Question

What is the RUN TIME COMPLEXITY of the following code:

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public void printLevelsRecursively(Node root) {

for (int i = 1; i <= heightOfTree(root); i++) {
System.out.print("Level " + i + " : ");
printSingleLevelRecursively(root, i);
System.out.print("\n");

}
}
public int heightOfTree(Node root) {
if (root != null)
   return super.max(heightOfTree(root.l), heightOfTree(root.r)) + 1;
return 0;
}

public void printSingleLevelRecursively(Node root, int level) {
if (root == null)
return;
if (level == 1)
System.out.print(root.key + " ");
else if (level > 1) {
printSingleLevelRecursively(root.l, level - 1);
printSingleLevelRecursively(root.r, level - 1);
}
}

Answer 1

Height Balanced Tree – (BST -binary search tree)
AVL tree is binary search tree with additional property that difference between height of left sub-tree and right sub-tree of any node can’t be more than 1. For example, BST shown in Figure 2 is not AVL as difference between left sub-tree and right sub-tree of node 3 is 2. However, BST shown Figure      

figure 1 figure 2. figure 3

3 is AVL tree.

• Searching: For searching element 1, we have to traverse elements (in order 5, 4, 1) = 3 = log₂n. Therefore, searching in AVL tree has worst case complexity of O(log₂n).
• Insertion: For inserting element 12, it must be inserted as right child of 9. Therefore, we need to traverse elements (in order 5, 7, 9) to insert 12 which has worst case complexity of O(log₂n).
• Deletion: For deletion of element 9, we have to traverse elements to find 9 (in order 5, 7, 9). Therefore, deletion in binary tree has worst case complexity of O(log₂n).