1. [n]  a car that is old and unreliable; "the fenders had fallen off that old bus"
2. [n]  a collection of objects laid on top of each other
3. [n]  (often followed by `of') a large number or amount or extent; "a batch of letters"; "a deal of trouble"; "a lot of money"; "he made a mint on the stock market"; "it must have cost plenty"
4. [v]  fill to overflow; "heap the platter with potatoes"
5. [v]  arrange in stacks; "heap firewood around the fireplace"; "stack your books up on the shelves"
6. [v]  bestow in large quantities; "He heaped him with work"; "She heaped scorn upon him"

1. \Heap\, n. [OE. heep, heap, heap, multitude, AS. he['a]p;
   akin to OS. h?p, D. hoop, OHG. houf, h?fo, G. haufe, haufen,
   Sw. hop, Dan. hob., Icel. h?pr troop, flock, Russ. kupa heap,
   crowd, Lith. kaupas. Cf. {Hope}, in Forlorn hope.]
   1. A crowd; a throng; a multitude or great number of persons.
      [Now Low or Humorous]
            The wisdom of a heap of learned men.  --Chaucer.
            A heap of vassals and slaves.         --Bacon.
            He had heaps of friends.              --W.Black.
   2. A great number or large quantity of things not placed in a
      pile. [Now Low or Humorous]
            A vast heap, both of places of scripture and
            quotations.                           --Bp. Burnet.
            I have noticed a heap of things in my life. --R. L.
                                                  Stevenson.
   3. A pile or mass; a collection of things laid in a body, or
      thrown together so as to form an elevation; as, a heap of
      earth or stones.
            Huge heaps of slain around the body rise. --Dryden.
   

2. \Heap\, v. t. [imp. & p. p. {Heaped}; p. pr. & vb. n.
   {Heaping}.] [AS. he['a]pian.]
   1. To collect in great quantity; to amass; to lay up; to
      accumulate; -- usually with up; as, to heap up treasures.
            Though he heap up silver as the dust. --Job. xxvii.
                                                  16.
   2. To throw or lay in a heap; to make a heap of; to pile; as,
      to heap stones; -- often with up; as, to heap up earth; or
      with on; as, to heap on wood or coal.
   3. To form or round into a heap, as in measuring; to fill (a
      measure) more than even full.
   

1. 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.

2. 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.

When Joshua took the city of Ai (Josh. 8), he burned it and "made it an heap [Heb. tel] for ever" (8:28). The ruins of this city were for a long time sought for in vain. It has been at length, however, identified with the mound which simply bears the name of "Tel." "There are many Tels in modern Palestine, that land of Tels, each Tel with some other name attached to it to mark the former site. But the site of Ai has no other name 'unto this day.' It is simply et-Tel, 'the heap' par excellence."