(b) You are given four numbers a,b,c,d. You want to sort them in increasing order. It is known that they are all different, and furthermore a

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(b) You are given four numbers a,b,c,d. You want to sort them in increasing order. It is known
that they are all different, and furthermore a <b and c<d. Only comparison-based sorting
is allowed.
i. Prove a worst-case lower bound of 3 on the number of comparisons needed to sort
the numbers.
ii. Give an algorithm, in the form of a decision tree, that sorts the numbers in the worst-
case optimal number of comparisons.
Transcribed Image Text:(b) You are given four numbers a,b,c,d. You want to sort them in increasing order. It is known that they are all different, and furthermore a <b and c<d. Only comparison-based sorting is allowed. i. Prove a worst-case lower bound of 3 on the number of comparisons needed to sort the numbers. ii. Give an algorithm, in the form of a decision tree, that sorts the numbers in the worst- case optimal number of comparisons.
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