Min heap is a complete binary tree. A complete binary tree is a binary tree in which all levels are completely filled and all the nodes in the last level are as left as possible. Min heap should meets this criteria: the parent’s key is less than both children’s keys. The smallest value is at the root.

This post is min heap implementation. The max heap is opposite order. Note the search and traversal in min-heap implementation is the same as max-heap.

min heap

Table of Content


What is behind min-heap?

A heap is a complete binary tree conceptually. The underlying data structure is an array. Each node’s position in the heap is corresponding to the index in the array. The root’s position is 0, corresponding to the index 0. The node’s position increases by 1 from left to right, from upper level to lower level.

The formula to get the parent and two children’s positions from the current node’s position:

parentPos = (pos-1)/2
left = 2*pos+1
right=2*pos+2


Map of heap implementations

Part 1 – Max-heap implementation

you are here

Part 2 – Min-heap implementation
Part 3 – Priority queue implementation with heap iterative solution
Part 4 – Priority queue implementation with heap recursive solution


Insert

We declare three attributes: heap, length and maxSize. heap is an array. maxSize is the max length of the array. It is used to initialize the array. length is actual number of elements in the array. It starts from 0.

To insert a new element, we put the new value at the end of the array. Then we move it up based on its value compared to its parent. If it’s value less than its parent, it should be switched the position with its parent, until it is below a smaller node and above a larger one. We call this process heap up (or trickle up).

Java

Javascript

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Remove

The remove operation is to remove the element with the smallest value, which is the first one in the array. When we remove the first element in the array, we move the last element to the first to fill out the empty spot. But this element’s value might be larger than its children’s. To correct this, we compare its value with its children’s values, and switch with the child with the smaller value, until it is below a smaller node and above a larger one. This process is called heap down (or trickle down). Heap down is more complicated than heap up because it has two children to compare.

Java

Javascript

Python


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What is time complexity of insertion and deletion in min-heap?

They have O(h) time complexity. h is the height of the tree. Since heap is a complete binary tree, h is logn.