Question

I am getting closer to debunking this recursive mystery, there is only one thing left that I can not trace in this line of the code, and that is the final return value wich is 243 if i call rec() passing it the value 5. this should be the trace:

n: 4 *3: 12
n: 3 *3: 9
n: 2 *3: 6
n: 1 *3: 3
n: 0 *3: 0
n: 1 *3: 3

result: 243

Correct? how does it get the result of 243?

int rec(int n)
{
if (n == 0)
    return 1;


return 3 * rec(n-1);
}

Answer 1

Your function computes : 3^n.

The number 3 is multiplied with the result of the n-1 calls.

f(n) = 3 * f(n-1);

f(0) = 1;

f(1) = 3 * f(0) = 3 * 1 = 3;

f(2) = 3 * f(1) = 3 * 3 = 9;

f(3) = 3 * f(2) = 3 * 3 * f(1) = 3 * 3 * 3 = 27

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.
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f(5) = 3 * 3 * 3 *3 * 3 = 243