![1. Suppose that an array al] is a max-heap that contains the distinct integer keys 1, 2,.., N with N> 7. The key N must be in gl1] and the key N-1 must be in either al2) or al3) a. Give all possible positions for the key N-2 as a function of N. b. Repeat the same question for the key 2](http://img.homeworklib.com/questions/885750c0-c745-11eb-8b78-c9bf9e15c553.png?x-oss-process=image/resize,w_560)
Homework Answers
a.
The possible position of key N-2 if N> 7 is in either at level 1 or level 2.
At level 0, only N could be possible.
So the possible position of key N-2 is a[2],a[3],a[4],a[5],a[6],a[7] which is independent of N
All the red nodes in foll. diagram are possible position of key N-2.
b. The possible position of 2 is either the leaf node or the parent of last node if N is even and value of last node is 1.
Any other position is not possible because if no. of children is two, key of the node must be greater than 2.
So, if N is odd, possible position of key 2 is a[(N+1)/2],a[(N+1)/2 + 1], ......... a[N]
and if N is even, possible position of key 2 is a[N/2],a[N/2 + 1], ......... a[N].
Diagram of this is not possible to draw.
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