If the number of nodes in a binary tree is 2ⁿ (where n is a positive integer), then the entire tree would contain at least A) 2ⁿ^{+ 1} nodes B) 2²ⁿ nodes C) 2ⁿ^{+ 1} - 1 nodes D) 2ⁿ^{+ 2} nodes

Question

Quizplus · Accepted Answer

Starting from the root, we have 2 children which are both subtrees with the tag 2S1U1P1, giving us a total of 4 nodes. Each of these subtrees also have 2 children which are both subtrees with the tag 1S1S1P0, giving each subtree a total of 4+2=6 nodes. Continuing down, each of these 1S1S1P0 subtrees have 2 children which are both subtrees with the tag 0, giving each subtree a total of 6+2=8 nodes. Finally, we have n leaves, each with the tag S1S1P0. Therefore, the total number of nodes in the tree would be:
2(4 + 2(6 + 2(8)) + n) - 1 = 2S1U1P1nS1S1P0S1U1P1 + 1S1S1P0 - 1, which matches option C.

If the Number of Nodes in a Binary Tree Is