http://www.spoj.com/problems/FACVSPOW/ 求解n! > a^n最小的整数n 对于有n!和a^n的东西,一般是取ln 然后就是求解 (ln(1) + ln(2) + .... + ln(n)) / n > ln(a)的最小整数n 发现左边的函数单调,所以可以预处理出来,右边最大值是ln(1e6) 所以预处理5e6个. #include <cstdio> #include <cstdlib> #include <cstring>…

Consider two integer sequences f(n) = n! and g(n) = an, where n is a positive integer. For any integer a > 1 the second sequence is greater than the first for a finite number of values. But starting from some integer k, f(n) is greater than g(n) for…

Counting trailing 0s of n! It is not very hard to figure out how to count it - simply count how many 5s. Since even numbers are always more than 5s, we don't have to consider even numbers. But counting 5, is tricky. Naive method is quite slow - I got…

[SPOJ]Power Modulo Inverted(拓展BSGS) 题面 洛谷 求最小的\(y\) 满足 \[k\equiv x^y(mod\ z)\] 题解 拓展\(BSGS\)模板题 #include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> #include<cmath> #include<algorithm> #include<set…

「SPOJ 3105」Power Modulo Inverted 传送门 题目大意: 求关于 \(x\) 的方程 \[a^x \equiv b \;(\mathrm{mod}\; p) \] 的最小自然数解,不保证 \(a,p\) 互质 如果保证 \(a,p\) 互质,那么可以直接使用 \(\texttt{BSGS}\) 算法通过本题. 对于这道题目,我们考虑将式子变形 令 \(t=\gcd(a,p)\),则有 \[\frac{a}{t}a^{x-1} \equiv \frac{b}{t} \;…

Factorial numbers are getting big very soon, you'll have to compute the number of divisors of such highly composite numbers. Input The first line contains an integer T, the number of test cases.On the next T lines, you will be given two integers N an…

By property of mod operations , we can simply use Divide and Conquer + Recursion to solve it. Reference: https://www.khanacademy.org/math/applied-math/cryptography/modarithmetic/a/modular-exponentiation My Ruby version is: DIV = 20 def ferma(x, y, n)…

此课程(MOOCULUS-2 "Sequences and Series")由Ohio State University于2014年在Coursera平台讲授. PDF格式教材下载 Sequences and Series 本系列学习笔记PDF下载(Academia.edu) MOOCULUS-2 Solution Summary Let $(a_n)$ be a sequence of real numbers starting with $a_0$. Then the power…

2616: SPOJ PERIODNI Time Limit: 10 Sec  Memory Limit: 128 MBSubmit: 128  Solved: 48[Submit][Status][Discuss] Description Input 第1行包括两个正整数N,K,表示了棋盘的列数和放的车数. 第2行包含N个正整数,表示了棋盘每列的高度. Output 包括一个非负整数,表示有多少种放置的方案,输出答案mod 1000000007后的结果即可. Sample Input 5 2…

Rotate Array 本题目收获: 题目: Rotate an array of n elements to the right by k steps. For example, with n = 7 and k = 3, the array [1,2,3,4,5,6,7] is rotated to [5,6,7,1,2,3,4]. 思路: 我的思路:新建一个数组存放旋转后的内容,但是怎么把原数组的内容存放在数组中,不清楚. leetcode/discuss思路: 思路一:新建数组,复制原…