# CodeStepByStep ## bigoh5

Language/Type: C++ algorithm analysis big-oh

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; i++) { for (int j = 1; j <= 2 * N; j++) { sum++; } } cout << sum << endl;``` answer: ```// b) int sum = 0; for (int i = 1; i <= 100000; i++) { for (int j = 1; j <= i; j++) { for (int k = 1; k <= N; k++) { sum++; } } } for (int x = 1; x <= N; x += 2) { sum++; } cout << sum << endl;``` answer: ```// c) vector v; for (int i = 1; i <= N; i++) { v.insert(v.begin(), i); } unordered_set s; for (int k : v) { s.insert(k); } cout << "done!" << endl;``` answer: ```// d) queue q; for (int i = 1; i <= 2*N; i++) { q.push(i); } map map; while (!q.empty()) { int k = q.front(); q.pop(); map[k] = -k; } cout << "done!" << endl;``` answer: ```// e) unordered_map map; for (int i = 1; i <= N * N; i++) { map[i] = i*i; } unordered_set set; for (auto kv : map) { set.insert(auto.second); } cout << "done!" << endl;``` answer: