HDU 5860 Death Sequence(递推) 题目链接http://acm.split.hdu.edu.cn/showproblem.php?pid=5860 Description You may heard of the Joseph Problem, the story comes from a Jewish historian living in 1st century. He and his 40 comrade soldiers were trapped in a cave…

题目: A single positive integer i is given. Write a program to find the digit located in the position i in the sequence of number groups S1S2...Sk. Each group Sk consists of a sequence of positive integer numbers ranging from 1 to k, written one after…

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…

Recursive sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 2882    Accepted Submission(s): 1284 Problem Description Farmer John likes to play mathematics games with his N cows. Recently,…

Problem Description You may heard of the Joseph Problem, the story comes from a Jewish historian living in 1st century. He and his 40 comrade soldiers were trapped in a cave, the exit of which was blocked by Romans. They chose suicide over capture an…

题目链接 题意 给定\(c_0,c_1,求c_n(c_0,c_1,n\lt 2^{31})\),递推公式为 \[c_i=c_{i-1}+2c_{i-2}+i^4\] 思路 参考 将递推式改写\[\begin{pmatrix}f(n)\\f(n-1)\\n^4\\n^3\\n^2\\n\\1\end{pmatrix}=\begin{pmatrix}1&2&1&4&6&4&1\\1&0&0&0&0&0&0\\0&a…

链接:https://www.luogu.org/problemnew/show/P1216 题面: 题目描述 观察下面的数字金字塔. 写一个程序来查找从最高点到底部任意处结束的路径,使路径经过数字的和最大.每一步可以走到左下方的点也可以到达右下方的点. 7 3 8 8 1 0 2 7 4 4 4 5 2 6 5 在上面的样例中,从7 到 3 到 8 到 7 到 5 的路径产生了最大 输入输出格式 输入格式: 第一个行包含 R(1<= R<=1000) ,表示行的数目. 后面每行为这个数字金字…

2656: [Zjoi2012]数列(sequence) Time Limit: 2 Sec  Memory Limit: 128 MB[Submit][Status][Discuss] Description 小白和小蓝在一起上数学课,下课后老师留了一道作业,求下面这个数列的通项公式: 小白作为一个数学爱好者,很快就计算出了这个数列的通项公式.于是,小白告诉小蓝自己已经做出来了,但为了防止小蓝抄作业,小白并不想把公式公布出来.于是小白为了向小蓝证明自己的确做出来了此题以达到其炫耀的目的,想出了…

给一个只含‘I','D','?'三种字符的字符串,I表示当前数字大于前面的数字,D表示当前的数字小于前面一位的数字,?表示当前位既可以小于又可以大于. 问1~n的排列中有多少个满足该字符串. http://blog.csdn.net/shiqi_614/article/details/7983298 http://www.cnblogs.com/kuangbin/archive/2012/10/04/2711330.html http://blog.csdn.net/cc_again/artic…

解题心得: 1.对于数据很大,很可怕,不可能用常规手段算出最后的值在进行mod的时候,可以思考找规律. 2.找规律时不必用手算(我傻,用手算了好久).直接先找前100项进行mod打一个表出来,直接看就行了. 3.对于像斐波那契数列(本题)的那样,凭借肉眼无法找到规律的时候,可以观察本题的特点.那就是,第一项和第二项不会变,都为1,1.所以循环的时候必定是以1.1为开始,中间的数可以直接记录,很玄幻. 4.还是边界问题,这很重要,这时候数列尽量从1开始,因为在询问的时候都是询问的第n个数,要时刻保…

Recursive sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 249    Accepted Submission(s): 140 Problem Description Farmer John likes to play mathematics games with his N cows. Recently, t…

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…

一.题目 The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are F2 = {1/2} F3 = {1/3, 1/2, 2/3} F4 = {1/4, 1/3, 1/2, 2…

题目传送门 题目描述:给出一个数列的第一项和第二项,计算第n项. 递推式是 f(n)=f(n-1)+2*f(n-2)+n^4. 由于n很大,所以肯定是矩阵快速幂的题目,但是矩阵快速幂只能解决线性的问题,n^4在这个式子中是非线性的,后一项和前一项没有什么直接关系,所以模拟赛的时候想破头也不会做. 这里要做一个转换,把n^4变成一个线性的,也就是和(n-1)^4有关系的东西,而这个办法就是: n^4=(n-1+1)^4=(n-1)^4+4*(n-1)^3+6*(n-1)^2+4*(n-1)^1+(…

