题目:传送门 题意: 给你m个病毒串,只由(A.G.T.C) 组成, 问你生成一个长度为 n 的 只由 A.C.T.G 构成的,不包含病毒串的序列的方案数. 解: 对 m 个病毒串,建 AC 自动机, 然后, 这个AC自动机就类似于一张有向图, 可以用邻接矩阵存这张有向图. 最多10个病毒串, 每个病毒串长度不超过 10, 那最多是个 100 * 100 的矩阵, 可以接受. 最后用矩阵快速幂加速推导. #include<cstdio> #include<cstring> #inc…

poj 3070 && nyoj 148 矩阵快速幂 题目链接 poj: http://poj.org/problem?id=3070 nyoj: http://acm.nyist.net/JudgeOnline/problem.php?pid=148 思路: 矩阵快速幂 直接求取 代码: #include <iostream> #include <string.h> #include <math.h> #include <stdio.h>…

DNA Sequence Description It's well known that DNA Sequence is a sequence only contains A, C, T and G, and it's very useful to analyze a segment of DNA Sequence,For example, if a animal's DNA sequence contains segment ATC then it may mean that the ani…

题意 : 给出一些病毒串,问你由ATGC构成的长度为 n 且不包含这些病毒串的个数有多少个 分析 : 这题搞了我真特么久啊,首先你需要知道的前置技能包括 AC自动机.构建Trie图.矩阵快速幂,其中矩阵快速幂和AC自动机可能都熟悉,但是这题为什么和矩阵有关系?Trie图是什么呢?好像只听说过Trie树啊!下面我慢慢展开,首先声明本人水平实在实在有限,理解错误的地方请批评指证,万分感激! 与矩阵的联系( 你可能需要百度.... ) ==> 解决此题就要先了解到如何用矩阵去解决 求从A点到B点刚好经…

题意:给出m个模式串,要求你构造长度为n(n <= 2000000000)的主串,主串不包含模式串,问这样的主串有几个 思路:因为要不包含模式串,显然又是ac自动机.因为n很大,所以用dp不太好. 在图论中,如果我们知道一个图的邻接矩阵A,$A_{ij}$ = 1表示i走一步到j有一条路,那么$A^n$中的$A_{ij}$就是这个图中从i走n步到j的路径数. 所以用ac自动机我们创造一个所有后缀的邻接矩阵A,那么用矩阵快速幂$A^n$就求出了所有的路径数,$\sum_{i = 1}^n A_{0…

题意 : 给出一些病毒串,问你由ATGC构成的长度为 n 且不包含这些病毒串的个数有多少个 分析: 我们先分析Tire 图的结构 : Trie图是在AC自动机的原型上增添边使得状态可以快速转移,标记危险的节点(后缀是不良单词的节点): 那我们是想构造长度是n不包含不良串对不对 , 那是不是在trie图上从0节点走n步到安全节点的方案数(Trie图也是状态转移图) 在一个有向图中,A走k步到B的方案数(这显然是经典的矩阵快速幂问题),(原理需要自己搜索)先对原图建立一个邻接表M[i][j] , M…

DNA Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 9899   Accepted: 3717 Description It's well known that DNA Sequence is a sequence only contains A, C, T and G, and it's very useful to analyze a segment of DNA Sequence,For exa…

题意:给定一些串,然后让你构造出一个长度为 m 的串,并且不包含以上串,问你有多少个. 析:很明显,如果 m 小的话 ,直接可以用DP来解决,但是 m 太大了,我们可以认为是在AC自动机图中,根据离散中的矩阵的幂可以表示 从 i 到 j 需要 x 步的有多少条.比如A[1][2]^5 = 10,表示从结点 1 到结点 2 走五步有10种方法,利用这种方法,就可以直接进行矩阵快速幂了. 代码如下: #pragma comment(linker, "/STACK:1024000000,1024000…

题目链接: Sequence Time Limit: 2000/1000 MS (Java/Others)     Memory Limit: 65536/65536 K (Java/Others) Problem Description Holion August will eat every thing he has found. Now there are many foods,but he does not want to eat all of them at once,so he fi…

HDU - 1005 Number Sequence Problem Description A number sequence is defined as follows:f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.Given A, B, and n, you are to calculate the value of f(n). Input The input consists of multiple test…

<题目链接> Description In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2. For example, the first ten terms of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … An alternative formula for the Fibonacci seq…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5950 Farmer John likes to play mathematics games with his N cows. Recently, they are attracted by recursive sequences. In each turn, the cows would stand in a line, while John writes two positive numbers…

题目链接:传送门 题目: Recursive sequence Time Limit: / MS (Java/Others) Memory Limit: / K (Java/Others) Total Submission(s): Accepted Submission(s): Problem Description Farmer John likes to play mathematics games with his N cows. Recently, they are attracted…

题意:个n个方块涂色, 只能涂红黄蓝绿四种颜色,求最终红色和绿色都为偶数的方案数. 该题我们可以想到一个递推式 .   设a[i]表示到第i个方块为止红绿是偶数的方案数, b[i]为红绿恰有一个是偶数的方案数, c[i]表示红绿都是奇数的方案数. 那么有如下递推可能: 递推a[i+1]:1.到第i个为止都是偶数,且第i+1个染成蓝或黄:2.到第i个为止红绿恰有一个是奇数,并且第i+1个方块染成了奇数对应的颜色. 递推b[i+1]:1.到第i个为止都是偶数,且第i+1个染成红或绿:2.到第i个为止…

