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…

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…

\(\mathcal{Description}\)   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…