Multiplication Made Simple

Computer Science Level 3

Chris wrote a multiplication function which he believes is the next big thing.

def mult(a,b):
    if b == 0:
        return 0
    return a + mult(a,b-1)

Which of the options best describes the domain of $a$ and $b$ respectively, such that the above function works as intended?

Real numbers; Integers Real numbers; Real numbers Real numbers; Non-negative integers Non-negative integers; Integers Integers; Integers Positive integers; Non-negative integers Real numbers; Positive integers Integers; Non-negative integers

2 solutions

Jaydee Lucero
Jul 13, 2016

The given function is a recursive function, with $b$ decremented by $1$ at each loop. For the function to work properly, $b$ must end with $0$ which is a nonnegative integer, which implies that $b$ must be a nonnegative integer . Otherwise, the function will never reach $b=0$ and hence will create an infinite loop.

On the other hand, $a$ is not affected by any operation contained in the function. Hence, we can say that $a$ must be a real number .

展豪張
Jul 12, 2016

Intuitively this programme is to break $a\times b$ into $a+a+\cdots+a$ . Clearly this works only for positive $b$ and $0$ (case $0$ is handled by the if statement).
The answer is: $a$ is real number, $b$ is non-negative integer.

Multiplication Made Simple

2 solutions

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