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bigoh9

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++) {
    for (int j = 0; j < N; j++) {
        sum++;
    }
    for (int j = 1; j < N + 5; j++) {
        for (int k = 1; k < 99999; k++) {
            sum++;
        }
    }
}
cout << sum << endl;
answer:
// b)
Stack<int> stack;
Set<int> set;
for (int i = 0; i < N; i++) {
    stack.push(N);
    set.add(N);
}
while (!stack.isEmpty()) {
    set.remove(stack.pop());
}
cout << "done!" << endl;
answer:
// c)
Map<int, int> map;
for (int i = 0; i < N; i++) {
    for (int j = 4; j <= 2*N + 1; j++) {
        map.put(i, j);
    }
}
Queue<int> queue;
for (int k : map) {
    queue.enqueue(k);
}
cout << "done!" << endl;
answer:
// d)
Vector<int> vector;
HashSet<int> hashset;
for (int i = 4; i <= N + 7; i++) {
    hashset.add(i);
}
for (int num : hashset) {
    vector.add(num);
}
while (!vector.isEmpty()) {
    vector.remove(0);
}
cout << "done!" << endl;
answer:

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