（LeetCode）Happy Number -- 寻找快乐数

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

Credits:

Special thanks to @mithmatt and @ts for
adding this problem and creating all test cases.

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解题分析：

题意就是寻找一个符合每一位的平方和相加最后等于 1 的数，被称为Happy Number.

方法一，循环判断，如果满足要求，则返回True,不满足，返回False, 判断循环的话，可以用Dict记录之前的，重复出现

视为循环，则返回False.

# -*- coding:utf-8 -*-
__author__ = 'jiuzhang'
class Solution(object):
    def isHappy(self, n):
        num_dict = {}
        while True:
            num_dict[n] = True
            sum = 0
            while(n > 0):
                sum += (n % 10) * (n % 10)
                n /= 10
            if sum == 1:
                return True
            elif sum in num_dict:
                return False
            else:
                n = sum

方法二 : 在方法一的基础上进行修改，先计算出100以下的Happy Number 。其余的在套用公式。

# -*- coding:utf-8 -*-
__author__ = 'jiuzhang'
'''
optimized code
'''
class Solution(object):
    def isHappy(self, n):
        happySet = set([1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97])
        while n > 99:
            n = sum([int(x) * int(x) for x in list(str(n))])
        return n in happySet