Question

(b) Given a set S of integers, the range of S is defined as the difference between the largest and the smallest integers in S. Write an algorithm to find the range of S and analyze its run-time (use big-O) in terms of IS| for each of the following cases: i. S is a sorted array of integers. ii. S is an un-sorted array of integers.

Answer 1

(i)

Function findRange(S)

BEGIN

    // in a sorted set, the last element is the largest element

    largest = S[ S.length() ]

    // in a sorted set, the first element is the smallest element

    largest = S[ 1 ]

    range = largest - smallest

    return range

END

The Time Complexity of algorithm is O(1) as it takes constant time to subtract two variables.

(ii)

Function findRange(S)

BEGIN

    // store the largest element

    largest = -infinity

    // store the smallest element

    largest = +infinity

    for i = 1 to S.length()

    BEGIN

         If S[i] > largest

         BEGIN

        

             largest = S[i]

         END

         If S[i] < smallest

         BEGIN

        

             smallest = S[i]

         END

    END

    range = largest - smallest

    return range

END

The Time Complexity of algorithm is O(n) as we have to traverse the complete array of size n.