HDOJ 2114 Calculate S(n)（找周期）

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HDOJ 2114 Calculate S(n)（找周期）

Problem Description Calculate S(n). S(n)=1^3+2^3 +3^3 +--+n^3 . Input Each line will contain one integer N(1 < n < 1000000000). Process to end of file. Output For each case, output the last four dights of S(N) in one line. Sample Input 1 2 Sample Ou…

What day is that day?（快速幂，打表找周期,或者求通项公式）

有些题怎么都解不出来,这时候可以打表,找规律,求通项公式等,这些方法让人拍手叫绝,真不错…… Description It's Saturday today, what day is it after 11 + 22 + 33 + ... + NN days? Input There are multiple test cases. The first line of input contains an integer T indicating the number of test cases.…

A - Number Sequence（矩阵快速幂或者找周期）

Description A number sequence is defined as follows: f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7. Given A, B, and n, you are to calculate the value of f(n). Input The input consists of multiple test cases. Each test case contains…

HDU 2114 Calculate S(n)

http://acm.hdu.edu.cn/showproblem.php?pid=2114 Problem Description Calculate S(n). S(n)=13+23 +33 +......+n3 . Input Each line will contain one integer N(1 < n < 1000000000). Process to end of file. Output For each case, output the last four dig…

hdu 2114 Calculate S(n) 数论(简单题)

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=2114 自己对数论一窍不通啊现在,做了一道水题,贴出来吧...主要是让自己记住这个公式: 前n项和的立方公式为 : s(n)=(n*(n+1)/2)^2; 前n项和的平方公式为:s(n)=n*(n+1)(2*n+1)/6; 代码: #include<iostream> #include<cstdlib> #include<cstdio> using namespace s…

MT【104】高斯函数找周期

分析:$t(n)=n-[\frac{n}{2}]-[\frac{n}{3}]-[\frac{n}{6}]$的周期为6,故 $\sum\limits_{n=1}^{2014}(n-t(n))=\sum\limits_{n=1}^{2014}n-2014=2027091$ 评:在证明著名的埃尔米特恒等式:$\sum\limits_{k=0}^{n-1}[x+\frac{k}{n}]=[nx],x\ge0 ,n\in N^+$时也是用了同样的技巧.提示:构造$t(n)=\sum\limits_{k=0…