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Algorithm 1 exp(a, n): compute a" for integer a and n ≥ 0 if n = 0 then return 1 end if x if n is even then return xxx exp(a, floor (n/2)) else return a x x × x end if (a) Write a recurrence relation for the number of operations performed when the input size is n (we assume that the size of a does not matter for the complexity of integer multiplication). (b) What is the complexity of the algorithm?

Algorithm 1 exp(a, n): compute a" for integer a and n ≥ 0 if n = 0 then return 1 end if x if n is even then return xxx exp(a, floor (n/2)) else return a x x × x end if (a) Write a recurrence relation for the number of operations performed when the input size is n (we assume that the size of a does not matter for the complexity of integer multiplication). (b) What is the complexity of the algorithm?

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Algorithm 1 exp(a, n): compute a" for integer a and n ≥ 0 if n = 0 then return 1 end if x if n is even then return x x x exp(a, floor (n/2)) else return a Χχχχχ end if (a) Write a recurrence relation for the number of operations performed when the input size is n (we assume that the size of a does not matter for the complexity of integer multiplication). (b) What is the complexity of the algorithm?
Transcribed Image Text:Algorithm 1 exp(a, n): compute a" for integer a and n ≥ 0 if n = 0 then return 1 end if x if n is even then return x x x exp(a, floor (n/2)) else return a Χχχχχ end if (a) Write a recurrence relation for the number of operations performed when the input size is n (we assume that the size of a does not matter for the complexity of integer multiplication). (b) What is the complexity of the algorithm?
Expert Solution
Step 1: Explain the problem statement

A recursive is given in the problem statement and it is asked to 

  • create the recurrence relation for the given recursive function
  • Solve the recurrence relation to get the complexity

The function given is as follows:

public static int exp(int a, int n){
        if(n==0)
        return 1;

        int x = exp(a,(int)Math.floor(n/2));

        if(n % 2 == 0)
            return x * x;
        else
            return a * x * x;
    }
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