题目大意: \(n(n\le60)\)个数\(A_{1\sim n}\),将这些数随机打乱,问最后构成的数列满足对于所有的\(2\le i\le n-1\),都有\(2A_i\le A_{i-1}+A_{i+1}\)的概率. 思路: 显然题目要求的是构成下凸函数的概率. 将所有数排序,考虑最小值在中间,往两遍加数. \(f[i][j][k][l]\)表示左边第一个数是\(i\),左边第二个数是\(j\),右边第一个数是\(k\),右边第二个数是\(l\)的方案数.对于每个状态,枚举新增的数放左边…

Beautiful Sequence 给定一些数(可能相同),将它们随机打乱后构成凹函数,求概率 .N<=60 . 首先,这种题求概率事实上就是求方案.所以现在要求的是用这些数构成凹函数的方案数. 依稀记得上次的一道考试题,只是把凹函数变成了一个具有特殊性质的单调序列而已.这道题也是一样,由于它不关心数的位置,所以把数排序以后,可以统计把当前数插入凹函数的方案. exp1:与数的位置无关的计数题可以考虑排序. 用\(f[i][j][k][l]\)表示凹函数最左边的两个点,最右边的两个点.那么新来…

链接: https://codeforces.com/contest/1265/problem/D 题意: An integer sequence is called beautiful if the difference between any two consecutive numbers is equal to 1. More formally, a sequence s1,s2,-,sn is beautiful if |si−si+1|=1 for all 1≤i≤n−1. Trans…

Description Consider a positive integer sequence a[1], ..., a[n] (n ≥ 3). If for every 2 ≤ i ≤ n-1, a[i-1] + a[i+1] ≥ 2 × a[i] holds, then we say this sequence is beautiful. Now you have a positive integer sequence b[1], ..., b[n]. Please calculate t…

\(\mathcal{Description}\)   Link.   求长度为 \(n\),值域为 \([1,m]\) 的整数序列 \(\lang a_n\rang\) 的个数,满足 \(\not\exist i\in[1,n),~\max_{j=1}^i\{a_j\}=\min_{j=i+1}^n\{a_j\}\),答案对大素数 \(p\) 取模.   \(n\le400\),\(m\le10^8\). \(\mathcal{Solution}\)   前几天刚胡了一个 "DP and DP…

You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct. Find any beautiful seq…

D. Beautiful Pairs of Numbers time limit per test 3 seconds memory limit per test 256 megabytes input standard input output standard output The sequence of integer pairs (a1, b1), (a2, b2), ..., (ak, bk) is beautiful, if the following statements are…

Set of Strings time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings i…

You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct. Find any beautiful seq…

A. Set of Strings Time Limit: 20 Sec  Memory Limit: 256 MB 题目连接 http://codeforces.com/contest/544/problem/A Description You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is st…

感觉今天早上虽然没有睡醒但是效率还是挺高的... Pas和C++换着写... 544A. Set of Strings   You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q(formally, s1 + s2 + ... + sk = q) and the first cha…

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u Description You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q(formally, s1 + s2 + ...…

#1595 : Numbers 时间限制:8000ms 单点时限:1000ms 内存限制:256MB 描述 给定n个整数常数c[1], c[2], ..., c[n]和一个整数k.现在需要给2k个整数变量x[1], x[2], ..., x[k], y[1], y[2], ..., y[k]赋值,满足 (1)对于所有1 ≤ i ≤ k,都有x[i] ≤ y[i]. (2)对于所有1 ≤ i ≤ n,都存在至少一个j (1 ≤ j ≤ k),使得x[j] ≤ c[i] ≤ y[j]. 求出S=(y…

Beautiful Sequence Beautiful Mirrors Beautiful Bracket Sequence (easy version) Beautiful Sequence \[ Time Limit: 1000 ms\quad Memory Limit: 256 MB \] 首先我们可以考虑到 \(0\) 只能 和 \(1\) 放在一起.\(3\) 只能和 \(2\) 放在一起,那么我们想办法先把 \(0\) 和 \(3\) 凑出来,最后就剩下 \(1\) 和 \(2\)…

Beautiful Regional Contest 题意 题解 代码 Beautiful Sequence 题意 题解 代码 一个思路不够清晰的代码 Beautiful Mirrors with queries 题意 题解 代码 Beautiful Regional Contest 题目链接 http://codeforces.com/contest/1264/problem/A 题意 给出区域赛中 N 支队伍做出的题数,在一定规则下发奖时,金银铜牌奖牌数总和的最大值. 要求: 合法方案中每种…

