Question

Write a Recursive Function Algorithm to find the terms of following recurrence relation.

t(1)=3

t(k)=2×t(k-1)-5 (n>1).
and (ii) If you call z←t(4) in a program then what value the program will use for z?   

Answer 1

Algorithm:

Algorithm Recursive(n):
        
        if n = 1
        then return 3 
        
        else x = Recursive(n - 1)
             x = (2 * x) - 5    
        
        return x 
        
        endif

Trace of algorithm for t(4)

Manual trace of t(4):

Below is the C language code of this algorithm:

#include <stdio.h>

int Recursive(int n){
   int x;
   if(n == 1){
       return 3;
   }
    else{
        x =  Recursive(n -1);
        x = (2*x) - 5;
    }
    return x;

}


int main()
{
    int z = Recursive(4);
    printf("ans: %d \n", z);
    return 0;
}