C. Magic Grid time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output Let us define a magic grid to be a square matrix of integers of size n×nn×n, satisfying the following conditions. All integers…

Description Given a n × n matrix A and a positive integer k, find the sum S = A + A2 + A3 + … + Ak. Input The input contains exactly one test case. The first line of input contains three positive integers n (n ≤ 30), k (k ≤ 109) and m (m < 104). Then…

Number Sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 147964    Accepted Submission(s): 35964 Problem Description A number sequence is defined as follows: f(1) = 1, f(2) = 1, f(n) = (A…

http://acm.hdu.edu.cn/showproblem.php?pid=5015 由于是个二维的递推式,当时没有想到能够这样构造矩阵.从列上看,当前这一列都是由前一列递推得到.依据这一点来构造矩阵.令b[i]代表第i列,是一个(n+2)*1的矩阵,即b[1] = [1,233......],之所以在加了两行,是要从前一个矩阵b[i-1]得到b[i]中的第二个数2333...,再构造一个转换矩阵a,它是一个(n+2)*(n+2)的矩阵,那么a^(m-1) * b就是第m列. /* a矩…

Magic Bracelet Time Limit: 2000MS   Memory Limit: 131072K Total Submissions: 4990   Accepted: 1610 Description Ginny’s birthday is coming soon. Harry Potter is preparing a birthday present for his new girlfriend. The present is a magic bracelet which…

Thanks a lot for helping Harry Potter in finding the Sorcerer's Stone of Immortality in October. Did we not tell you that it was just an online game ? uhhh! now here is the real onsite task for Harry. You are given a magrid S ( a magic grid ) having…

依据题意.我已经推导出tn的公式.ti=ti.a+ti.b,ti.a=5*t(i-1).a+4*t(i-1).b,ti.b=t(i-1).a+t(i-1).b 然而以下居然不能继续推到sn的公式!!! ! 这道题考察的就是求随意数列的前n项和,在sn的递推公式不太明显的时候.用矩阵解决. 设矩阵A=.矩阵F0= " /> 那么设矩阵S=(A+A2+A3-. + An)*F0 终于答案就是矩阵S内两个元素之和. 那么怎么求A+A2+A3-. + An ? 能够继续构造例如以下的分块矩阵,当中…

http://poj.org/problem?id=3735 大致题意: 有n仅仅猫,開始时每仅仅猫有花生0颗,现有一组操作,由以下三个中的k个操作组成: 1. g i 给i仅仅猫一颗花生米 2. e i 让第i仅仅猫吃掉它拥有的全部花生米 3. s i j 将猫i与猫j的拥有的花生米交换 现将上述一组操作循环m次后,问每仅仅猫有多少颗花生? 非常明显,要先构造矩阵.构造一个(n+1)*(n+1)的矩阵a,初始化为单位矩阵. g i : a[i][n+1] += 1; e i : a[i][j]…

Another kind of Fibonacci Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 1219    Accepted Submission(s): 466 Problem Description As we all known , the Fibonacci series : F(0) = 1, F(1) = 1, F(N…

矩阵的又一个新使用方法,构造矩阵进行高速幂. 比方拿 nyoj299 Matrix Power Series 来说 给出这样一个递推式: S = A + A2 + A3 + - + Ak. 让你求s.A是一个矩阵,而k很大. 怎么办呢? 推理发现:Fn = A + A*F(n-1) 然后我们能够构造矩阵: (Fn .1 ) =  (Fn-1 ,1) * (A.0. A,1) = (F1 , 1) * (A,0. A,1)^K-1 那么我们就能够用一个矩阵高速幂了. 以下是模板题目的代码: #in…