LeetCode 202 Happy number

 

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
• 本來以爲出現重複就能判斷是否進入死循環（即：判斷digit root的平方和是否和輸入的n重複） 但是遇到了特殊的2 ，會進入2 ，4,16,37,58,89,145,42,20,4,16,37...的循環  就加入了一個循環次數的限制 最後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;
    }
    
};