# GATE | GATE-CS-2016 (Set 2) | Question 21

Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is ________

[This Question was originally a Fill-in-the-blanks Question]

(A) 15
(B) 16
(C) 31
(D) 32

Explanation: It would be node number 31 for given distance 4.

For example if we consider at distance 2, below highlighted node G can be the farthest node at position 7.

```            A
/    \
B       C
/ \     / \
D   E   F   G
```

Alternative Solution :
t is the n-th vertex in this BFS traversal at distance four from the root. So height of tree is 4.
Max number of nodes = 2^{h+1} − 1 = 2^{5} − 1 = 31
At distance four, last node is 31. option (C)

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