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11. Happy Number

easyAsked at N26

Determine if a number eventually reaches 1 when repeatedly replaced by the sum of squares of its digits. N26 uses it to gauge cycle-detection instinct before harder ACH retry-loop questions.

By Sam K., Founder, InterviewChamp.AI · Last verified

Problem

A happy number is defined by replacing the number with the sum of squares of its digits and repeating until it reaches 1 or loops endlessly. Return true if n is happy, otherwise false.

Constraints

  • 1 <= n <= 2^31 - 1

Examples

Example 1

Input
n=19
Output
true

Example 2

Input
n=2
Output
false

Approaches

1. Hash set cycle detection

Track every seen value; return false when one repeats.

Time
O(log n)
Space
O(log n)
const seen = new Set();
while (n !== 1 && !seen.has(n)) {
  seen.add(n);
  n = [...String(n)].reduce((s,d)=>s+d*d,0);
}
return n === 1;

Tradeoff:

2. Floyd's tortoise and hare

Two pointers running at different speeds detect any cycle in O(1) memory. If they meet at 1 it is happy; otherwise it is a non-1 cycle.

Time
O(log n)
Space
O(1)
function isHappy(n) {
  const next = x => [...String(x)].reduce((s,d)=>s+d*d,0);
  let slow = n, fast = next(n);
  while (fast !== 1 && slow !== fast) {
    slow = next(slow);
    fast = next(next(fast));
  }
  return fast === 1;
}

Tradeoff:

N26-specific tips

N26 likes Floyd's answer because it mirrors how their ACH retry workers detect a payment stuck in a bounce-loop without holding state in Redis.

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