logo CodeStepByStep logo

bigoh1

Language/Type: C++ algorithm analysis big-oh
Related Links:
Author: Marty Stepp (on 2016/06/16)

Give a tight bound of the nearest runtime complexity class for each of the following code fragments in Big-Oh notation, in terms of the variable N. In other words, write the code's growth rate as N grows. Write a simple expression that gives only a power of N using a caret ^ character for exponentiation, such as O(N^2) to represent O(N2) or O(log N) to represent O(log2 N). Do not write an exact calculation of the runtime such as O(2N3 + 4N + 14).

// a)
int sum = 0;
for (int i = 1; i <= N + 2; i++) {
    sum++;
}
for (int j = 1; j <= N * 2; j++) {
    sum += 5;
}   
cout << sum << endl;
answer:
// b)
int sum = 0;
for (int i = 1; i <= N - 5; i++) {
    for (int j = 1; j <= N - 5; j += 2) {
        sum++;
    }
}
cout << sum << endl;
answer:
// c)
int sum = N;
for (int i = 0; i < 1000000; i++) {
    for (int j = 1; j <= i; j++) {
        sum += N;
    }
    for (int j = 1; j <= i; j++) {
        sum += N;
    }
    for (int j = 1; j <= i; j++) {
        sum += N;
    }
}
cout << sum << endl;
answer:
// d)
Vector<int> list;
for (int i = 1; i <= N * N; i++) {
    for (int j = 1; j <= N; j++) {
        list.add(i + j);
    }
}

for (int i = 1; i <= 2 * N; i++) {
    list.remove(list.size() - 1);
}
cout << "done!" << endl;
answer:
// e)
HashSet<int> set1;
for (int i = 1; i <= N; i++) {
    set1.add(i);
}

Set<int> set2;
for (int i = 1; i <= N; i++) {
    set1.remove(i);
    set2.add(i + N);
}
cout << "done!" << endl;
answer:

You must log in before you can solve this problem.


Log In

Need help?

If you do not understand how to solve a problem or why your solution doesn't work, please contact your TA or instructor.
If something seems wrong with the site (errors, slow performance, incorrect problems/tests, etc.), please

Is there a problem? Contact a site administrator.

© Marty Stepp, all rights reserved.