Discription 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…

题意:已知斐波那契数列fib(i) , 给你n 和 k , 求∑fib(i)*ik (1<=i<=n) 思路:不得不说,这道题很有意思,首先我们根据以往得出的一个经验,当我们遇到 X^k 的形式,当 X 很大,k很小时,我们可以利用二项式定理进行展开,然后求出递推式在利用矩阵加速 推导过程: 已知 fib(1) = 1, fib(2) = 1,fib(i) = fib(i-1) + fib(i-2); Ai(k) =fib(i)*i^k; 根据数学归纳法,我们可知 fib(i+1)*(i+1)…

题意: \(F_n\)为斐波那契数列,\(F_1=1,F_2=2\). 给定一个\(k\),定义数列\(A_i=F_i \cdot i^k\). 求\(A_1+A_2+ \cdots + A_n\). 分析: 构造一个列向量, \({\begin{bmatrix} F_{i-1}i^0 & F_{i-1}i^1 & \cdots & F_{i-1}i^k & F_{i}i^0 & F_{i}i^1 & \cdots & F_{i}i^k &…

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(…

Number Sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 154923    Accepted Submission(s): 37854 Problem Description A number sequence is defined as follows: f(1) = 1, f(2) = 1, f(n) = (A…

找规律,先找属于第几个循环,再找属于第几个数的第几位...... Number Sequence Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 31552 Accepted: 8963 Description A single positive integer i is given. Write a program to find the digit located in the position i in the sequ…

Number Sequence Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 8600    Accepted Submission(s): 3953 Problem Description Given two sequences of numbers : a[1], a[2], ...... , a[N], and b[1], b[…

Number Sequence   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…

AX2012的number sequence framework中引入了两个Scope和segment两个概念,它们的具体作用从下面序列的例子说起. 法国/中国的法律要求财务凭证的Journal number包含公司代码和财务期间,比如这样的号码J-20-Jan11-000340,J表上Journal,20代表的是公司代码,Jan11为财务期间,000340才是系统生成的流水号. 在创建Numer sequence的界面上可以选择需要的Scope: Company and fiscal cale…

题目大意 给一个数列,长度不超过 5000,每次可以将其中的一个数加 1 或者减 1,问,最少需要多少次操作,才能使得这个数列单调不降 数列中每个数为 -109-109 中的一个数 做法分析 先这样考虑:如果操作的次数最少,那么最终得到的不降的数列,必然是由原始数列中的数组成的,具体的证明可以使用反证法 知道了上面讲述的性质,这题就好搞了 先将原始数列(设为 A,共 n 个数)中所有的数去重并从小到达排序,保存在另一个数列中(设为 B,共 m 个数) 定义状态:f[i][j] 表示将原始数列中的…