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(…

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 &…

A Very Simple Problem Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 1022    Accepted Submission(s): 500 Problem Description This is a very simple problem. Given three integers N, x, and M, you…

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…

A Very Simple Problem Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 589    Accepted Submission(s): 305 Problem Description This is a very simple problem. Given three integers N, x, and M, you…

题目连接:http://acm.hdu.edu.cn/showproblem.php?pid=1005 Number Sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 131753    Accepted Submission(s): 31988 Problem Description A number sequence…

已经128天了?怎么觉得上次倒计时150天的日子还很近啊 ....好吧为了把AC自动机搞透我也是蛮拼的..把1030和这道题对比了无数遍...最终结论是...无视时间复杂度,1030可以用这种写法解..但是!!对于26个字母的就算了吧... 其实这道题体现的是一个对于AC自动机等价态,即fail的表示和处理上: 通常有两种方法处理等价态,第一是互为等价态的点各自记录各自的信息.匹配的时候需要遍历所有等价态以判断是否匹配成功.next指针可能为空,需要匹配时进行判断是否需要走fail指针. 第二是…

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…

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…