Topic 10: Recursion Study Guide Understand base case and how to reduce problems

Question

Topic 10: Recursion Study Guide Understand base case and how to reduce problems to smaller subproblems Being able to read and write recursion code . . 1. Read the following code. What is fun0 actually doing? public int fun(int a, int b) if (b 0) return e; if(b % 2 == 0) return fun (ata, b/2); return fun (ata, b/2) a; 2. Implement the following power) method, where x is the base and n is the exponent. private static long power(int x, int n) long y - e; // base case return 1; return x; else if( /I recursion and local work else f y power(--(3) return y return x * y; Stretch question: why do we return y when n%2-0 and return x * y at the end of the method

Explanation / Answer

1)

fun() is computing the product of a and b. That is a *b.

If a=3 and b=2 , the function will ouput 6.

2)

private static long power(int x,int n)

{

long y=0;

if(n==0)
        return 1;
    else if(n==1)
        return x;
    else
    {
        y=power(x,n/2);
        y=y*y;
        if(n%2==0)
            return y;

    }
    return x*y;

}

Here

1) n==0

2) n==1

3) x

4) n/2

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