Happy Number Problem & Solution

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.

See the happy number problem on LeetCode.

C++ Solution

#pragma GCC optimize("Ofast")
#pragma GCC optimization("unroll-loops")

static const int _=[](){std::ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);return 0;}();

class Solution {
  bool isHappy(int n) {
    int slow = happy(n);
    int fast = happy(slow);

    while (slow != fast) {
      slow = happy(slow);
      fast = happy(happy(fast));

    return slow == 1;

  int happy(int n) {
    int sum = 0;

    while (n > 0) {
      sum += pow(n % 10, 2);
      n /= 10;

    return sum;

Start Here

Many paths, there are. Follow yours, you must.