题目:Fibonacci Check-up 链接:http://acm.hdu.edu.cn/showproblem.php?pid=2855 分析: 1)二项式展开:$(x+1)^n = \sum^n_{k=0}{C^k_n * x^k}$ 2)Fibonacci数列可以写为:$ \left[ \begin{array}{cc} 0 & 1 \\ 1 & 1 \end{array} \right]^n$的左下角项. 3)构造矩阵$ T = Fib+E = \left[ \begin{ar…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=2855 题目意思:求一个式子g[n]=∑C(n,k)*f[k],n很大,很明显是一个矩阵快速幂.可以打表发现g[n]=f[2*n]划开可以发现g[n]=3*g[n-1]-f[n-2]. 思路:我们现在可以证明一下 f[2*n]=f[2*n-1]+f[2*n-2]; 其中f[2*n-1]=f[2*n-2]+f[2*n-3] f[2*n-2]=f[2*n-3]+f[2*n-4] 所以f[2*n]=f[2*…

原题目: Write a recursive program that extends the range of the Fibonacci sequence.  The Fibonacci sequence is 1, 1, 2, 3, 5, 8, etc., where each element is the sum of the previous two elements. For this problem, instead of only adding the last two elem…

http://scottsievert.github.io/blog/2015/01/31/the-mysterious-eigenvalue/ The Fibonacci problem is a well known mathematical problem that models population growth and was conceived in the 1200s. Leonardo of Pisa aka Fibonacci decided to use a recursiv…

Fibonacci Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others) Problem Description Following is the recursive definition of Fibonacci sequence: Fi=⎧⎩⎨01Fi−1+Fi−2i = 0i = 1i > 1 Now we need to check whether a number can…

Fibonacci Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 795    Accepted Submission(s): 213 Problem Description Following is the recursive definition of Fibonacci sequence: Fi=⎧⎩⎨01Fi−1+Fi−2i =…

Problem Description Following is the recursive definition of Fibonacci sequence: Fi=⎧⎩⎨01Fi−1+Fi−2i = 0i = 1i > 1 Now we need to check whether a number can be expressed as the product of numbers in the Fibonacci sequence.   Input There is a number T …

For Fibonacci Sequence, the space complexity should be the O(logN), which is the height of tree. Check the source…

fibonacci数列的性质和实现方法 1.gcd(fib(n),fib(m))=fib(gcd(n,m)) 证明:可以通过反证法先证fibonacci数列的任意相邻两项一定互素,然后可证n>m时gcd(fib(n),fib(m))=gcd(fib(n-m),fib(m)),递归可 求gcd(fib(n),fib(m))=gcd(fib(k),fib(l)),最后k=l,不然继续递归.K是通过展转相减法求出,易证k=gcd(n,m),所以gcd(fib(n),fib(m)) =fib(gcd(n…

原题链接在这里:https://leetcode.com/problems/split-array-into-fibonacci-sequence/ 题目: Given a string S of digits, such as S = "123456579", we can split it into a Fibonacci-like sequence [123, 456, 579]. Formally, a Fibonacci-like sequence is a list F o…