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

按照上述规则，如果能够满足上述规则得数那么就是一个Happy Number

 

用一个set来记录已经出现过得数，避免死循环

public class Solution {
    
    
    public boolean isHappy(int n) {
        Set<Integer> set = new HashSet();
        return isHappyNum(n, set);    
    }
    
    public boolean isHappyNum(int n, Set set){
        if (set.contains(n)){
            return false;
        }
        set.add(n);
        int num = 0;
        while (n != 0){
            num += (n % 10) * (n % 10);
            n /= 10;
        }
        if (num == 1){
            return true;
        } else {
            return isHappyNum(num, set);
        }
    }
}

2、使用O（1）的空间复杂度。很巧妙，如果会出现循环的情况，那么x和y一定会相遇，也就一定会跳出循环。

 

public class Solution {
    public boolean isHappy(int n) {
        int x = n;
        int y = n;
        while(x>1){
            x = cal(x) ;
            if(x==1) return true ;
            y = cal(cal(y));
            if(y==1) return true ;

            if(x==y) return false;
        }
        return true ;
    }
    public int cal(int n){
        int x = n;
        int s = 0;
        while(x>0){
            s = s+(x%10)*(x%10);
            x = x/10;
        }
        return s ;
    }
}