A full binary tree with height 4 has ______ nodes.
A)7
B)8
C)15
D)31

Question

Quizplus · Accepted Answer

A binary tree with height h has at most 2⁽ʰ⁺¹⁾-1 nodes. Thus, a full binary tree with height 4 can have at most 2⁽⁴⁺¹⁾-1 = 31 nodes. However, a full binary tree has all levels filled completely, except possibly the last level. The last level is filled from left to right, so if there are any missing nodes, they must be on the right. In a full binary tree, the number of nodes at the last level is equal to 2⁰ + 2¹ + 2² + … + 2⁽ʰ⁻¹⁾ = 2⁴⁻¹ = 8. Therefore, the total number of nodes in a full binary tree with height 4 is 2⁽⁴⁺¹⁾-1 - 8 = 15.

A Full Binary Tree with Height 4 Has ______ Nodes