虽然做起来有一点裸……但是就是想不到啊…… 首先令 $d_i=p_i\oplus p_{i-1}$,那么 $d_i$ 都是 $S$ 中的数,$a_i=d_i\oplus d_{i-1}\oplus \cdots\oplus d_2$.也就是每个数都能被表示成 $S$ 的某个子集的异或和. 要用 $S$ 表示出 $1$ 到 $2^x-1$ 的所有数(不用考虑 $0$,因为每个数是可以重复用的,可以 $S_i\oplus S_i=0$).怎么求出最大的 $x$? 其实就是建出线性基,然后最小的没有数…

题目描述:输入一个大小为\(n\)的正整数集合\(S\),求最大的\(x\),使得能构造一个\(0\)到\(2^x-1\)的排列\(p\),满足\(p_i\oplus p_{i+1}\in S\) 数据范围:\(n,S_i\le 2^{18}\) 什么?NTF在很多年前就把这东西给切了? 首先要把\(S\)缩成一个大小为\(x\)的线性无关组,而且每个数\(<2^x\),这样就可以构造出\(p\)了.(之后再说) 直接丢进线性基里就可以了吗?不行,应该是把\(<2^x\)的数全部加进去之后,看…

题意:给定集合,求一个最大的x,使得存在一个0 ~ 2x - 1的排列,满足每相邻的两个数的异或值都在S中出现过.Si <= 2e5 解:若有a,b,c,令S1 = a ^ b, S2 = b ^ c,则有a ^ c = S1 ^ S2 因为有0存在,所以每个数都能表示成它到0路径上的所有间隔的异或和,也就是每个数都能被表示出来.我们用线性基来判断. 找到最大的x之后,我们可以发现,线性基中x个数的2x种选法一一对应这2x个数.于是直接采用格雷码来找这个排列,每加一位,就在x个数中添加 / 删除…

codeforces 思路 我顺着图论的标签点进去的,却没想到-- 可以发现排列内每一个数都是集合里的数异或出来的. 考虑答案的上界是多少.如果能用小于\(2^k\)的数构造出\([0,2^k-1]\)内所有的数,那么答案就对这个\(k\)取\(\max\).很显然这一定是上界. 考虑能不能构造出一组解.把\([1,2^k-1]\)的数拎出来插入线性基里得到一组极大线性无关组,那么显然它的\(size\)就是\(k\).由于它线性无关,所以任意选取一个子集得到的异或和都不会相同,所以考虑把\(0…

目录 Codeforces Round #558 (Div. 2) 题解 A Eating Soup B Cat Party C Power Transmission D Mysterious Code E Magical Permutation Codeforces Round #558 (Div. 2) 题解 A Eating Soup 分类讨论一下 \(m\) 个断点最多可以将环分成 \(m\) 段,而剩下 \(n-m\) 个点最多可以成为 \(n-m\) 段,取个 \(\min\) 即可…

The set [1,2,3,-,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…

Given a string s, return all the palindromic permutations (without duplicates) of it. Return an empty list if no palindromic permutation could be form. For example: Given s = "aabb", return ["abba", "baab"]. Given s = "a…

Given a string, determine if a permutation of the string could form a palindrome. For example,"code" -> False, "aab" -> True, "carerac" -> True. Hint: Consider the palindromes of odd vs even length. What difference d…

The set [1,2,3,…,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). The replaceme…

The set [1,2,3,-,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…

这些天闲来无事,就整理了一些类库.jQuery插件和自定义控件.今天和大家分享下Magical平台类库代码. 下图为整个解决方案图.MagicalPlatForm里面定义的是众多的Layer层:Magical里面定义的是基本类库和操作类,以及一些自定义的控件:MainFramework里面存放的是该项目的基类库和操作类库:MainProject里面存放的是主项目,这里是WinForm项目NoteSystem:TestProject里面存放的是测试用和实验用的项目:然后部署里存放的是用于部署的Wi…

UVA - 11525 Permutation 题意:输出1~n的所有排列,字典序大小第∑k1Si∗(K−i)!个 学了好多知识 1.康托展开 X=a[n]*(n-1)!+a[n-1]*(n-2)!+...+a[i]*(i-1)!+...+a[1]*0! 其中a[i]为第i位是i往右中的数里 第几大的-1(比他小的有几个). 其实直接想也可以,有点类似数位DP的思想,a[n]*(n-1)!也就是a[n]个n-1的全排列,都比他小 一些例子 http://www.cnblogs.com/hxsyl…

For research purpose, I've read a lot materials on permutation test issue. Here is a summary. Should be useful. Still, thanks for contributors online. P value calculation Because the actual value is one of those permutations, I would like to change t…

(M) Permutations (M) Permutations II (M) Permutation Sequence (M) Palindrome Permutation II…

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). The replaceme…

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). The replaceme…

题目链接:https://leetcode.com/submissions/detail/55876321/ 自己的做法,30个测试用例通过了29例,终究还是有一个系列类型的是无法通过的,因为自己妄想在permutation的代码上,通过排序来进行.然而,每一次同第一个元素交换位置之后,进入了递归,此时数组nums并不是有序的!!! 来看看自己的这段代码,谨记教训,然后还是去看看大神们的思路吧! class Solution { public: vector<vector<int>>…

Magical Forest Time Limit: 24000/12000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 724    Accepted Submission(s): 343 Problem Description There is a forest can be seen as N * M grid. In this forest, there is so…

B. New Year Permutation time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output User ainta has a permutation p1, p2, ..., pn. As the New Year is coming, he wants to make his permutation as pretty…

来源:Public Library of Bioinformatics 显著性检验通常可以告诉我们一个观测值是否是有效的,例如检测两组样本均值差异的假设检验可以告诉我们这两组样本的均值是否相等(或者那个均值更大).我们在实验中经常会因为各种问题(时间.经费.人力.物力)得到一些小样本结果,如果我们想知道这些小样本结果的总体是什么样子的,就需要用到置换检验. Permutation test 置换检验是Fisher于20世纪30年代提出的一种基于大量计算(computationally inten…

2014多校7最水的题   Magical Forest Magical Forest Time Limit: 24000/12000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others) Total Submission(s): 253    Accepted Submission(s): 120 Problem Description    There is a forest can be seen as N * M…

4271: Love Me, Love My Permutation Description Given a permutation of n: a[0], a[1] ... a[n-1], ( its elements range from 0 to n-1, For example: n=4, one of the permutation is 2310) we define the swap operation as: choose two number i, j ( 0 <= i <…

Next Permutation Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending orde…

The set [1,2,3,…,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). The replaceme…

题目: The set [1,2,3,…,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order, We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" &q…

C16H:Magical Balls 总时间限制:  1000ms 内存限制:  262144kB 描述 Wenwen has a magical ball. When put on an infinite plane, it will keep duplicating itself forever. Initially, Wenwen puts the ball on the location (x0, y0) of the plane. Then the ball starts to dup…

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). The replaceme…

The set [1,2,3,…,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…