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Binary heap
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964 as a data structure for implementing heapsort.
A binary heap is defined as a binary tree with two additional constraints:
Heaps where the parent key is greater than or equal to (≥) the child keys are called max-heaps; those where it is less than or equal to (≤) are called min-heaps. Efficient (that is, logarithmic time) algorithms are known for the two operations needed to implement a priority queue on a binary heap:
Binary heaps are also commonly employed in the heapsort sorting algorithm, which is an in-place algorithm as binary heaps can be implemented as an implicit data structure, storing keys in an array and using their relative positions within that array to represent child–parent relationships.
Both the insert and remove operations modify the heap to preserve the shape property first, by adding or removing from the end of the heap. Then the heap property is restored by traversing up or down the heap. Both operations take O(log n) time.
To insert an element to a heap, we perform the following steps:
Steps 2 and 3, which restore the heap property by comparing and possibly swapping a node with its parent, are called the up-heap operation (also known as bubble-up, percolate-up, sift-up, trickle-up, swim-up, heapify-up, cascade-up, or fix-up).
The number of operations required depends only on the number of levels the new element must rise to satisfy the heap property. Thus, the insertion operation has a worst-case time complexity of O(log n). For a random heap, and for repeated insertions, the insertion operation has an average-case complexity of O(1).
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Binary heap AI simulator
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Binary heap
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964 as a data structure for implementing heapsort.
A binary heap is defined as a binary tree with two additional constraints:
Heaps where the parent key is greater than or equal to (≥) the child keys are called max-heaps; those where it is less than or equal to (≤) are called min-heaps. Efficient (that is, logarithmic time) algorithms are known for the two operations needed to implement a priority queue on a binary heap:
Binary heaps are also commonly employed in the heapsort sorting algorithm, which is an in-place algorithm as binary heaps can be implemented as an implicit data structure, storing keys in an array and using their relative positions within that array to represent child–parent relationships.
Both the insert and remove operations modify the heap to preserve the shape property first, by adding or removing from the end of the heap. Then the heap property is restored by traversing up or down the heap. Both operations take O(log n) time.
To insert an element to a heap, we perform the following steps:
Steps 2 and 3, which restore the heap property by comparing and possibly swapping a node with its parent, are called the up-heap operation (also known as bubble-up, percolate-up, sift-up, trickle-up, swim-up, heapify-up, cascade-up, or fix-up).
The number of operations required depends only on the number of levels the new element must rise to satisfy the heap property. Thus, the insertion operation has a worst-case time complexity of O(log n). For a random heap, and for repeated insertions, the insertion operation has an average-case complexity of O(1).