GATE | GATE-CS-2015 (Set 3) | Question 65

Consider the following array of elements. 〈89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100〉. The minimum number of interchanges needed to convert it into a max-heap is
(A) 4
(B) 5
(C) 2
(D) 3


Answer: (D)

Explanation: 〈89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100〉

           89
      /         \
     19          50
    /  \        /  \  
  17    12     15    2
 /  \   / \   /  \
5   7  11  6  9  100

Minimum number of swaps required to convert above tree 
to Max heap is 3. Below are 3 swap operations.
Swap 100 with 15
Swap 100 with 50
Swap 100 with 89 

           100
      /         \
     19          89
    /  \        /  \  
  17    12     50    5 
 /  \   / \   /  \
7   11  6  9  2   15

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