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An area of memory used for dynamic memory allocation where blocks of memory are allocated and freed in an arbitrary order and the pattern of allocation and size of blocks is not known until run time. Typically, a program has one heap which it may use for several different purposes.

Heap is required by languages in which functions can return arbitrary data structures or functions with free variables (see closure). In C functions malloc and free provide access to the heap.

Contrast stack. See also dangling pointer.


A data structure with its elements partially ordered (sorted) such that finding either the minimum or the maximum (but not both) of the elements is computationally inexpensive (independent of the number of elements), while both adding a new item and finding each subsequent smallest/largest element can be done in O(log n) time, where n is the number of elements.

Formally, a heap is a binary tree with a key in each node, such that all the leaves of the tree are on two adjacent levels; all leaves on the lowest level occur to the left and all levels, except possibly the lowest, are filled; and the key in the root is at least as large as the keys in its children (if any), and the left and right subtrees (if they exist) are again heaps.

Note that the last condition assumes that the goal is finding the minimum quickly.

Heaps are often implemented as one-dimensional arrays. Still assuming that the goal is finding the minimum quickly the invariant is

heap[i] <= heap[2*i] and heap[i] <= heap[2*i+1] for all i,

where heap[i] denotes the i-th element, heap[1] being the first. Heaps can be used to implement priority queues or in sort algorithms.


In programming, it refers to a common pool of memory that is available to the program. The management of the heap is either done by the applications themselves, allocating and deallocating memory as required, or by the operating system or other system program.
References in classic literature ?
with only the thinnest vesture of human similitude about it, through which was evident the stiff, rickety, incongruous, faded, tattered, good-for-nothing patchwork of its substance, ready to sink in a heap upon the floor, as conscious of its own unworthiness to be erect.
Imagine these cells, some two or three hundred in number, and in every one a man locked up; this one at his door for air, with his hands thrust through the grate; this one in bed (in the middle of the day, remember); and this one flung down in a heap upon the ground, with his head against the bars, like a wild beast.
There was a sharp crack, and we were in a heap upon the ground with coils of rope all over us.