LeetCode上的原题,讲解请参见我之前的博客Factorial Trailing Zeroes. 解法一: int trailing_zeros(int n) { ; while (n) { res += n / ; n /= ; } return res; } 解法二: int trailing_zeros(int n) { ? : n / + trailing_zeros(n / ); } CareerCup All in One 题目汇总…

Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. Credits:Special thanks to @ts for adding this problem and creating all test cases. 这道题并没有什么难度,是让求一个数的阶乘末尾0的个数,也就是要找乘数中10的个数,…

Given an integer n, return the number of trailing zeroes in n!. Example 1: Input: 3 Output: 0 Explanation: 3! = 6, no trailing zero. Example 2: Input: 5 Output: 1 Explanation: 5! = 120, one trailing zero. Note: Your solution should be in logarithmic…

Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. 题目标签:Math 题目要求我们找到末尾0的数量. 只有当有10的存在,才会有0,比如 2 * 5 = 10; 4 * 5 = 20; 5 * 6 = 30; 5 * 8 = 40 等等,可以发现0 和 5 的联系. 所以这一题也是在问 n 里有多…

求阶乘末尾0的个数 (1)给定一个整数N,那么N的阶乘N!末尾有多少个0?比如:N=10,N!=3628800,N!的末尾有2个0. (2)求N!的二进制表示中最低位为1的位置. 第一题 考虑哪些数相乘能得到10,N!= K * 10M其中K不能被10整除,则N!末尾有M个0. 对N!进行质因数分解: N!=2X*3Y*5Z…,因为10=2*5,所以M与2和5的个数即X.Z有关.每一对2和5都可以得到10,故M=min(X,Z).因为能被2整除的数出现的频率要比能被5整除的数出现的频率高,所以M…

Given an integer n, return the number of trailing zeroes in n!. Example 1: Input: 3 Output: 0 Explanation: 3! = 6, no trailing zero. Example 2: Input: 5 Output: 1 Explanation: 5! = 120, one trailing zero. 考虑n!的质数因子.后缀0总是由质因子2和质因子5相乘得来的.如果我们可以计数2和5的个数…

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 /= ;…

Well, to compute the number of trailing zeros, we need to first think clear about what will generate a trailing 0? Obviously, a number multiplied by 10 will have a trailing 0 added to it. So we only need to find out how many 10's will appear in the e…

题目 Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. 分析 Note中提示让用对数的时间复杂度求解,那么如果粗暴的算出N的阶乘然后看末尾0的个数是不可能的. 所以仔细分析,N! = 1 * 2 * 3 * ... * N 而末尾0的个数只与这些乘数中5和2的个数有关,因为每出现一对5和2就会产生…

Write an algorithm which computes the number of trailing zeros in n factorial. Have you met this question in a real interview? Yes Example 11! = 39916800, so the out should be 2 Challenge O(log N) time LeetCode上的原题,请参见我之前的博客Factorial Trailing Zeroes.…

问题一解法:     我们知道求N的阶乘结果末尾0的个数也就是说我们在从1做到N的乘法的时候里面产生了多少个10, 我们可以这样分解,也就是将从0到N的数分解成因式,再将这些因式相乘,那么里面有多少个10呢? 其实我们只要算里面有多少个5就可以了?     因为在这些分解后的因子中,能产生10的可只有5和2相乘了,由于2的个数是大于5的个数的,因此 我们只要算5的个数就可以了.那么这个题目就是算这些从1到N的数字分解成因子后,这些因子里面 5的个数.   Python代码 def factori…

Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. (1) class Solution { public: int trailingZeroes(int n) { ; ; n / i; i *= ) { ans += n / i; } return ans; } }; (2) class Solu…

链接 Description 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 inte…

题目连接 /* £:离散数学. £:n!中2的个数>5的个数. £:2*5=10: */ #include<cstdio> #include<cstring> #include<iostream> using namespace std; typedef long long LL; int N; int main () { int T;scanf("%d",&T); while(T--) { scanf("%d",&…

Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. 此题是求阶乘后面零的个数. public class Solution { public int trailingZeroes(int n) { int t=0; while(n!=0){ n/=5; t+=n; } return t; } }…

2. Trailing Zeros[easy] Write an algorithm which computes the number of trailing zeros in n factorial. Have you met this question in a real interview? Yes Example 11! = 39916800, so the out should be 2 Challenge O(log N) time 解法一: class Solution { /*…

