You have an array of integers A1, A2, …, AN. The function F(P), where P is a subset of A, is defined as the XOR (represented by the symbol ⊕) of all the integers present in the subset. If P is empty, then F(P)=0.
Given an integer K, what is the maximum value of K ⊕ F(P), over all possible subsets P of A?
Read MoreChef loves to prepare delicious dishes. This time, Chef has decided to prepare a special dish for you, and needs to gather several apples to do so.
Chef has N apple trees in his home garden. Each tree has a certain (non-zero) number of apples on it. In order to create his dish, Chef wants to pluck every apple from every tree.
Chef has an unusual method of collecting apples. In a single minute, he can perform the following task:
Pick any subset of trees such that every tree in the subset has the same number of apples.
From each tree in the subset, pluck any number of apples, as long as the number of apples left on the tree equals the number of apples on a tree not in the subset.
If all trees have the same number of apples left, Chef can pluck all of the apples remaining in a single minute.
Chef does not want to keep you waiting, so wants to achieve this task in the minimum possible time. Can you tell him what the minimum time required is?
Read More现在我们的手头有 N 个软件，对于一个软件 i，它要占用 Wi 的磁盘空间，它的价值为 Vi。我们希望从中选择一些软件安装到一台磁盘容量为 M 计算机上，使得这些软件的价值尽可能大（即 Vi 的和最大）。
但是现在有个问题：软件之间存在依赖关系，即软件 i 只有在安装了软件 j（包括软件 j 的直接或间接依赖）的情况下才能正确工作（软件 i 依赖软件 j)。幸运的是，一个软件最多依赖另外一个软件。如果一个软件不能正常工作，那么它能够发挥的作用为 0。
我们现在知道了软件之间的依赖关系：软件 i 依赖软件 Di。现在请你设计出一种方案，安装价值尽量大的软件。一个软件只能被安装一次，如果一个软件没有依赖则 Di=0，这时只要这个软件安装了，它就能正常工作。
Read More杭州人称那些傻乎乎粘嗒嗒的人为 62（音：laoer）。
杭州交通管理局经常会扩充一些的士车牌照，新近出来一个好消息，以后上牌照，不再含有不吉利的数字了，这样一来，就可以消除个别的士司机和乘客的心理障碍，更安全地服务大众。
不吉利的数字为所有含有 4 或 62 的号码。例如：
62315 73418 88914
都属于不吉利号码。但是，61152 虽然含有 6 和 2，但不是 62 连号，所以不属于不吉利数字之列。
你的任务是，对于每次给出的一个牌照区间号，推断出交管局今次又要实际上给多少辆新的士车上牌照了。
Read MoreYou are given a function f which is defined as :
\[ f(N)=1^1*2^2*3^2*...*(N-1)^{N-1}*N^N \]
Your task is to find the value of \(\frac{f(N)}{f(r)*f(N-r)}\). As it will be a large number output it modulo \(M\).
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