For each sample of code given below, indicate precisely how many times each line

Question

For each sample of code given below, indicate precisely how many times each line runs in terms of the variables given. Your answer will be in terms of n or some other variable or combination of variables. If the snippet of code is a method, you do not have to write the number of times the top line (the method declaration itself) is executed. Providing a detailed explanation would be greatly appreciated.

Q3.

for (int i=0; i<n; i++) {

for (int j=n; j>=i; j--)

cout << i << “,” << j <<endl;

}

Q4.

for (int i=0; i<n; i++) { //assume n is divisible by 2 => n = 2*k

for (j=n/2; j>i; j--)

sum = i+j;

}

Explanation / Answer

Q3
for (int i=0; i<n; i++) { =-======> Runs n times

for (int j=n; j>=i; j--)=======> Runs n, n-1, n-2....1

cout << i << “,” << j <<endl;

}
Inner loops runs: 1+ +2+3...+n-2+n-2 = n(n-1)/2 .

Q4.

for (int i=0; i<n; i++) { //assume n is divisible by 2 => n = 2*k ==========> Runs N times

for (j=n/2; j>i; j--)==========> Runs N/2 , N/2-1 , N/2- 2 , N/2-3 .........1

sum = i+j;

}

Total runs : n/2 + n/2 -1 + n/2-2+ .... + 1

=> n(n-1)/4

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