题目链接:https://vjudge.net/problem/HDU-5950 Recursive sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 2727    Accepted Submission(s): 1226 Problem Description Farmer John likes to play mat…

                  Yet another Number Sequence Let’s define another number sequence, given by the following function:f(0) = af(1) = bf(n) = f(n − 1) + f(n − 2), n > 1When a = 0 and b = 1, this sequence gives the Fibonacci Sequence. Changing the values…

Description Everyone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation: F1 = 1, F2 = 2, Fi = Fi - 1 + Fi - 2 (i > 2). We'll define a new number sequence Ai(k) by the formula: Ai(k) = Fi × ik (i ≥ 1). In thi…

Problem Description A number sequence is defined as follows: f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7. Given A, B, and n, you are to calculate the value of f(n).   Input The input consists of multiple test cases. Each test case…

A number sequence is defined as follows:  f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.  Given A, B, and n, you are to calculate the value of f(n). Input The input consists of multiple test cases. Each test case contains 3 integers…

题目 还是一道基础的矩阵快速幂. 具体的居者的幂公式我就不明示了. #include<stdio.h> #include<string.h> #include<algorithm> using namespace std; ; struct matrix { ][]; }; matrix multiply(matrix x,matrix y)//矩阵乘法 { matrix temp; ;i<num;i++) { ;j<num;j++) { ; ;k<n…

题目链接 题意 : 用矩阵相乘求斐波那契数的后四位. 思路 :基本上纯矩阵快速幂. #include <iostream> #include <cstring> #include <cstdio> using namespace std; struct Matrix { ][]; }; int n; Matrix matrix_mul(Matrix a,Matrix b) { Matrix c; ; i < ; i++) { ; j < ; j++) { c…

题意: 一条路上有n个地雷,你从1开始走,单位时间内有p的概率走一步,1-p的概率走两步,问安全通过这条路的概率 解析: 很容易想到 dp[i] = p * dp[i-1] + (1 - p) * dp[i]; 然而...t,但这个式子明显可以用矩阵快速幂加个氮气一下加速一下... 把所有的点输入之后 sort一下,那么就能把这条路分成很多段 每一段以地雷为分界线 1 - x[0]  x[0]+1 - x[1]  x[1]+1 - x[2] ````````` 然后求出安全通过每一段的概率  …

题目链接 Description Panda has received an assignment of painting a line of blocks. Since Panda is such an intelligent boy, he starts to think of a math problem of painting. Suppose there are N blocks in a line and each block can be paint red, blue, gree…

题意:递推公式 Fn = Fn-1 + 2 * Fn-2 + n*n,让求 Fn; 析:很明显的矩阵快速幂,因为这个很像Fibonacci数列,所以我们考虑是矩阵,然后我们进行推公式,因为这样我们是无法进行运算的.好像有的思路,最后也没想出来,还是参考的大牛的博客 http://blog.csdn.net/spring371327/article/details/52973534 那是讲的很详细了,就不多说了,注意这个取模不是1e9+7,一开始忘了.. 代码如下: #pragma comment…

题意 设 $$f_i = \left\{\begin{matrix}1 , \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  i < k\\ \prod_{j=1}^k f_{i-j}^{b_j} \ mod \ p, \ \ \ \ \ i > k\end{matrix}\right.$$ 求 $f_k$($1 \leq f_k < p$),使得 $f_m = n$.($1 \leq k\leq 100$) 分析 $f_n$ 可以表示…

题意: F(1)=A,F(2)=B,F(n)=C*F(n-2)+D*F(n-1)+P/n 给定ABCDPn,求F(n) mod 1e9+7 思路: P/n在一段n里是不变的,可以数论分块,再在每一段里用矩阵快速幂 debug了一下午.. 坑点: 1.数论分块的写法要注意,已更新 2.矩阵乘法在赋值回去的时候记得模一下 3.矩阵相乘不可逆,注意看一下 代码: #include<iostream> #include<cstdio> #include<algorithm> #…

题目链接 题意 给定\(m\)个字符串,问长度为\(n\)的字符串中有多少个不包含那\(m\)个字符串. (字符集为\(A,T,C,G\),\(m\leq 10\),长度\(\leq 10\),\(n\leq 2e9\)) 思路 状态转移--矩阵 构造一个矩阵\(m[\ ][\ ]\),\(m[i][j]\)代表有多少种方式可以走一步从第\(i\)个节点到第\(j\)个节点, 则\(m^n[i][j]\)即代表有多少种方式可以走\(n\)步从第\(i\)个节点到第\(j\)个节点, 于是答案呼之…

DNA Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 11860   Accepted: 4527 Description It's well known that DNA Sequence is a sequence only contains A, C, T and G, and it's very useful to analyze a segment of DNA Sequence,For ex…

题意:给定n个不能出现的模式串,给定一个长度m,要求长度为m的合法串有多少种. 思路:用AC自动机,利用AC自动机上的节点做矩阵乘法. #include<iostream> #include<cstdio> #include<cstring> #include<cmath> #include<string> #include<algorithm> #include<queue> #define MOD 100000 ];…

DNA Sequence   Description It's well known that DNA Sequence is a sequence only contains A, C, T and G, and it's very useful to analyze a segment of DNA Sequence,For example, if a animal's DNA sequence contains segment ATC then it may mean that the a…