POJ3233中矩阵快速幂的优化技巧有哪些? 题意 题目链接 给出$n \times n$的矩阵$A$,求$\sum_{i = 1}^k A^i $,每个元素对$m$取模 Sol 考虑直接分治 当$k$为奇数时 $\sum_{i = 1}^k A^i = \sum_{i = 1}^{k / 2 + 1} A^i + A^{k / 2 + 1}(\sum_{i = 1}^{k / 2...
typedef long long ll; const int N = 65; struct Matrix { ll mat[N][N]; }A, B, tmp, C, Ans; ll n, K, m; Matrix matMul(Matrix x, Matrix y) { for(int i = 0; i < 2 * n; i++) for(int j = 0; j < 2 * n; j++) { tmp.mat[i][j] = 0; for(int k = 0;...
{intmat[MAXN][MAXN]; } a,ans; inline Matrix add(Matrix a,Matrix b) {inti,j; Matrix ans; memset(ans.mat,0,sizeof(ans.mat));for(i =1; i <= n; i++) {for(j =1; j <= n; j++) { ans.mat[i][j]= (a.mat[i][j] + b.mat[i][j]) %m; } }returnans; } inline...
Input The input contains exactly one test case. The first line of input contains three positive integersn(n≤ 30),k(k≤ 109) andm(m< 104). Then follownlines each containingnnonnegative integers below 32,768, givingA’s elements in row-major order. Output Output the elements ofSmodulomin...
POJ 3233 Matrix Power Series(矩阵快速幂) 题面 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 ...
poj 3233 Matrix Power Series Matrix Power Series 思路 题意比较简单,就是要求S(n)=∑i=1nAiS(n) = \sum _{i = 1} ^{n} A^ {i}S(n)=∑i=1nAi,显然有S(n)=S(n−1)∗A+AS(n) = S(n - 1) * A + AS(n)=S(n−1)∗A+A,看到这里,那就简单了,递推式,加矩......
POJ3233:Matrix Power Series(矩阵快速幂+递推式) 传送门 题意 给出n,m,k,求\[\sum_{i=1}^kA^i\] A是矩阵 分析 我们首先会想到等比公式,然后得到这样一个式子:\[\frac{A^{k+1}-E}{A-E}\] 发现要用矩阵除法,可以用求矩阵逆来做,现在我们换一种做法,我们发现有这样一个性质:\[\left[ \...
POJ 3233 快速幂和二分。。。基本上是别人的代码,自己改动一些,不过收获很大。 1/*这道题目借鉴他人的思路和代码,很有收获 2先看下面这个快速幂求余的运算 3递归用二分法,每个过程都求余。 4long exp_mod(long a,long n,long b) 5{ 6long t;...
POJ 3233 Matrix Power Serie 题意:给一个n×n的矩阵A,求S = A + A2+ A3+ … + Ak。 解法:从式子中可得递推式S(n) = S(n - 1) + An,An= An-1×A,可得矩阵递推式 [S(n), An] = [S(n - 1), An-1] * [1 0] [A A] <-orz画不出二维矩阵了...
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. The first line of input con...