In a complete binary tree, how many nodes are there at level k?
Practice Questions
Q1
In a complete binary tree, how many nodes are there at level k?
2^k
2^(k+1)
2^(k-1)
k^2
Questions & Step-by-Step Solutions
In a complete binary tree, how many nodes are there at level k?
Step 1: Understand what a complete binary tree is. A complete binary tree is a type of binary tree where every level, except possibly the last, is fully filled.
Step 2: Identify the levels in the tree. The root level is level 0, the next level is level 1, and so on.
Step 3: Recognize that at each level k, the number of nodes doubles compared to the previous level. This means level 0 has 1 node, level 1 has 2 nodes, level 2 has 4 nodes, and so forth.
Step 4: Realize that the pattern of nodes at each level can be expressed mathematically as 2^k, where k is the level number.
Step 5: Conclude that to find the number of nodes at level k, you simply calculate 2 raised to the power of k (2^k).
