A heap is a data structure that can be visualized as a binary tree with two properties: the heap property and the shape property. The heap property specifies that for every node in the tree, its parent node is either smaller (in a min-heap) or larger (in a max-heap) than its child nodes. The shape property specifies that the tree is a complete binary tree, meaning that all levels of the tree are completely filled except possibly the last level, which is filled from left to right.
The difference between a min-heap and a max-heap is in the ordering of the nodes with respect to the heap property. In a min-heap, the value of the parent node is smaller than the value of its child nodes, while in a max-heap, the value of the parent node is larger than the value of its child nodes.
Here are some examples of min-heaps and max-heaps:
Min-heap:
2
/
3 5
/ \ /
8 9 7 6Max-heap:
8
/
7 6
/ \ /
2 3 5 4Min-heaps and max-heaps are useful for implementing priority queues, where the smallest (or largest) element is always at the top of the heap and can be efficiently accessed and removed. They are also used in various graph algorithms such as Dijkstra’s shortest path algorithm and Prim’s minimum spanning tree algorithm.