binary heaps

Binary heaps are a type of data structure used to efficiently store and retrieve elements with specific priority or value. They are mainly used in priority queues, where the element with the highest priority is always accessible in constant time. A binary heap consists of a binary tree with two properties – 1. Complete binary tree property: All levels of the tree are filled except the last, which is filled from left to right. 2. Heap property: In a max heap, for every node, the value of the parent node is greater than or equal to the values of its children nodes. In a min heap, the value of the parent node is less than or equal to the values of its children nodes. Binary heaps can be efficiently implemented using an array, where each element represents a node in the heap and its position corresponds to its index in the array. The binary heap operations include insertion, deletion, and retrieval of the highest priority element, all of which have a time complexity of O(log n), where n is the number of elements in the heap. The binary heap structure makes it an efficient choice for applications requiring efficient priority-based operations.

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