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18 March, 03:52

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.

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  1. 18 March, 05:23
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    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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