Data Structures | Binary Trees | Question 1

Which of the following is true about Binary Trees?

(A)

Every binary tree is either complete or full.

(B)

Every complete binary tree is also a full binary tree.

(C)

Every full binary tree is also a complete binary tree.

(D)

No binary tree is both complete and full.

(E)

None of the above

Answer: (E)

Explanation:

A full binary tree (sometimes proper binary tree or 2-tree or strictly binary tree) is a tree in which every node other than the leaves has two children. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. A) is incorrect. For example, the following Binary tree is neither complete nor full

     12
   /  
  20
 /
30

B) is incorrect. The following binary tree is complete but not full

     12
   /   \\
  20    30
 /
30

C) is incorrect. Following Binary tree is full, but not complete

     12
   /   \\
  20    30
       /  \\  
      20   40

D) is incorrect. Following Binary tree is both complete and full

      12
    /   \\
   20    30
  /  \\  
 10   40

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