Code samples on asymptotic complexity
For each of the following C++ code segments using a for loop, you will need to be able to evaluate the
asymptotic complexity, we can assume that each cout statement will have a constant run time, i.e. O(1)
1. for (int i = 0; i < n; i ++)
cout << " H e ll o Wo rl d " << endl;
Solution:
Pn−1
i=0 1 = O(n)
2. for (int i = 0; i < n * n; i ++)
cout << " H e ll o Wo rl d " << endl;
Solution:
Pn2
−1
i=0 1 = O(n2)
3. for (int i = 0; i < n; i ++)
for (int j = 0; j < n; j ++)
cout << " H e ll o Wo rl d " << endl;
Solution:
Pn−1
i=0 Pn−1
j=0 1=Pn−1
i=0 n=O(n2)
4. for (int i = 0; i < n; i ++)
for (int j = 0; j < n * n; j ++)
cout << " H e ll o Wo rl d " << endl;
Solution:
Pn−1
i=0 Pn2
j=0 1=Pn−1
i=0 n2=O(n3)
5. for (int i = 0; i < n; i ++)
for (int j = 0; j < i; j ++)
cout << " H e ll o Wo rl d " << endl;
Solution: Uses Gauss’s formula Pn
i=1 i=n(n+1)
2
Pn−1
i=0 Pi
j=0 1=Pn−1
i=0 i=(n−1)(n−1+1)
2=n2
−n
2=O(n2)
6. for (int i = n; i > 0; i = i / 2)
cout << " H e ll o Wo rl d " << endl;
Solution:
This is literally the definition of log2nso O(log n)
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