【刷题-LeetCode】202. Happy Number

1. Happy Number

Write an algorithm to determine if a number n 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.

Return True if n is a happy number, and False if not.

Example:

Input: 19
Output: true
Explanation:
12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1

对于happy number的操作，最终的结局可能是：

• 收敛到1
• 陷入循环
• n不断增大直到无穷大

但是第三种情况肯定不会发生

Digits	Largest	Next
1	9	81
2	99	162
3	999	243
4	9999	324
13	9999999999999	1053

从表中可以看出，三位数最大的下一位是243，四位数最大的下一位小于999，因此最终也会小于243

解1 hashset判断是否出现环

class Solution {
public:
    bool isHappy(int n) {
        unordered_map<int, bool>mp;
        while(!mp[n]){
            mp[n] = true;
            n = happy(n);
            if(n == 1)return true;
        }
        return false;
    }
    int happy(int n){
        int res = 0;
        while(n){
            int tmp = n % 10;
            res += tmp * tmp;
            n /= 10;
        }
        return res;
    }
};

解2 Floyd环检测算法（龟兔赛跑）

class Solution {
public:
    unordered_map<int, int>mp;
    bool isHappy(int n) {
        int faster = happy(happy(n)), slower = happy(n);
        while(faster != 1 && faster != slower){
            faster = happy(happy(faster));
            slower = happy(slower);

        }
        return faster == 1;
    }
    int happy(int n){
        if(mp[n])return mp[n];
        int res = 0;
        while(n){
            int tmp = n % 10;
            res += tmp * tmp;
            n /= 10;
        }
        return mp[n] = res;
    }
};