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  • Empire Strikes Back(素数的理解)

    In a far away galaxy there is war again. The treacherous Republic made k precision strikes of power ai on the Empire possessions. To cope with the republican threat, the Supreme Council decided to deal a decisive blow to the enemy forces.

    To successfully complete the conflict, the confrontation balance after the blow should be a positive integer. The balance of confrontation is a number that looks like , where p = n! (n is the power of the Imperial strike), . After many years of war the Empire's resources are low. So to reduce the costs, n should be a minimum positive integer that is approved by the commanders.

    Help the Empire, find the minimum positive integer n, where the described fraction is a positive integer.

    Input

    The first line contains integer k (1 ≤ k ≤ 106). The second line contains k integers a1, a2, ..., ak (1 ≤ ai ≤ 107).

    Output

    Print the minimum positive integer n, needed for the Empire to win.

    Please, do not use the %lld to read or write 64-but integers in С++. It is preferred to use the cin, cout streams or the %I64dspecificator.

    题意就是: 给定k个数字,求最小的正整数n,使得“n的阶乘”是“这k个数字的阶乘的积”的倍数。

    这个题明显是可以二分的,然后就是素数p在n的阶乘中出现的次数,就是: n/p+n/p^2......,。 现在我们遇到的问题就是如何求符合情况的n

    然后二分答案就行了。我们现在知道的就是阶乘相乘,就相当于他们的指数相加,就是这个东西,然后我们用一个查分的数组弄一下。

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  • 原文地址:https://www.cnblogs.com/Heilce/p/6556177.html
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