技术

202.happy number

  • 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
3
4
1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1

解析

  • 翻译： 判断一个正整数是否为一个happy-number，一个正整数各位的平方和代替次正整数，不断迭代，如果迭代出1，则为happy-number，否则不是而且会出现无限循环。
  • 思路：写一个函数分离正整数的各位，计算平方和并返回，主函数中需要有两类迭代，一类迭代每次迭代一次，一类迭代两次，这两如果出现无限重复循环肯定OK；循环结束的条件为迭代结果为1（这就是happy number）或者两类迭代结果相等（出现无限重复循环，不是happy number）。

C/C++

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
int sum(int n) {
    int i=0;
    int sum=0;
    while(n) {
        i=n%10;
        n=n/10;
        sum=sum+i*i;
    }
    return sum;
}

bool isHappy(int n) {
    int temp=n;
    bool overflag=true;
    bool flag=true;
    int temp1= temp;   
    while(overflag) {
      temp = sum(temp); 
      temp1=sum(temp1);
      temp1=sum(temp1);
      if(temp1==1) {       
          flag=true;
          break;
      }
      if(temp==temp1) {   
          flag=false;
          break;
      }
    }
    return flag;
}

Python

Java