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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

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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.

This problem has been solved

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