题目描述:

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

最直观的解法可以使用hash表.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
class Solution {
public:
    bool isHappy(int n) {
        unordered_set<int> s;
        s.insert(n);
        int t = n;
        while(t != 1){
            long long sum = 0;
            while(t > 0){
                sum += ((t % 10) * (t % 10));
                t /= 10;
            }
            t = sum;
            if(s.count(t)) return false;
            else s.insert(t);
        }
        return true;
    }
};

但是仔细想想, 输入数据最多为一个十位数, 每一位数字的平方最多为81, 因此中间过程所产生的数肯定落在[1,810]之间, 我们只要开一个较大的数组来保存某个数是否出现过就可以了.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
class Solution {
public:
    bool isHappy(int n) {
        vector<int> s(1000, 0);
        int t = n;
        while(t != 1){
            int sum = 0;
            while(t > 0){
                sum += ((t % 10) * (t % 10));
                t /= 10;
            }
            t = sum;
            if(s[t]) return false;
            else s[t] = 1;
        }
        return true;
    }
};