Brooke

一、題目

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.
• 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.

Return true if n is a happy number, and false if not.

 

Example 1:

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

Example 2:

Input: n = 2 Output: false

 

Constraints:

• 1 <= n <= 231 - 1

 

二、程式作法

public class Solution
{
    public bool IsHappy(int n)
    {
        HashSet<int> set = new HashSet<int>();

        while (n != 1)
        {
            set.Add(n);
            int sum = 0;
            while (n > 0)
            {
                sum += (int)Math.Pow(n % 10, 2);
                n /= 10;
            }
            n = sum;
            if (set.Contains(n))
                return false;
        }
        return true;
    }
}

 

三、思路筆記

題目要的是針對一整數 n 將其每位數字個別做平方後相加，其得出的整數如果等於 1 時，則為 happy number，

如否，則將其結果繼續上一流程處理後，再來判斷其得出的整數是否為 1。

看到題目一開始就直接愣住，看了相關參考解時，其解法也有好幾種，我就選我能理解的作法來做。

在做 i 次每位數字個別做平方後相加後，會發現其一連串結果會循環出現而跳不出迴圈，

這時可知得不出 happy number。