LeetCode 202 Happy number

最新推荐文章于 2019-10-08 22:22:07 发布

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本文介绍了一种用于判断一个正整数是否为快乐数的算法。快乐数是指通过反复替换该数为它每个位数的平方和，最终能够得到1的数字。文章详细解释了判断流程，并提供了一个具体的例子，如数字19如何被确认为快乐数。

Write an algorithm to determine if a number is "happy".

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

Example: 19 is a happy number

12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1
本来以为出现重复就能判断是否进入死循环（即：判断digit root的平方和是否和输入的n重复）但是遇到了特殊的2 ，会进入2 ，4,16,37,58,89,145,42,20,4,16,37...的循环就加入了一个循环次数的限制最后AC.

class Solution {
public:
int length(int n){
		int length = 0;
		while (n != 0){
			length++;
			n = n / 10;
		}
		return length;
	}
	int digital_root(int n,int &sum)
	{
		int Length = length(n);
		int tail;
		sum = 0;
		while (Length--)
		{
			tail = n % 10;
			n /= 10;
			sum = tail*tail + sum;
		}
		return sum;
	}

    bool isHappy(int n){
        int add=0;
        int times=0;
	  digital_root(n,add);
	  while (add != 1)
	  {
		   digital_root(add, add);
		  if (add == n||times==9999)
			  return false;
	times++;
	 
	  }
	  return true;
    }
    
};