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    Big O - algorithm comparison

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    Suppose program A takes (2^n)/1000 units of time and program B takes 1000(n^2) units. For what values of n does program A take less time than program B.

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    Solution Preview

    Ta = 2^n/1000; Tb = 1000*(n^2)

    If Ta < Tb,

    2^n/1000 < 1000*(n^2)
    (2^n)/n^2 < 1,000,000
    Take log on both sides,

    n*log 2 - 2log n < 6

    n < (6 + 2logn)/log ...

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    This solution helps with a problem about algorithm comparison.