GATE CS 2014 Set 1 — Question 49
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Question
The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is _________________.
Correct answer
147.1 to 148.1
Solution
To find the minimum and maximum of elements using the minimum number of comparisons, the tournament method is used:
For even , this simplifies to .For :
Comparisons = .
1.Compare elements in pairs. This takes comparisons.
2.The winners of these pairs are candidates for the maximum, and the losers are candidates for the minimum.
3.Find the maximum among the winners. This takes comparisons.
4.Find the minimum among the losers. This takes comparisons.
Total comparisons = .For even , this simplifies to .For :
Comparisons = .
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