What is the minimum number of nodes in a complete binary tree with depth 3?(A) 4(B) 5(C) 6(D) 7
Question
What is the minimum number of nodes in a complete binary tree with depth 3?(A) 4(B) 5(C) 6(D) 7
Solution
A complete binary tree of depth 3 means that there are 3 layers of nodes in the tree, including the root.
In a complete binary tree, every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible.
So, for a complete binary tree of depth 3:
- The first level (root level) has 1 node.
- The second level can have up to 2 nodes.
- The third level can have up to 4 nodes.
Adding these up, the minimum number of nodes in a complete binary tree with depth 3 is 1 (root) + 2 (second level) + 4 (third level) = 7 nodes.
So, the answer is (D) 7.
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