C programming

Question

Consider the following program fragment:

int d = 0;
int i,j,k;
for(i=1; i<31; ++i)
        for(j=1; j<31; ++j)
	        for(k=1; k<31; ++k)
		        if(((i+j+k)%3) == 0)
		                d=d+1;
printf("%d",d);

The number of additions performed by the above program fragment is?

a. 27,000

b. 27,000 x 3

c. 27,000 x 3 + 9,000

d. 9,930 + 2,700 x 3

Comments

is it option C?

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answer is d. i dont know how

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We are checking the if condition every time, means the number of times the loop is executed=30*30*30=27,000. Inside the if condition two addition operation is performed. So, total of 27,000*2 times.Now for every loop iteration we are doing (++i or ++j or ++k) a single addition operation which is 27,000 times. So till now in total 3*27,000 addition operations performed.oop will execute 30x30x30 =27000 times but since the condition is for multiples of 3  so
value of d incremented for (i+j+k) =3,6,9......etc.
i.e  for i=1, j=1,k=1,4,7,10...28(10 times) .
similarly for i= 1 , j=2 ,k=3,6,9...29(10 times)  so in general for i=1 there will be 30*10 =300 such combinations for each i
and in total (i=1 to 30 )  =30*30 *10=9000.

So, the final answer will be 27,000*3+9000.

Answer 1

9000 is the correct answer.