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TOTAL POINTS 6
1.
How many edges of this binary tree violate the min-heap property? In other words, for how many edges of the tree, the parent value is greater than the value of the child?
1 point
2.
This binary tree contains 13 nodes, and hence we have 13 subtrees here (rooted at each of 13 nodes). How many of the subtrees are complete?
1 point
3. Consider a complete binary tree represented by an array [19,14,28,15,16,7,27,15,21,21,5,2][19,14,28,15,16,7,27,15,21,21,5,2].
How many edges of this tree violate the max-heap property? In other words, for how many edges of the tree, the parent value is smaller than the value of the child?
1 point
4. Assume that a max-heap with 10^5105 elements is stored in a complete 5-ary tree. Approximately how many comparisons a call to {\tt Insert()}Insert() will make?
1 point
5. Assume that a max-heap with 10^6106 elements is stored in a complete 7-ary tree. Approximately how many comparisons a call to {\tt ExtractMax()}ExtractMax() will make?
1 point
6. Assume that we represent a complete dd-ary tree in an array A[1\dots n]A[1…n] (this is a 1-based array of size nn). What is the right formula for the indices of children of a node number ii?
1 point
{id+2,…,min{n,id+d+1}}
{(i−1)d+2,…,(i−1)d+d+1}
{(i−1)d+2,…,min{n,(i−1)d+d+1}}
{(i−1)d+1,…,min{n,(i−1)d+d}}
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