Algorithm design technique

Question

Design a recursive algorithm for computing 2^n for any non-negative integer n by the formula 2^n = 2^(n-1) + 2^(n-1). Prerequisites : There must be an addition operation perform

int computepowerOfTwo(int power) {
    if(power == 1) 
        return 1;
    else 
        return (2*computepowerOfTwo(power-1))  + (2*computepowerOfTwo(power-1)) 
}

When I supply power as 3 initially it returns 16

Answer 1

As the other answer points out 2^1 is 2 , not 1 .

... but your code should actually stop at 0 instead:

if(power == 0) 
    return 1;

This is a good opportunity to learn the value of unit testing. A simple test case of the following...

for i in range(0, 11):                                                       
    assert computepowerOfTwo(i) == 2 ** i  

...would show you that (1) you didn't handle the case of 0 and (2) your answer for 2^1 was wrong.

Answer 2

Errors in your code:-

1. if(power == 1) you should return 2^1 which is 2 .
2. in else part what you are returning is equivalent to 2*2^(power-1) + 2*2^(power-1) which will result 2^(n+1) which is wrong, so you should just return 2*2^(power-1)

According to your question your function should be as follow:-

int computepowerOfTwo(int power) {
    if(power == 0) 
        return 1;
    else 
        return computepowerOfTwo(power-1) + computepowerOfTwo(power-1);
}