http://lightoj.com/volume_showproblem.php?problem=1138 Trailing Zeroes (III) Time Limit:2000MS     Memory Limit:32768KB     64bit IO Format:%lld & %llu Submit Status Practice LightOJ 1138 Description You task is to find minimal natural number N, so t…

1138 - Trailing Zeroes (III)   You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input sta…

题目链接:http://lightoj.com/volume_showproblem.php?problem=1138 题意:给你一个数n,然后找个一个最小的数x,使得x!的末尾有n个0:如果没有输出impossible 可以用二分求结果,重点是求一个数的阶乘中末尾含有0的个数,一定和因子5和2的个数有关,因子为2的明显比5多,所以我们只需要求一个数的阶乘的因子中一共有多少个5即可; LL Find(LL x) { LL ans = ; while(x) { ans += x/; x /= ;…

题目链接:http://lightoj.com/volume_showproblem.php? problem=1138 题意:问 N. 末尾 0 的个数为 Q 个的数是什么? 解法:二分枚举N,由于0是由5×2 出现的,2的个数比5多故计算5的个数就可以. 代码: #include <stdio.h> #include <ctime> #include <math.h> #include <limits.h> #include <complex>…

题目链接:http://lightoj.com/volume_showproblem.php?problem=1138 题目就是给你一个数表示N!结果后面的0的个数,然后让你求出最小的N. 我们可以知道N!里5(包括5的倍数)的个数比2(包括2的倍数)的个数多,所以1对应5!,2对应10!... 而末尾0的个数与N成正比,1e8对应的N最大是400000015.我用二分查询N对应末尾0的个数,要是计算出来末尾0的个数比给你的数还大就L=mid+1,否则就R=mid. #include <iost…

就是统计5,然后当时因为发现最多有8000w个5的倍数,然后8000w/100,是80w,打表,二分找 然后我看网上的都是直接二分找,真是厉害 #include <cstdio> #include <iostream> #include <ctime> #include <vector> #include <cmath> #include <map> #include <queue> #include <algori…

题目描述: 假设有一个数n,它的阶乘末尾有Q个零,现在给出Q,问n最小为多少? 解题思路: 由于数字末尾的零等于min(因子2的个数,因子5的个数),又因为2<5,那么假设有一无限大的数n,n=2^x=5^y,可知x<<y. 所以我们可以直接根据因子5的个数,算阶乘末尾的零的个数.1<=Q<=10^8,所以可以用二分快速求解. 代码: #include<cstdio> #include<cstring> #include<iostream>…

1138 - Trailing Zeroes (III) PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. F…

1138 - Trailing Zeroes (III)   PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N.…

1138 - Trailing Zeroes (III) problem=1138"> problem=1138&language=english&type=pdf">PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactl…

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input starts with an integer T (≤ 10000)…

1138 - Trailing Zeroes (III)   PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N.…

1138 - Trailing Zeroes (III) PDF (English) problem=1138" style="color:rgb(79,107,114)">Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the…

Trailing Zeroes (III)   PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For ex…

/** 题目:Trailing Zeroes (III) 链接:https://vjudge.net/contest/154246#problem/N 题意:假设n!后面有x个0.现在要求的是,给定x,要求最小的n: 思路:判断一个n!后面有多少个0,通过n/5+n/25+n/125+... */ #include<iostream> #include<cstring> #include<cstdio> #include<algorithm> #includ…

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input starts with an integer T (≤ 10000)…

Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. In…

其实有几个尾零代表10的几次方但是10=2*510^n=2^n*5^n2增长的远比5快,所以只用考虑N!中有几个5就行了 代码看别人的: https://blog.csdn.net/qq_42279796/article/details/88218061…

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input starts with an integer T (≤ 10000)…

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input starts with an integer T (≤ 10000)…

嗯... 题目链接:https://vjudge.net/contest/318956#problem/E 这道题是二分答案+数论,但首先是数论,否则你不知如何二分... 首先关于一个阶乘的结果最后会出现0(即10),肯定是由2 * 5所造成的,而对于正整数 N,在[0, N]范围内,质因子中含有 2 的总是会比质因子含有 5 的要多.所以,只要需要知道质因数含有 5 的数字有多少个,即可知道末尾连续出现 0 的个数有多少... 然后我们进行二分答案,从1~5e8 + 5(一定要足够大!)进行二…

题目链接:http://lightoj.com/volume_showproblem.php?problem=1090 题意:给你四个数 n, r, p, q 求C(n, r) * p^q的结果中末尾0的个数;(1<=n, r, p, q <= 10^6, r ≤ n) 要求末尾0的个数,一定和2和5有关,例如num1 * num2结果中末尾0的个数可以表示成min(num1中2的个数+num2中2的个数, num1中5的个数+num2中5的个数); 对于C(n, r)中0的2的个数可以写成f…

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input starts with an integer T (≤ 10000)…

题目连接: http://www.lightoj.com/volume_showproblem.php?problem=1090 题目大意: 给出n,r,p,q四个数字1<=n,r,p,q<=1000000,求出的末尾有几个0? 解题思路: 是不是一下子懵了,数字好大,复杂度好高,精度怎么办···············,就问你怕不怕? 其实都是纸老虎啦,因为10的因子只有2和5,所以可以打表保存从1到当前数字相乘的积中分别含有2,5的个数.然后算出中分别含有2,5的个数,取其最小就是结果.(…

题目链接:https://cn.vjudge.net/problem/ 题意 找一个最小的正整数n 使得n!有a个零 思路 就是有几个因数10呗 考虑到10==2*5,也就是说找n!因数5有几个 数据量略大(N<=1e8),打表之类的O(N)算法是直接不可以 分析到这里,可能的算法也就是二分了 找了找很久规律,发现可以有O(log5(n))的方法确定n!的因数5的个数 于是有二分 代码 // binary search // [f(m)<n, f(m)=n, f(m)>n] // [l,…

We know what a base of a number is and what the properties are. For example, we use decimal number system, where the base is 10 and we use the symbols - {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. But in different bases we use different symbols. For example in b…

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail. Input Input starts with an integer T (≤ 10000)…

题意:10000组数据 问一个数n[1,1e12] 在k进制下有末尾0的k的个数. 思路:题意很明显,就是求n的因子个数,本来想直接预处理欧拉函数,然后拿它减n就行了.但注意是1e12次方法不可行.而一般的求因子显然也太慢,所有要想另一个办法.已知任意数可以分解成几个质因数幂的乘积,所以求出n所有的质因数和它的指数再进行排列组合就可以得到答案了. #include <stdio.h> #include <iostream> #include <string.h> #in…

1138 - Trailing Zeroes (III)   PDF (English) Statistics Forum Time Limit: 2 second(s) Memory Limit: 32 MB You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N.…

原题描述: 原题地址: Factorial Trailing Zeroes 题目描述很直接, 给出一个整数N, 求这个N的阶乘后尾有几个零.(要求O(logN)时间复杂度) 个人思路: 一开始,最简单的思维就是直接求要知道, n!的增长速度, 比O(n^2)还要大, 对于32位整型来说, 当N=13的时候, 数据就已经开始溢出了, 好吧, 就算使用long型也是到N=21时,表示数位也不够用了,        那么, 这条路其实是走不通的, (就算考虑使用大数阶乘解决方案, 但这背离了这道题目的…