GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
169 views

The number of min heap trees are possible with 15 elements such that every leaf node must be greater than all non-leaf nodes of the tree are ________

asked in DS by Boss (8.6k points)   | 169 views

2 Answers

0 votes

Suppose consider 15 elements 1,2,3,4,....15.

It is min heap ,level by level elements are stored.Root is at 1st level.

1st level; 1

2nd level: 2,3

3rd level: 4,5,6,7

4th level: 8,9,10,11,12,13,14,15.

In the second level elements are nodes 2,3 occupies 2 ways.no matter because it satisfies the heap property.

In the 3rd level also same nodes are 4,5,6,7 can be arranged in 4! ways.

In the 4th level 8!

SO TOTAL NO OF TREES ARE 1!*2!*4!*8*=1935360

answered by Veteran (10.7k points)  
What about a heap like this:

1st level: 1

2nd level: 2 5

3rd level: 3 4 6 7

4th level: 8 9 10 11 12 13 14 15

This is also valid according to the question but the answer does not account for these type of heaps.
i miss it,but this type of problems construct every min heap tree construction is so difficult.

so i think nearest no of min neaps consideration is better.
0 votes
Ans should be 8!*7! max 8 values will be tere in leaf, there are 8 nodes they can be arrange in any way and 7 in non leaf they can be arrange in any way.
answered by Junior (711 points)  


Top Users Apr 2017
  1. akash.dinkar12

    3660 Points

  2. Divya Bharti

    2580 Points

  3. Deepthi_ts

    2040 Points

  4. rude

    1966 Points

  5. Tesla!

    1768 Points

  6. Debashish Deka

    1614 Points

  7. Shubham Sharma 2

    1610 Points

  8. Prashant.

    1492 Points

  9. Arjun

    1472 Points

  10. Arunav Khare

    1464 Points

Monthly Topper: Rs. 500 gift card

22,088 questions
28,063 answers
63,298 comments
24,173 users