202. Happy Number

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202. Happy Number

Description

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:

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Input: n = 19
Output: true
Explanation:
1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1

Example 2:

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Input: n = 2
Output: false

Constraints:

  • 1 <= n <= 2^31 - 1

Hints/Notes

  • 2025/01/02
  • The important thing is the proof
  • No solution from 0x3F

Solution

Language: C++

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class Solution {
public:
    bool isHappy(int n) {
        unordered_set<int> s;
        while (!s.contains(n) && n != 1) {
            s.insert(n);
            int next = 0;
            while (n) {
                int rev = n % 10;
                n /= 10;
                next += rev * rev;
            }
            n = next;
        }
        return n == 1;
    }
};