HDU 1588 Gauss Fibonacci(矩阵高速幂+二分等比序列求和) ACM 题目地址:HDU 1588 Gauss Fibonacci 题意:  g(i)=k*i+b;i为变量.  给出k,b,n,M,问( f(g(0)) + f(g(1)) + ... + f(g(n)) ) % M的值. 分析:  把斐波那契的矩阵带进去,会发现这个是个等比序列. 推倒: S(g(i)) = F(b) + F(b+k) + F(b+2k) + .... + F(b+nk) // 设 A = {1…

题目大意: 求出斐波那契中的 第 k*i+b 项的和. 思路分析: 定义斐波那契数列的矩阵 f(n)为斐波那契第n项 F(n) = f(n+1) f(n) 那么能够知道矩阵 A = 1 1 1  0 使得 F(n) = A * F(n+1) 然后我们化简最后的答案 sum = F(b) +   F(K+b) +  F (2*k +b).... sum = F(b) +  A^k F(b)    +   A^2k F(b)..... sum = (E+A^k + A^2k.....)*F(b) 那…

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Gauss Fibonacci Time Limit: 3000/1000 MS (Java/Others)     Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 27    Accepted Submission(s): 5 Problem Description Without expecting, Angel replied quickly.She says: "I'v heard that you'r a ve…

http://acm.hdu.edu.cn/showproblem.php?pid=1588 Problem Description Without expecting, Angel replied quickly.She says: "I'v heard that you'r a very clever boy. So if you wanna me be your GF, you should solve the problem called GF~. " How good an…

题目的大意就是求等差数列对应的Fibonacci数值的和,容易知道Fibonacci对应的矩阵为[1,1,1,0],因为题目中f[0]=0,f[1]=1,所以推出最后结果f[n]=(A^n-1).a,所以 f(g(i))= f(k*i+b)= (A^(k*i+b-1)).a,i从 0取到 n-1,取出公因式 A^(b-1)(因为矩阵满足分配率),然后所求结果可化为 A^(b-1) * (A^0 + A^k + A^2k +....+ A^(n-1)k),化到这里后难点就是求和了,一开始我尝试暴力…

Fibonacci Check-up Problem Description Every ALPC has his own alpc-number just like alpc12, alpc55, alpc62 etc.As more and more fresh man join us. How to number them? And how to avoid their alpc-number conflicted? Of course, we can number them one by…

题目:Matrix Power Series 传送门:http://poj.org/problem?id=3233 分析: 方法一:引用Matrix67大佬的矩阵十题:这道题两次二分,相当经典.首先我们知道,A^i可以二分求出.然后我们需要对整个题目的数据规模k进行二分.比如,当k=6时,有:$ S(6)= A + A^2 + A^3 + A^4 + A^5 + A^6 =\underline{(A + A^2 + A^3)} + A^3*\underline{(A + A^2 + A^3)}.…

Gauss Fibonacci Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 3149    Accepted Submission(s): 1323 Problem Description Without expecting, Angel replied quickly.She says: "I'v heard that you'r…

CRB and Puzzle Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others) Total Submission(s): 483    Accepted Submission(s): 198 Problem Description CRB is now playing Jigsaw Puzzle. There are  kinds of pieces with infinite…