LeetCode172 Factorial Trailing Zeroes. LeetCode258 Add Digits. LeetCode268 Missing Number

Posted wangxiaobao的博客

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了LeetCode172 Factorial Trailing Zeroes. LeetCode258 Add Digits. LeetCode268 Missing Number相关的知识,希望对你有一定的参考价值。

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比他小能被5整除的数的个数是一定的(n / 5),由此再考虑能被25整除,125整除的数的个数,得到如下算法:

代码:

 1 class Solution {
 2 public:
 3     int trailingZeroes(int n) {
 4         int sum = 0;
 5         while (n > 0) {
 6             sum += (n / 5);
 7             n /= 5;
 8         }
 9         return sum;
10     }
11 };

 

258. Add Digits

Given a non-negative integer num, repeatedly add all its digits until the result has only one digit.

For example:

Given num = 38, the process is like: 3 + 8 = 111 + 1 = 2. Since 2 has only one digit, return it. (Easy)

Follow up:
Could you do it without any loop/recursion in O(1) runtime?

 

 

分析:

考虑到

ab % 9 = (9a + a + b) % 9 = (a + b) % 9;

abc % 9 = (99a + 9 b + a + b + c) % 9 = (a + b + c) % 9;

所以求到其只有个位数位置即用其mod 9即可,考虑到被9整除的数应该返回9而非0,采用先减一再加一方式处理。

代码:

1 class Solution {
2 public:
3     int addDigits(int num) {
4         if (num == 0) {
5             return 0;
6         }
7         return (num - 1) % 9 + 1;
8     }
9 };

 

268. Missing Number

Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array.

For example,
Given nums = [0, 1, 3] return 2. (Medium)

 

分析:

采用先求和(前n项和),再将求和结果与数组和相减的方法,求得差哪个数

代码:

 1 class Solution {
 2 public:
 3     int missingNumber(vector<int>& nums) {
 4         int n = nums.size();
 5         int sum1 = n * (n + 1) / 2;
 6         int sum2 = 0;
 7         for (int i = 0; i < nums.size(); ++i) {
 8             sum2 += nums[i];
 9         }
10         return sum1 - sum2;
11     }
12 };

 

 


以上是关于LeetCode172 Factorial Trailing Zeroes. LeetCode258 Add Digits. LeetCode268 Missing Number的主要内容,如果未能解决你的问题,请参考以下文章

Leetcode 172 Factorial Trailing Zeroes

Java [Leetcode 172]Factorial Trailing Zeroes

leetcode 172. Factorial Trailing Zeroes

leetcode-172-Factorial Trailing Zeroes

LeetCode 172. 阶乘后的零(Factorial Trailing Zeroes)

LeetCode 172 Factorial Trailing Zeroes(阶乘后的零)(*)