题目:利用递归方法求5!.分析:递归公式:n*factorial(n-1); public class Prog22 { public static void main(String[] args) { System.out.println(factorial(5)); } //递归求阶乘 public static long factorial(int n) { if(n==0||n==1) { return 1L; } return n*factorial(n-1); } } /*运行结果…

Factorial Time Limit: 1500MS   Memory Limit: 65536K Total Submissions: 15137   Accepted: 9349 Description The most important part of a GSM network is so called Base Transceiver Station (BTS). These transceivers form the areas called cells (this term…

172. 阶乘后的零 172. Factorial Trailing Zeroes 题目描述 给定一个整数 n,返回 n! 结果尾数中零的数量. LeetCode172. Factorial Trailing Zeroes 示例 1: 输入: 3 输出: 0 解释: 3! = 6,尾数中没有零. 示例 2: 输入: 5 输出: 1 解释: 5! = 120,尾数中有 1 个零. 说明: 你算法的时间复杂度应为 O(log n). Java 实现 递归 class Solution { publi…

Write an algorithm which computes the number of trailing zeros in n factorial. Have you met this question in a real interview? Yes Example 11! = 39916800, so the out should be 2 /* * param n: As desciption * return: An integer, denote the number of t…

问题描述: Write a program that will calculate the number of trailing zeros in a factorial of a given number. N! = 1 * 2 * 3 * ... * N Be careful 1000! has 2568 digits... For more info, see: http://mathworld.wolfram.com/Factorial.html Examples zeros(6) =…

题目: 尾部的零 设计一个算法,计算出n阶乘中尾部零的个数 样例 11! = 39916800,因此应该返回 2 挑战 O(logN)的时间复杂度 解题: 常用方法: 也许你在编程之美中看到,通过求能够被2 整除和能够被5整除个数的最小值就是答案,或者直接求能够被5整除的个数就是答案<能够被5整除的数显然比较小>,但是在这里,java python都试了,结果都会出现运行超时或者越界的问题. 维基百科中有如下计算方法: Java程序: class Solution { /* * param n…

Factorial Trailing Zeroes Given an integer n, return the number of trailing zeroes in n!. 题目意思: n求阶乘以后,其中有多少个数字是以0结尾的. 方法一: class Solution: # @return an integer def trailingZeroes(self, n): res = 0 if n < 5: return 0 else: return n/5+ self.trailingZe…

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…

数学题 172. Factorial Trailing Zeroes Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. (Easy) 分析:求n的阶乘中末位0的个数,也就是求n!中因数5的个数(2比5多),简单思路是遍历一遍,对于每个数,以此除以5求其因数5的个数,但会超时. 考虑到一个数n比他小…

Factorial Trailing Zeroes Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. Credits:Special thanks to @ts for adding this problem and creating all test cases. 对n!做质因数分解n!=2x*…

问题描述: 林记在做数学习题的时候,经常遇到这种情况:苦思冥想了很久终于把问题解出来,结果发现答案是0,久而久之林记在得到习题答案是0的时候就没有了做出一道难题的成就感.于是林记决定:以后出题,答案一定不能是0,例如求n!最低位非零数这样的习题就很不错了. 现在林记提出了一个更难一点的问题:求n!在K进制下的最低位非零数.其中K符合一些特殊的条件:K是由若干个互不相同的质数相乘得出来的,例如K=2,3,5,6,7,10…… 输入格式: 首先输入的第一行是一个整数Q,表示询问的个数. 接下来是Q个…

一天一道LeetCode 本系列文章已全部上传至我的github,地址:ZeeCoder's Github 欢迎大家关注我的新浪微博,我的新浪微博 欢迎转载,转载请注明出处 (一)题目 Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. (二)解题 题目大意:求n的阶乘算出来的数尾部有多少个0.如5…

题目: Given an integer n, return the number of trailing zeroes in n!. Note: Your solution should be in logarithmic time complexity. 思路: 题意是要求一个数字的阶乘,末尾有多少个0 要求是对数级别的时间,所以考虑用递归 分析一下,产生一个10,后面加0,找到所有的2*5,或者2的次方×5的次方,任何情况下因子2的个数永远大于5 所以只需要计算因子5的个数,(25*4 =…

题目:求1+2!+3!+...+20!的和分析:使用递归求解 0的阶乘和1的阶乘都为1 public class Prog21{ public static void main(String[] args){ long sum=0L; for(int i=1;i<=20;i++) { sum+=factorial(i); } System.out.println(sum); } //递归求阶乘 public static long factorial(int n) { if(n==0||n==1…