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bigoh4

Language/Type: C++ algorithm analysis big-oh
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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 = 0; i < N; i++) {
    sum++;
}
for (int i = 100*N; i >= 0; i--) {
    sum++;
}
cout << sum << endl;
answer:
// b)
int sum = 0;
for (int i = 1; i < N - 2; i++) {
    for (int j = 0; j < N * 3; j += 2) {
        for (int k = 0; k < 1000; k++) {
            sum++;
        }
    }
}
cout << sum << endl;
answer:
// c)
Vector<int> v;
for (int i = 0; i < N; i++) {
    v.add(i);
}
while (!v.isEmpty()) {
    v.remove(0);
}
cout << "done!" << endl;
answer:
// d)
Set<int> set;
for (int i = 0; i < N/2; i++) {
    set.add(i);
}
Stack<int> stack;
for (int i = 0; i < N/2; i++) {
    set.remove(i);
    stack.push(i);
}

cout << "done!" << endl;
answer:
// e)
Queue<int> queue;
for (int i = 1; i <= N; i++) {
    queue.enqueue(i * i);
}
HashMap<int, int> map;
while (!queue.isEmpty()) {
    int k = queue.dequeue();
    map.put(k, N * N);
}
cout << "done!" << endl;
answer:

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