Check if a number is a “happy number”, constant-space algorithm, with visualization of the algorithm. (https://en.wikipedia.org/wiki/Happy_number)

happy.cpp

#include <iostream>
#include <vector>
#include <iomanip>

int sumSqDigits(int n)
{
    int result = 0;
    while(n > 0)
    {
        int digit = n % 10;
        result += digit * digit;
        n /= 10;
    }
    return result;
}

class HappyPointer
{
public:
    HappyPointer() = default;
    HappyPointer(int initial, size_t index) : n(initial), i(index) {}
    HappyPointer& advance()
    {
        n = sumSqDigits(n);
        i++;
        return *this;
    }

    int n;
    size_t i;
};

class Happy
{
public:
    Happy(int n) : initial(n), history(1, n) {}

    bool isHappy()
    {
        slow = HappyPointer(initial, 0);
        fast = HappyPointer(initial, 0);
        fast.advance();

        while(true)
        {
            expandHistory();
            print();
            if(slow.n == 1 || fast.n == 1)
            {
                return true;
            }
            if(slow.n == fast.n)
            {
                return false;
            }
            slow.advance();
            fast.advance();
            expandHistory();
            fast.advance();
        }
    }

private:
    void print() const
    {
        for(size_t i = 0; i < history.size(); i++)
        {
            std::cout << std::setw(3) << history[i];
            if (i != history.size() - 1)
            {
                std::cout << " -> ";
            }
        }
        std::cout << std::endl;
        std::cout << std::string(slow.i * 7, ' ') << "^";
        std::cout << std::string((fast.i - slow.i) * 7, ' ') << "*";
        std::cout << std::endl;
    }

    void expandHistory()
    {
        if(fast.i >= history.size())
        {
            history.resize(fast.i + 1);
        }
        history[slow.i] = slow.n;
        history[fast.i] = fast.n;
    }

    int initial;
    std::vector<int> history;
    HappyPointer slow;
    HappyPointer fast;
};

int main()
{
    Happy h(8);
    std::cout << h.isHappy() << std::endl;
}