.

If Store is a range, the BinaryHeap cannot grow beyond the size of that range. If Store is a container that supports insertBack, the BinaryHeap may grow by adding elements to the container.
Example from "Introduction to Algorithms" Cormen et al, p 146
import std.algorithm : equal;
int[] a = [ 4, 1, 3, 2, 16, 9, 10, 14, 8, 7 ];
auto h = heapify(a);
// largest element
assert(h.front == 16);
// a has the heap property
assert(equal(a, [ 16, 14, 10, 8, 7, 9, 3, 2, 4, 1 ]));
BinaryHeap implements the standard input range interface, allowing

lazy iteration of the underlying range in descending order.
import std.algorithm : equal;
import std.range : take;
int[] a = [4, 1, 3, 2, 16, 9, 10, 14, 8, 7];
auto top5 = heapify(a).take(5);
assert(top5.equal([16, 14, 10, 9, 8]));
this(Store s, size_t initialSize = size_t.max);
Converts the store s into a heap. If initialSize is specified, only the first initialSize elements in s are transformed into a heap, after which the heap can grow up to r.length (if Store is a range) or indefinitely (if Store is a container with insertBack). Performs Ο(min(r.length, initialSize)) evaluations of less.
void acquire(Store s, size_t initialSize = size_t.max);
Takes ownership of a store. After this, manipulating s may make the heap work incorrectly.
void assume(Store s, size_t initialSize = size_t.max);
Takes ownership of a store assuming it already was organized as a heap.
auto release();
Clears the heap. Returns the portion of the store from 0 up to length, which satisfies the heap property.
@property bool empty();
Returns true if the heap is empty, false otherwise.
@property BinaryHeap dup();
Returns a duplicate of the heap. The underlying store must also support a dup method.
@property size_t length();
Returns the length of the heap.
@property size_t capacity();
Returns the capacity of the heap, which is the length of the underlying store (if the store is a range) or the capacity of the underlying store (if the store is a container).
@property ElementType!Store front();
Returns a copy of the front of the heap, which is the largest element according to less.
void clear();
Clears the heap by detaching it from the underlying store.
size_t insert(ElementType!Store value);
Inserts value into the store. If the underlying store is a range and length == capacity, throws an exception.
void removeFront();
alias popFront = removeFront;
Removes the largest element from the heap.
ElementType!Store removeAny();
Removes the largest element from the heap and returns a copy of it. The element still resides in the heap's store. For performance reasons you may want to use removeFront with heaps of objects that are expensive to copy.
void replaceFront(ElementType!Store value);
Replaces the largest element in the store with value.
bool conditionalInsert(ElementType!Store value);
If the heap has room to grow, inserts value into the store and returns true. Otherwise, if less(value, front), calls replaceFront(value) and returns again true. Otherwise, leaves the heap unaffected and returns false. This method is useful in scenarios where the smallest k elements of a set of candidates must be collected.
BinaryHeap!(Store, less) heapify(alias less = "a < b", Store)(Store s, size_t initialSize = size_t.max);
Convenience function that returns a BinaryHeap!Store object initialized with s and initialSize.