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…

                                    Bracket Sequence Time Limit: 3000MS   Memory Limit: 65536KB   64bit IO Format: %lld & %llu [Submit]   [Go Back]   [Status] Description There is a sequence of brackets, which supports two kinds of operations.1. we c…

[#138 div 1 A. Bracket Sequence] [原题] A. Bracket Sequence time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output A bracket sequence is a string, containing only characters "(", ")"…

E. Correct Bracket Sequence Editor time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output Recently Polycarp started to develop a text editor that works only with correct bracket sequences (abbrev…

C. Replace To Make Regular Bracket Sequence 题目连接: http://www.codeforces.com/contest/612/problem/C Description You are given string s consists of opening and closing brackets of four kinds <>, {}, [], (). There are two types of brackets: opening and…

C. Longest Regular Bracket Sequence Time Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://codeforces.com/problemset/problem/5/C Description This is yet another problem dealing with regular bracket sequences. We should remind you that a bracket sequence…

There is a sequence of brackets, which supports two kinds of operations. we can choose a interval [l,r], and set all the elements range in this interval to left bracket or right bracket. we can reverse a interval, which means that for all the element…