Happy Number

📌 Definition:

📖 Detailed Explanation:

Repeatedly transform the number into the sum of its squared digits. Because unhappy numbers fall into a cycle, detect repetition with a seen-set (or Floyd's slow/fast on the transform). Stop when you reach 1 (happy) or revisit a number (unhappy). Effectively O(log n) work per step.

💻 Solutions:

• Java
• JavaScript
• Python

public static boolean isHappy(int n) {
    Set<Integer> seen = new HashSet<>();
    while (n != 1 && !seen.contains(n)) {
        seen.add(n);
        int sum = 0;
        while (n > 0) { int d = n % 10; sum += d * d; n /= 10; }
        n = sum;
    }
    return n == 1;
}

function isHappy(n) {
  const seen = new Set();
  while (n !== 1 && !seen.has(n)) {
    seen.add(n);
    let sum = 0;
    while (n > 0) { const d = n % 10; sum += d * d; n = Math.floor(n / 10); }
    n = sum;
  }
  return n === 1;
}

def is_happy(n):
    seen = set()
    while n != 1 and n not in seen:
        seen.add(n)
        n = sum(int(d) ** 2 for d in str(n))
    return n == 1

🔑 Key Points:

• Transform = sum of squared digits
• Unhappy numbers form a cycle
• Detect cycles with a set or slow/fast pointers
• Stop at 1 (happy) or a repeat (unhappy)

🌍 Real-World Example: