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

解题思路

判断中间结果是否出现重复即可

实现代码[C++]

//Rumtime:10ms
class Solution {
public:
    bool isHappy(int n) {
        set<int> nums;
        while(true)
        {
            if (n == 1)
            {
                return true;
            }
            if (nums.find(n) == nums.end())
            {
                nums.insert(n);
                int sum = 0;
                while(n)
                {
                    int x = n % 10;
                    sum += x * x;
                    n /= 10;
                }
                n = sum;
            }
            else
            {
                return false;
            }
        }
    }
};

实现代码[Python]

# Runtime:76ms
class Solution:
    # @param {integer} n
    # @return {boolean}
    def isHappy(self, n):
        SQUARE = dict([(c, int(c)**2) for c in "0123456789"])
        s = set()
        while n != 1 and n not in s:
            s.add(n)
            n = sum(SQUARE[d] for d in str(n))
        return n == 1