Question

1.23 "The median of an ordered set is an element such that the number of elements less than the median is within one of the number that are greater, assuming no ties. a. Write an algorithm to find the median of three distinct integers a, b, and c. b. Describe D. the set of inputs for your algorithm. in light of the discussion in Sec- tion 1.4.3 following Example 1.9. c. How many comparisons does your algorithm do in the worst case? On the average? d. How many comparisons are necessary in the worst case to find the median of three numbers? Justify your answer.

Example 1.9:

Answer 1

a)

Algorithm->

median(a,b,c)

if a>b and a<c then return a

if a>c and a<b then return a

if b>a and b<c then return b

if b>c and b<a then return b

return c

b) Dn = {a,b,c} in any order

c) assuming two comparison in one statements, if c is median, it requires 8 comparisons

d) 3 comparison required in minimum

if (a > b)

    {

        if (b > c)

            return b;

        else if (a > c)

            return c;

        else

            return a;

    }

    else

    {

        // Decided a is not greater than b.

        if (a > c)

            return a;

        else if (b > c)

            return c;

        else

            return b;

    }