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

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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.

1) Rate your knowledge in C. 2) what do your friends think about you?

1 Answer

2. Are you ready to work in different job profile as you have scientific writing experience?

1 Answer

1. Are you ready to work in shifts? which will be 6 am to 2:30 pm or 2:30 pm to 11 pm. Shifts will be decided by your manager and it will be fixed.

1 Answer

You will have to deal with authors query and will have to interact with them. Are you ready?

1 Answer

To run them through my CV

1 Answer

Tell about yourself, parts of speech, why you want to join publishing industry

1. Describe Yourself. 2. How do you feel about working in night shifts and weekends? 3. What are your expectations?

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