1065 - Number Sequence &&1070 - Algebraic Problem

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1065 - Number Sequence &&1070 - Algebraic Problem

1065 - Number Sequence PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB Let's define another number sequence, given by the following function: f(0) = a f(1) = b f(n) = f(n-1) + f(n-2), n > 1 When a = 0 and b = 1, this sequ…

LightOJ 1070 - Algebraic Problem 矩阵高速幂

题链:http://lightoj.com/volume_showproblem.php?problem=1070 1070 - Algebraic Problem PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB Given the value of a+b and ab you will have to find the value of an+bn. a and b not necessar…

LightOJ 1070 Algebraic Problem （推导+矩阵高速幂）

题目链接:problem=1070">LightOJ 1070 Algebraic Problem 题意:已知a+b和ab的值求a^n+b^n.结果模2^64. 思路: 1.找递推式 watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQv/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center" alt=""> 得到递推式之后就是矩…

LightOJ 1070 - Algebraic Problem 推导+矩阵快速幂

http://www.lightoj.com/volume_showproblem.php?problem=1070 思路:\({(a+b)}^n =(a+b){(a+b)}^{n-1} \) \((ab)C_{n}^{r}a^{n-r}b{r} = C_{n+2}^{r}a^{n-r+2}b{r} - a^{n+2} - b^{n+2} \) 综上\( f(n) = (a+b)f(n-1)-(ab)f(n-2) \) /** @Date : 2016-12-19-19.53 * @Author…

LightOJ 1065 - Number Sequence 矩阵快速幂水题

http://www.lightoj.com/volume_showproblem.php?problem=1065 题意:给出递推式f(0) = a, f(1) = b, f(n) = f(n - 1) +f(n - 2) 求f(n) 思路:给出了递推式就是水题. /** @Date : 2016-12-17-15.54 * @Author : Lweleth (SoungEarlf@gmail.com) * @Link : https://github.com/ * @Version : *…

LightOJ 1070 Algebraic Problem：矩阵快速幂 + 数学推导

题目链接:http://lightoj.com/volume_showproblem.php?problem=1070 题意: 给你a+b和ab的值,给定一个n,让你求a^n + b^n的值(MOD 2^64). 题解: a + b也就是a^1 + b^1,然后要从这儿一直推到a^n + b^n. 矩阵快速幂?o(￣▽￣)d 那么主要解决的就是如何从a^n + b^n推到a^(n+1) + b^(n+1). 下面是推导过程: 由于推a^(n+1) + b^(n+1)要用到a^n + b^n和a^…