can someone please explain this c++ behaviour

November 5, 2023

i am getting wrong answer with :

int N = 6;
int r = 3;
long result = 1;
for(int i=1;i<=r;++i){
   result *= (N-r+i)/(i);
}

output: 16

But this one is giving the correct answer:

for(int i=1;i<=r;++i){
        result *= N-r+i;
        result /= i;
}

output: 20

please explain the behaviour

>Solution :

The first code snipped you are multiplying the current value of result by ((N-r+i)/(i)). Which is equal to saying result = result * ((N-r+i)/(i));.

In the second code snipped you are multiplying the current value of result by (N-r+i) then after the value of result gets updated. You then take the updated result and then dividing it by i. You are performing the operation result = (result * (N-r+i)) / i;

So in the first code snipped you are updating result once and in the second code snipped you are updating result twice.