There is a set of matrixes that are constructed subject to the following constraints: 1. The matrix is a S(n)×S(n) matrix; 2. S(n) is the sum of the first n Fibonacci numbers modulus m, that is S(n) = (F1 + F2 + … + Fn) % m; 3. The matrix contains on…

题目链接:fzu 1911 Construct a Matrix 题目大意:给出n和m,f[i]为斐波那契数列,s[i]为斐波那契数列前i项的和.r = s[n] % m.构造一个r * r的矩阵,只能使用-1.0.1.使得矩阵的每行每列的和都不相同,输出方案,不行的话输出No. 解题思路:求r的话用矩阵快速幂求,每次模掉m, { {1, 1, 0}, {1, 0, 0}, {1, 1, 1} } * { f[i], f[i -1], s[i] } = { f[i + 1], f[i], s[i…

In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333...…

In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333...…

题意:求A + A^2 + A^3 + ... + A^m. 析:主要是两种方式,第一种是倍增法,把A + A^2 + A^3 + ... + A^m,拆成两部分,一部分是(E + A^(m/2))(A + A^2 + A^3 + ... + A^(m/2)),然后依次计算下去,就可以分解,logn的复杂度分解,注意要分奇偶. 另一种是直接构造矩阵,,然后就可以用辞阵快速幂计算了,注意要用分块矩阵的乘法. 代码如下: 倍增法: #pragma comment(linker, "/STACK:10…

题意:给出矩阵的第0行(233,2333,23333,...)和第0列a1,a2,...an(n<=10,m<=10^9),给出式子: A[i][j] = A[i-1][j] + A[i][j-1],要求A[n][m]. 解法:看到n<=10和m<=10^9 应该对矩阵有些想法,现在我们假设要求A[a][b],则A[a][b] = A[a][b-1] + A[a-1][b] = A[a][b-1] + A[a-1][b-1] + A[a-2][b] = ... 这样相当于右图:,红…

In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333...…

题目链接:https://vjudge.net/problem/HDU-5015 233 Matrix Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 2805    Accepted Submission(s): 1611 Problem Description In our daily life we often use 233 t…

题意: 给出一个\(n \times n\)的矩阵\(A\),求\(A+A^2+A^3+ \cdots + A^k\). 分析: 这题是有\(k=0\)的情况,我们一开始先特判一下,直接输出单位矩阵\(E\). 下面讨论\(k > 0\)的情况: 方法一 设答案为\(S_k(k > 0)\) 把矩阵增广一下 \(\begin{bmatrix} A & O \\ E & E \end{bmatrix} \begin{bmatrix} A^n\\ S_{n-1} \end{bmat…

http://acm.hdu.edu.cn/showproblem.php?pid=6470 题意 \(f[n]=2f[n-2]+f[n-1]+n^3,n \leq 10^{18}\),求f[n] 题解 每一项只能由上一项经线性变换转移过来 代码 #include<bits/stdc++.h> #define P 123456789 #define ll long long using namespace std; struct N{ ll a[10][10]; }; N mul(N x,N…