Suppose that a computer can run an algorithm on a problem of size 1,024 in time t. We do not know the complexity of the algorithm. We note that when we run the same algorithm on a computer 8 times faster, in the same time t, we can solve a problem of size 8,192. We also note that when we run the same algorithm on a computer 8 times slower, in the same time t, we can solve a problem of size 128.

Time Complexity of Problem - O(n)

Explanation:

When n= 1024 time taken is t. on a particular computer.

When computer is 8 times faster in same time t , n can be equal to 8192. It means on increasing processing speed input grows linearly.

When computer is 8 times slow then with same time t , n will be 128 which is (1/8)th time 1024.

It means with increase in processing speed by x factor time taken will decrease by (1/x) factor. Or input size can be increased by x times. This signifies that time taken by program grows linearly with input size n. Therefore time complexity of problem will be O(n).

If we double the speed of original machine then we can solve problems of size 2n in time t.

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