C. DZY Loves Fibonacci Numbers time limit per test 4 seconds memory limit per test 256 megabytes input standard input output standard output In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation F1 = 1; F2 …

我这种maintain写法好zz.考试时获得了40pts的RE好成绩 In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation F1 = 1; F2 = 1; Fn = Fn - 1 + Fn - 2 (n > 2). DZY loves Fibonacci numbers very much. Today DZY gives you an array con…

有两个性质需要知道: $1.$ 对于任意的 $f[i]=f[i-1]+f[i-2]$ 的数列,都有 $f[i]=fib[i-2]\times f[1]+fib[i-1]\times f[2]$ 其中 $fib[i]$ 为第 $i$ 项斐波那契数列. $2$. 对于任意满足上述条件的数列,都有 $\sum_{i=1}^{n}f[i]=f[n+2]-f[2]$ $3.$ 任意两断满足上述条件的数列每一项依次叠加,依然满足 $g[i]=g[i-1]+g[i-2]$,且上述两个性质都满足. $4.$ 任…

「CF446C」 DZY Loves Fibonacci Numbers 这里提供一种优美的根号分治做法. 首先,我们考虑一种不太一样的暴力.对于一个区间加斐波那契数的操作 \([a,b]\),以及一个区间求和的操作 \([p,q]\),仅需预处理斐波那契数列前缀和,我们就可以在 \(O(1)\) 的时间内算出 \([a,b]\) 对 \([p,q]\) 的贡献. 这样的复杂度为 \(O(n^2)\). 再考虑传统暴力:对于一个区间加斐波那契数的操作 \([a,b]\),直接将其作用到原数列 \…

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation F1 = 1; F2 = 1; Fn = Fn - 1 + Fn - 2 (n > 2). DZY loves Fibonacci numbers very much. Today DZY gives you an array consisting of n integers: a1, a2, ...,…

C. DZY Loves Fibonacci Numbers time limit per test 4 seconds memory limit per test 256 megabytes input standard input output standard output In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation F1 = 1; F2 …

參考:http://www.cnblogs.com/chanme/p/3843859.html 然后我看到在别人的AC的方法里还有这么一种神方法,他预先设定了一个阈值K,当当前的更新操作数j<K的时候,它就用一个类似于树状数组段更的方法,用一个 d数组去存内容,譬如它要在区间 [3,6]上加一段fibonacci 原来: id 0 1 2 3 4 5 6 7 8 9 10 d  0 0 0 0 0 0 0 0 0 0 0 更新: id 0 1 2 3 4 5 6  7  8  9 10 d  0…

Portal Description 给出一个\(n(n\leq3\times10^5)\)个数的序列,进行\(m(m\leq3\times10^5)\)次操作,操作有两种: 给区间\([L,R]\)加上一个斐波那契数列,即\(\{a_L,a_{L+1},...,a_R\} \rightarrow \{a_L+F_1,a_{L+1}+F_2,...,a_R+F_{R-L+1}\}\) 询问区间\([L,R]\)的和,对\(10^9+9\)取模. 斐波那契数列:\(F_1=1,F_2=2\)且满足…

E  DZY Loves Fibonacci Numbers In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation F1 = 1; F2 = 1; Fn = Fn - 1 + Fn - 2 (n > 2). DZY loves Fibonacci numbers very much. Today DZY gives you an array consist…

Description In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation F1 = 1; F2 = 1; Fn = Fn - 1 + Fn - 2 (n > 2). DZY loves Fibonacci numbers very much. Today DZY gives you an array consisting of n integers: …

DZY Loves Fibonacci Numbers Time Limit:4000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u Submit Status Appoint description:  System Crawler  (2014-07-14) Description In mathematical terms, the sequence Fn of Fibonacci numbers is defi…

题目:DZY Loves Fibonacci Numbers 题意比較简单,不解释了. 尽管官方的题解也是用线段树,但还利用了二次剩余. 可是我没有想到二次剩余,然后写了个感觉非常复杂度的线段树,还是mark一下吧. 我是这样考虑这个问题的,首先准备三个数组F,G,K,功能后面解释. 然后对它们有这样一个计算: F[0] = G[0] = 0; F[1] = 1; G[1] = 0; K[0] = 1; K[1] = 0; for(int i=2; i<N; i++){ F[i] = (F[i-…

更好的阅读体验 Portal Portal1: Codeforces Portal2: Luogu Description In mathematical terms, the sequence \(F_n\) of Fibonacci numbers is defined by the recurrence relation \[F_1 = 1; F_2 = 1; F_n = F_n - 1 + F_n - 2 (n > 2)\] DZY loves Fibonacci numbers ver…

Description ​ 看题戳我 给你一个序列,要求支持区间加斐波那契数列和区间求和.\(~n \leq 3 \times 10 ^ 5, ~fib_1 = fib_2 = 1~\). Solution ​ 先来考虑一段斐波那契数列如何快速求和,根据性质有 \[ \begin {align} fib_n &= fib_{n - 1} + fib_{n - 2} \\ &= fib_ {n - 2} + fib_{n - 3} + fib_{n - 2} \\ &= fib_{n…

