Difference between Min Heap and Max Heap
Heap is a binary tree with two unique properties: all nodes must be in a particular order, and its form must be complete. A min heap is a heap in which the value of each parent node, including the root, is less than or equal to that of its children nodes. On the other hand, a max heap is the exact opposite of a min heap; in this structure, every parent node, including the root, is larger than or equal to the value of its children nodes.
Following a quick introduction to min heap and max heap, we will examine the whole list and the distinction between min heap and max heap. Let's examine the differences between min heap and max heap in detail.
What is Min Heap?
The Min heap is a form of heap similar to the Max heap; however, its state is virtually the opposite. In a min heap, the value of each node is less than or equal to that of its children.
Specifically:
To qualify as a max heap, a tree must satisfy both of the following conditions:
- The tree must be an exhaustive binary tree (this is the condition for the heap).
- Each node's value must be less than that of all its children.
This indicates that the node with the lowest value will be the tree's root.
Every node in the following example of the min heap is smaller than both of its children.
Advantages:
- It aids in locating the smallest and largest numbers. To only examine the last element, the time complexity is constant O. (1).
- It may be accomplished using an array and requires no additional space for the pointer. A binary heap is an easily implementable balanced binary tree.
Disadvantages:
- O is the search time complexity for Heap elements (N).
- The heap requires O(N) time to locate the successor or predecessor of an element, but the BST requires just O(log N) time.
What is Max Heap?
Max heap is a sort of heap data structure with a unique characteristic. In a Max heap, the value of each node is larger than or equal to the value of both of its children. How would this benefit us? Which node would have the highest value if every parent is larger than its children? Specifically, the root node. You may visit the root node of a max heap to get its maximum element.
Specifically:
To qualify as a max heap, a tree must satisfy both of the following conditions:
- The tree must be an exhaustive binary tree (this is the condition for heap)
- Each node's value must exceed that of all its children.
Every node in the following max heap example is larger than both of its children.
Advantages:
- To only examine the last element, the time complexity is constant O. (1).
- It may be accomplished using an array and requires no additional space for the pointer.
Disadvantages:
- Printing all heap members in sorted order requires O(N*log N) time complexity, while BST merely requires O(N) time.
- Globally used heap memory makes memory management more complicated. During Java garbage collection, heap memory is separated into two parts: the old generation and the new generation.
Min Heap vs. Max Heap
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Max Heap |
- A min heap is a complete binary tree in which each node has a value that is less than or equal to the values of its children. The root node of a min heap has the minimum value.
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- A max heap is a complete binary tree in which each node has a value that is greater than or equal to the values of its children. The root node of a max heap has the maximum value.
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- In a min heap, the left and right children of a node must have values that are greater than or equal to the value of the node.
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- In a max heap, the left and right children of a node must have values that are less than or equal to the value of the node.
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- When inserting a new value into a min heap, it is added to the next available position in the tree and then compared to its parent. If the value is less than its parent, it is swapped with the parent. This process is repeated until the value is in its correct position.
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- When inserting a new value into a max heap, it is added to the next available position in the tree and then compared to its parent. If the value is greater than its parent, it is swapped with the parent. This process is repeated until the value is in its correct position.
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- To delete a value from a min heap, the value is removed from the root node and replaced with the last value in the tree. The new root value is then compared to its children and swapped with the smaller of the two if necessary. This process is repeated until the value is in its correct position.
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- To delete a value from a max heap, the value is removed from the root node and replaced with the last value in the tree. The new root value is then compared to its children and swapped with the larger of the two if necessary. This process is repeated until the value is in its correct position.
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- Min heaps are used to implement priority queues and can be used for sorting data. They are also used in graph algorithms, such as Dijkstra's algorithm.
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- Max heaps are used to implement priority queues and can be used for sorting data in descending order. They are also used in graph algorithms, such as the heap-based version of Prim's algorithm.
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Conclusion
Min heap and max heap are, thus, entire binary trees. The minimum and maximum heap sizes may both be specified using an array. The Min Heap data structure is helpful when the least element in a collection of items must be retrieved constantly. Max heap is the inverse of the minimum heap. In constant time, Max Heap retrieves the maximum element from a collection.
We hope you like this article. We have begun with a quick overview of the min heap and max heap. We also compared the benefits, drawbacks, and features of min heap vs. max heap.
Related Questions
1. What is min/max heap used for?
There are two different sorts of heaps: the Min-heap and the Max-heap. A min-heap is used to access the smallest element in the heap, whereas a Max-heap is used to access the largest member.
2. Can a min-heap have duplicates?
First, duplicate values are always permitted in a heap; there is no constraint against this. The left node of a heap does not have to be smaller than the right node, unlike a binary search tree.
3. Is min-heap always sorted?
Yes, assuming the standard array-stored heap convention is used.
4. Is min-heap a binary tree?
The root node of a Min Heap Binary Tree has the smallest key in the tree. The above definition applies to all subtrees inside the tree. This is known as the Min Heap estate. Almost every node outside of the last two levels must have two children.
