Leetcode——202. Happy Number

Question

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

1^2 + 9^2 = 828^2 + 2^2 = 686^2 + 8^2 = 1001^2 + 0^2 + 0^2 = 1

Answer

Properity1
不是快乐数的数称为不快乐数（unhappy number），所有不快乐数的数位平方和计算，最後都会进入 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 的循环中。

class Solution {public:    bool isHappy(int n) {        if(n<=0) return false;        while(1)        {            if(n==1) return true;            if(n==4) return false;            int sum_n=0;            while(n)            {                sum_n=sum_n+(n%10)*(n%10);                n=n/10;            }            n=sum_n;        }    }};

next solution!

class Solution {public:    bool isHappy(int n) {        int slow,fast;        slow=fast=n;        do{            slow=next(slow);            fast=next(next(fast));            if(fast==1) return 1;        }while(slow!=fast);        return 0;    }private:    int next(int n)    {       int sum_n=0;        while(n)        {            sum_n=sum_n+(n%10)*(n%10);            n=n/10;        }        return sum_n;    }};