A. Beautiful String (暴力) 题目链接 题目大意: 给定一个字符串,只有 \(?a\ b\ c\ ?\) ,问是否存在一种将所有的 \(?\) 替换成 \(a\ b\ c\) ,使得任意相邻的字符不同的方法. 大致思路: 其实可以发现问号都可以通过枚举使得其合法,若出现不合法必然除去问好已经不合法,暴力枚举即可. 代码: 点击展开代码 #include<bits/stdc++.h> using namespace std; const int N=1e5+10; char…

我们枚举每两个字符的空档,统计一个空档左边有 \(l\) 个左括号, 右边有 \(r\) 个右括号,左边有 \(u\) 个问号,右边有 \(v\) 个问号. 则对于 \(p\) 的答案 \(ans_p\) 有: \[ans_p=\sum\limits_{i=0}^{u}(l+i)\dbinom{u}{i}\dbinom{v}{l+i-r} \] 解释: 对于每个左边的问号枚举有几个变成左括号,则左边有 \(l+i\) 个左括号,方案数为 \(C_{u}^{i}\) ,右边的问号显然有 \(l+i…

考虑\(D1\)的\(O(n^2)\),我们直接进行组合处理. 考虑在\(p\)这个位置,左边有\(l\)个(,右边有\(r\)个),左边有\(l\)个问号,右边有\(r\)个问号. 这个位置的贡献为: \(\sum_{i = 0} ^ x (l+i)\binom{x}{i}\binom{y}{l + i - r}\) 考虑我们拆项. \(l\sum_{i = 0} ^ x\binom{x}{i}\binom{y}{l + i - r} + \sum_{i = 0} ^ x i\binom{x}…

考虑在一个确定的括号序列中,我们可以枚举中间位置,按左右最长延伸出去的答案计算. 我们很自然的思考,我们直接维护左右两边,在删除一些字符后能够延伸的最长长度. 我们设\(f_{i,j}\)为\(i\)点合法删除向左延伸的最大长度. \( f_{i,j} = \left\{ \begin{aligned} &f_{i - 1,j} (a[i] = ')'\ )\\ &f_{i - 1,j - 1}(a[i] = ')'\ )\\ &f_{i - 1,j} + f_{i - 1 ,j…

Codeforces 题面传送门 & 洛谷题面传送门 首先对于这样的题目,我们应先考虑如何计算一个括号序列 \(s\) 的权值.一件非常显然的事情是,在深度最深的.是原括号序列的子序列的括号序列中,必定存在一个满足前面只由一段左括号,后面只由一段右括号组成,因此我们考虑枚举这中间位置在原括号序列中对应哪个位置,那么假设这个断点位于 \(i\) 和 \(i+1\) 之间,我们设 \(i\) 及之前有 \(x\) 个左括号,\(i+1\) 及之后有 \(y\)​​ 个右括号,那么显然以这个位置为端点…

题目链接: Beauty of Sequence Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 813    Accepted Submission(s): 379 Problem Description Sequence is beautiful and the beauty of an integer sequence is def…

B. Beautiful Paintings time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output There are n pictures delivered for the new exhibition. The i-th painting has beauty ai. We know that a visitor becomes…

I - Beautiful Spacing Time Limit:8000MS     Memory Limit:65536KB     64bit IO Format:%lld & %llu Submit cid=57803#status//I/0" class="ui-button ui-widget ui-state-default ui-corner-all ui-button-text-only" style="font-family:Verdan…

Difference Is Beautiful Time Limit:5000MS     Memory Limit:65536KB     64bit IO Format:%lld & %llu Submit Status Practice POJ 3419 Description Mr. Flower's business is growing much faster than originally planned. He has now become the CEO of a world-…

Beautiful Subarrays time limit per test 3 seconds memory limit per test 512 megabytes input standard input output standard output One day, ZS the Coder wrote down an array of integers a with elements a1,  a2,  ...,  an. A subarray of the array a is a…

There are n pictures delivered for the new exhibition. The i-th painting has beauty ai. We know that a visitor becomes happy every time he passes from a painting to a more beautiful one. We are allowed to arranged pictures in any order. What is the m…

time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output There are n pictures delivered for the new exhibition. The i-th painting has beauty ai. We know that a visitor becomes happy every time he pa…

题目链接: http://acm.hdu.edu.cn/showproblem.php?pid=5496 Beauty of Sequence Problem Description Sequence is beautiful and the beauty of an integer sequence is defined as follows: removes all but the first element from every consecutive group of equivalen…

E. Beautiful Subarrays 题目连接: http://www.codeforces.com/contest/665/problem/E Description One day, ZS the Coder wrote down an array of integers a with elements a1,  a2,  ...,  an. A subarray of the array a is a sequence al,  al  +  1,  ...,  ar for so…

B. Beautiful Paintings 题目连接: http://www.codeforces.com/contest/651/problem/B Description There are n pictures delivered for the new exhibition. The i-th painting has beauty ai. We know that a visitor becomes happy every time he passes from a painting…