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Minimize the number of comparisons for finding minimum and maximum of a given set of numbers.

6 Answers

Given n numbers, the optimal number of comparison should be 3n/2 Pairwise compare all numbers = n/2 comparisons It is easy to see that the max, min lies among the n/2 elements which are greater, smaller respectively. Pairwise compare the n/2 greater elements = n/4 comparisons. Again pairwise compare the n/4 greater elements obtained in previous step = n/8 comparions. ... You get max(min) in n/4+n/8+...1 = n/2 comparisons. initial comparisons = n/2 comparisons to get max number = n/2 comparisons to get min number = n/2 Total = 3n/2

Here is matlab code according to the suggested algorithm : clear; clc; vec=[3,8,7,2,1,6,5,4]; [max12,min12]=max_min(vec(1),vec(2)); [max34,min34]=max_min(vec(3),vec(4)); [max56,min56]=max_min(vec(5),vec(6)); [max78,min78]=max_min(vec(7),vec(8)); [max1234,~]=max_min(max12,max34); [max5678,~]=max_min(max56,max78); [max12345678,~]=max_min(max1234,max5678); fprintf('max=%d\n',max12345678); % Find Min [~,min1234]=max_min(min12,min34); [~,min5678]=max_min(min56,min78); [~,min12345678]=max_min(min1234,min5678); fprintf('min=%d\n',min12345678);

More on the above analytic solution: The resulting sequence is geometric with missing first two terms, n + n/2. Sum of a geometric sequence n + n/2 + n/4 + ... + 1 = 2n So for the present sequence: sum = 2n - n - n/2 = n/2 Thus the minimum number of steps required for finding BOTH the minimum and maximum of the set of numeric values is 3n/2. However, to calculate only minimum or maximum, the minimum number of steps would be (n-1) by pairwise comparison.

What is the expected number of tosses required to achieve 2 heads in an unbiased coin?

5 Answers

Buffon's Needle Problem

2 Answers

Describe any one sorting algorithm in detail one puzzle regarding uniform distribution with two players where one players valuation of an item is twice that of others. explain new, delete keywords what is vega of an instrument?

2 Answers

Salary expectation and When I can join?

1 Answer

How to find a loop in a linked list?

1 Answer

The interviewer first asked me to briefly introduce myself...Then went on to my resume and told me to tell about one of my projects....Then i had like 3 coding questions ....i was asked to tell the algorithm and the pesudo code...Others was a simple check on the basics and then a few probability questions

1 Answer

Technology questions, market analysis etc.

1 Answer

If there consist of two pipes connected to a tank in which one pipe is used to inject water to the tank at the rate of 2L/hr and the other pipe is used to eject water at the rate of 3L/hr.when do the tank completely fill?

1 Answer

Describe in brief about your project? Some basic OOPS concepts.

1 Answer
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