[算法]二分+矩阵快速幂 [题意]给定矩阵A和整数k,MOD,求A^0+A^1+A^2+...+A^k. [题解] 定义题目要求的答案为f(n),即: $$f_n=\sum_{i=0}^{n}A^i$$ 当n为偶数时,可以拆成两半,后一半由前一半集体乘A(n/2)得到,即: $$f_n=f_{\frac{n}{2}}(A^{\frac{n}{2}}+1)$$ 当n为奇数时,直接递推: $$f_n=f_{n-1}*A^n$$ 复杂度O(n^3 log k). 快速幂的单位矩阵是主对角线(左上到右下…

任意门:http://poj.org/problem?id=3233 Matrix Power Series Time Limit: 3000MS   Memory Limit: 131072K Total Submissions: 28619   Accepted: 11646 Description Given a n × n matrix A and a positive integer k, find the sum S = A + A2 + A3 + … + Ak. Input The…

poj 1575  Tr A 主题链接:http://acm.hdu.edu.cn/showproblem.php?pid=1575 题目大意:A为一个方阵,则Tr A表示A的迹(就是主对角线上各项的和),现要求Tr(A^k)%9973. 数据的第一行是一个T,表示有T组数据. 每组数据的第一行有n(2 <= n <= 10)和k(2 <= k < 10^9)两个数据.接下来有n行,每行有n个数据,每一个数据的范围是[0,9].表示方阵A的内容. 一个矩阵高速幂的裸题. 题解: #…

Matrix Power Series [题目链接]Matrix Power Series [题目类型]二分等比求和 &题解: 这题我原来用vector写的,总是超时,不知道为什么,之后就改用数组了,照着别人的代码敲了一遍 [时间复杂度]O(logn) &代码: #include <cstdio> #include <bitset> #include <iostream> #include <set> #include <cmath&g…

Matrix Power Series Time Limit: 3000MS   Memory Limit: 131072K Total Submissions: 11954   Accepted: 5105 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 cas…

Matrix Power Series Time Limit: 3000MS   Memory Limit: 131072K Total Submissions: 15417   Accepted: 6602 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 cas…

Matrix Power Series Time Limit: 3000MS Memory Limit: 131072K 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 po…

Matrix Power Series   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)…

Matrix Power Series Time Limit: 3000MS Memory Limit: 131072K Total Submissions: 19338 Accepted: 8161 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. T…

Matrix Power Series Time Limit: 3000MS   Memory Limit: 131072K Total Submissions: 15739   Accepted: 6724 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 cas…