Java Program to Implement Leftist Heap
A leftist heap is a priority Queue implemented with a binary heap. Every node has a sValue which is at the nearest Distance to the other nodes. Now we will write a java program for performing certain operations on a leftist Heap (Inorder Traversal) like insert, delete, clear, and check for empty.
A leftist tree is a binary tree with properties:
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- Normal Min Heap Property : key(i) >= key(parent(i))
- Heavier on left side : dist(right(i)) <= dist(left(i)). Here, dist(i) is the number of edges on the shortest path from node i to a leaf node in extended binary tree representation (In this representation, a null child is considered as an external or leaf node). The shortest path to a descendant external node is through the right child. Every subtree is also a leftist tree and dist( i ) = 1 + dist( right( i ) ).
Example: The below leftist tree is presented with its distance calculated for each node with the procedure mentioned above. The rightmost node has a rank of 0 as the right subtree of this node is null and its parent has a distance of 1 by dist( i ) = 1 + dist( right( i )). The same is followed for each node and their s-value( or rank) is calculated.
From the above second property, we can draw two conclusions :
- The path from the root to the rightmost leaf is the shortest path from the root to the leaf.
- If the path to the rightmost leaf has x nodes, then the leftist heap has at least 2x – 1 node. This means the length of the path to the rightmost leaf is O(log n) for a leftist heap with n nodes.
LEFTIST HEAP Functions to do 2. delete min 3. check empty 4. clear 2 Inorder Traversal: 53 52 54 If you wish to continue type Y or y y Functions to do 2. delete min 3. check empty 4. clear 3 Empty status = false Inorder Traversal: 53 52 54 If you wish to continue type Y or y y Functions to do 2. delete min 3. check empty 4. clear 4 Inorder Traversal: If you wish to continue type Y or y
- We will first take a class Node and create its constructor and various parameters.
- Then we will create a class LeftHeap, In this class, we will create various methods and try to perform their operations.
- We will create a constructor, where we keep the root null.
- We will create a method isEmpty() to check if the Heap is empty.
- We will create a method clear(), to clear the heap.
- We create a method to merge:
- Here we need to take two nodes, and then we would check for both of them being empty
- Then we would set the values right or left according to our convenience.
- This function is used to find the minimum element in the heap
- Then we declare a function named del().
- This function is used to find the minimum number, and then we remove it.
- Then we declare the main function and call the function and do operations performed with the help of a switch case. The operations performed are whether to check if it is empty or to empty the heap or delete the minimum element.