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…

题目大意: 将一个数字的相邻两位的差(的绝对值)组成一个新的数字.不断反复.假设最后得到7,就称这个数为July Number,比方9024 – 922 – 70 – 7. 题目要求1e9范围内给定区间[a, b]里July Number的个数. 思路:逆向递推,既然题目求能化成 7 的数的个数.那么就从 7 逆着找出去 18 .29.70,81.92等,(要注意的就是:还有从07,007.....等找出去的,每一个数同理: 代码: /* SKY */ #include<iostream> #…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5950 题意:求解递推式f(n)=f(n-1)+2*f(n-2)+n^4. 写了个小东西,不过我的文章里式子是2*f(n-1),内容差不多.凑合看 #include <bits/stdc++.h> using namespace std; typedef long long LL; ; ; LL n, a, b; typedef struct Matrix { LL m[maxn][maxn]; i…

题解见X姐的论文 矩阵乘法递推的优化.仅仅是mark一下. .…

题目链接 F[1] = a, F[2] = b, F[i] = 2 * F[i-2] + F[i-1] + i ^ 4, (i >= 3) 现在要求F[N] 类似于斐波那契数列的递推式子吧, 但是N最大能到int的最大值, 直接循环推解不了 所以就得用矩阵快速幂咯 现在就看转移矩阵长什么样了 Mi表示要求的矩阵 转移矩阵用A表示 A * Mi = Mi+1 矩阵Mi里面至少得有 F[i-1] F[i-2] i ^ 4 Mi+1就相应的有 F[i] F[i-1] (i+1)^4 (i+1)^4 =…

已知\(f_i = \prod \limits_{j = 1}^k f_{i - j}^{b_j}\;mod\;998244353\),并且\(f_1, f_2, ..., f_{k - 1} = 1\),\(f_k = a\),已知\(f_n = m\),试求\(a\) 易知\(f_n = f_k^p\) 对于\(p\)满足递推式\(g[i] = \sum \limits_{j = 1}^k b[j] * g[i - j]\) 这是常系数线性递推,由于\(k \leq 100\),因此矩阵快速…

哎呀大水题..我写了一个多小时..好没救啊.. 数论板子X合一? 注意: 本文中变量名称区分大小写. 题意: 给一个\(n\)阶递推序列\(f_k=\prod^{n}_{i=1} f_{k-i}b_i\mod P\)其中\(P=998244353\), 输入\(b_1,b_2,...,b_n\)以及已知\(f_1,f_2,...,f_{n-1}=1\), 再给定一个数\(m\)和第\(m\)项的值\(f_m\), 求出一个合法的\(f_n\)值使得按照这个值递推出来的序列满足第\(m\)项的值为…

计蒜客题目链接:https://nanti.jisuanke.com/t/41303 题目:给你一个序列a,你可以从其中选取元素,构建n个串,每个串的长度为n,构造的si串要满足以下条件, 1. si[1]=i . 2. si[j]<si[j-1] 3. |pos[j] -pos[j-1]|<=k 并且每个a中的元素只能用一次 4. 两个串大小的定义时 前k项相等的前提(k和前面不是一个),Ck>Dk,则C大于D 求Si的长度,并输出 由于Si[ j ] < Si[j - 1] ,…

题目链接: http://codeforces.com/problemset/problem/353/D?mobile=true H. Queue time limit per test 1 secondmemory limit per test 256 megabytes 问题描述 There are n schoolchildren, boys and girls, lined up in the school canteen in front of the bun stall. The b…

MathsTime Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://acm.hust.edu.cn/vjudge/contest/view.action?cid=87157#problem/B Description Android Vasya attends Maths classes. His group started to study the number theory recently. The teacher gave them seve…

Yet Another Number Sequence 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(…

Description In how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles? Here is a sample tiling of a 2x17 rectangle. Input Input is a sequence of lines, each line containing an integer number 0 <= n <= 250. Output For each line of input, outp…

主题链接: pid=1005">huangjing 题意: 就是给了一个公式,然后求出第n项是多少... 思路: 题目中n的范围实在是太大,所以肯定直接递推肯定会超时,所以想到的是暴力打表,找循环节,可是也不是那么easy发现啊,所以这时候分析一下,由于最后都会mod7,所以总共同拥有7X7总情况,即A 0,1,2,3,4,5,6,7.B也是如此,所以循环节为49,这么这个问题就攻克了. .. 题目: Number Sequence Time Limit: 2000/1000 MS (Ja…

Computer Transformation Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4561 Accepted: 1738 Description A sequence consisting of one digit, the number 1 is initially written into a computer. At each successive time step, the computer simul…

Description The short story titled Coconuts, by Ben Ames Williams, appeared in the Saturday Evening Post on October 9, 1926. The story tells about five men and a monkey who were shipwrecked on an island. They spent the first night gathering coconuts.…

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 co…