Description Transmission Gate 你需要维护一个长度为\(n \leq 300000\) 的数列,兹词两个操作: 1.给一个区间加上一个fibonacci数列,规定\(f[0] = 0, f[1] = 1, f[2] = 1\) 2.查询一段区间的和.对1e9+9取模 操作个数m不超过300000. Solution ​ 这一题其实要考虑Fibonacci数列的两个性质: ​ (i)\(\sum_{i = 1}^{n} fib(i) = f(n + 2) - 1\) ​…

第一次看到段更斐波那契数列的,整个人都不会好了.事后看了题解才明白了一些. 首先利用二次剩余的知识,以及一些数列递推式子有下面的 至于怎么解出x^2==5(mod 10^9+9),我就不知道了,但是要用的时候可以枚举一下,把这些参数求出来之后就题目就可以转化为维护等比数列. 由于前面的常数可以最后乘,所以就等于维护两个等比数列好了. 下面我们来看如何维护一个等比数列.假如我对区间[L,R]的加上1,2,4,8...2^n的话,那么我只需要加一个标记x表示这个区间被加了多少次这样的2^n. 举个例…

http://codeforces.com/contest/447/problem/E 题意: 给定一个数组, m次操作, 1 l r 表示区间修改, 每次 a[i] +  Fibonacci[i-l+] 2 l r 区间求和 每次修改操作,只需要记录 每个点前两个值就可以了, 后面的和以及孩子需要加的值都可以通过这两个求出来. 推推公式就出来了. 注意 溢出. #include <bits/stdc++.h> using namespace std; typedef long long LL…

假如F[1] = a, F[2] = B, F[n] = F[n - 1] + F[n - 2]. 写成矩阵表示形式可以很快发现F[n] = f[n - 1] * b + f[n - 2] * a. f[n] 是斐波那契数列 也就是我们如果知道一段区间的前两个数增加了多少,可以很快计算出这段区间的第k个数增加了多少 通过简单的公式叠加也能求和 F[n]  = f[n - 1] * b + f[n - 2] * a F[n - 1] = f[n - 2] * b + f[n - 3] * a ..…

洛谷 Codeforces 思路 这题知道结论就是水题,不知道就是神仙题-- 斐波那契数有这样一个性质:\(f_{n+m}=f_{n+1}f_m+f_{n}f_{m-1}\). 至于怎么证明嘛-- 即得易见平凡,仿照上例显然.留作习题答案略,读者自证不难. 反之亦然同理,推论自然成立,略去过程QED,由上可知证毕. 其实就是我不会 而且这个性质对于负数下标也是成立的. 负数下标的斐波那契数怎么求?你从\(f_{-1}+f_0=f_1\)可以得到\(f_{-1}=1\),后面的你也倒推回去就可以了…

Codeforces 题目传送门 & 洛谷题目传送门 你可能会疑惑我为什么要写 *2400 的题的题解 首先一个很明显的想法是,看到斐波那契数列和 \(10^9+9\) 就想到通项公式,\(F_i=\dfrac{1}{\sqrt{5}}((\dfrac{1+\sqrt{5}}{2})^n-(\dfrac{1-\sqrt{5}}{2})^n)\).并且 \(5\) 在模 \(10^9+9\) 意义下的二次剩余存在,为 \(383008016\). 我们建两棵线段树分别维护展开式中 \((\dfra…

DZY Loves Partition 题目连接: http://acm.hdu.edu.cn/showproblem.php?pid=5646 Description DZY loves partitioning numbers. He wants to know whether it is possible to partition n into the sum of exactly k distinct positive integers. After some thinking he f…

题目链接: DZY Loves Partition Time Limit: 4000/2000 MS (Java/Others)     Memory Limit: 262144/262144 K (Java/Others)Total Submission(s): 323    Accepted Submission(s): 127 Problem Description DZY loves partitioning numbers. He wants to know whether it is…

C. DZY Loves Colors time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output DZY loves colors, and he enjoys painting. On a colorful day, DZY gets a colorful ribbon, which consists of n units (they…

题目 Source http://codeforces.com/problemset/problem/444/C Description DZY loves colors, and he enjoys painting. On a colorful day, DZY gets a colorful ribbon, which consists of n units (they are numbered from 1 to n from left to right). The color of t…

DZY Loves Chemistry time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output DZY loves chemistry, and he enjoys mixing chemicals. DZY has n chemicals, and m pairs of them will react. He wants to pou…

DZY Loves Chemistry Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u Submit Status Practice CodeForces 445B Description DZY loves chemistry, and he enjoys mixing chemicals. DZY has n chemicals, and m pairs of them will re…

题目链接: http://codeforces.com/problemset/problem/444/C J. DZY Loves Colors time limit per test:2 secondsmemory limit per test:256 megabytes 问题描述 DZY loves colors, and he enjoys painting. On a colorful day, DZY gets a colorful ribbon, which consists of…

A. DZY Loves Hash time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output DZY has a hash table with p buckets, numbered from 0 to p - 1. He wants to insert n numbers, in the order they are given, i…

B. DZY Loves Chemistry time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output DZY loves chemistry, and he enjoys mixing chemicals. DZY has n chemicals, and m pairs of them will react. He wants to…

DZY loves colors, and he enjoys painting. On a colorful day, DZY gets a colorful ribbon, which consists of n units (they are numbered from 1 to n from left to right). The color of thei-th unit of the ribbon is i at first. It is colorful enough, but w…