Discussion
The minimum number of interchanges needed to convert the array 89,19,40,17,12,10,2,5,7,11,6,9,70 into a heap with maximum element at the root is
Answer: B
Correct answer: 2
Build the max-heap bottom-up. Numbering the array from 1:
1:89 2:19 3:40 4:17 5:12 6:10 7:2 8:5 9:7 10:11 11:6 12:9 13:70
- Node 6 holds 10 with children 9 and 70 - swap with 70.
- Nodes 5 and 4 are already correct (12 over 11 and 6; 17 over 5 and 7).
- Node 3 holds 40 with children 70 and 2 - swap. The 40 that sinks to node 6 still beats its children, 9 and 10.
- Node 2 (19 over 17 and 12) and the root (89 over 19 and 70) need nothing.
Two interchanges suffice, so the answer is 2.
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