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2 votes
2 votes

Maximum number of keys a B-Tree of order 5 and height 4 can have ?

Note: An order P B-Tree can have at most P-1 keys in a node.

(A) 2500

(B) 3905

(C) 3124

(D) 4500

3 Answers

Best answer
4 votes
4 votes
root level has 4 keys for maximum----4

so there will be 5 pointers so 5 child nodes so no. of keys will be 20

so there will be 25 pointers so 25 child nodes so no.of keys 25*4=100

so there will be 125 pointers so 125 child nodes no.of keys 125*4=500

so there will be 625 pointers so 625 child nodes no. of keys 625*4=2500

 

so total 3124
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1 votes
1 votes
Answer is C)3124 as the max no of keys in order p B tree and have with min height h= (p^(h+1))-1=(5^(4+1))-1=3124
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0 votes
Order=p

Key n= p-1

Level 1/height 1 will have n

Level 2/height 2 will have n(n+1)

Level 3/height 3 will have n(n+1)^2......

Total keys n+n(n+1)+n(n+1)^2....

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