1. 題目

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:

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Input: 19
Output: true

Explanation:

  • 1 * 1 + 9 * 9 = 82
  • 8 * 8 + 2 * 2 = 68
  • 6 * 6 + 8 * 8 = 100
  • 1 * 1 + 0 * 0 + 0 * 0 = 1

2. 思路

因為不是Happy number的話會進入迴圈 (loops endlessly in a cycle) 所以可想到 floyd’s cycle detection

3.解題

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int check_happy(int target)
{    
    int sum = (target % 10)*(target % 10);    
    /* Chech digit */
    while ((target / 10) > 0) {              
        target /= 10;
        sum += (target % 10)*(target % 10);
    }
    
    return sum;
}

bool isHappy(int n)
{
    int fast = n, slow = n;
    do {  
        /* slow calculate once per round*/
        slow = check_happy(slow);
        /* fast calculate two times per round*/
        fast = check_happy(fast);
        fast = check_happy(fast);
        if (slow == 1 || fast == 1)        
            return true;        
    } while (slow != fast);  

    return  false;
}