Happy Number: the idea to remember.

The core insight

Track generated values until reaching one or repeating a previously seen state.

Why it works

The digit square sequence eventually repeats within a finite bounded range; a repeated nonone state can never reach one later.

The mistake to avoid

Reset the digit square sum for each replacement rather than accumulating across rounds.

Commented Java solution

Use java.util.* imports and a surrounding solution class. Tree snippets assume the standard TreeNode definition; linked lists use ListNode and Clone Graph uses a Node with val and neighbors; Copy Random List uses Node with val, next and random. Read the input assumptions above.

// Java reference adapted from neetcode-gh/leetcode (MIT).
// Track generated values until reaching one or repeating a previously seen state.
public boolean isHappy(int n) {
    if (n == 1 || n == -1) {
        return true;
    }

    Set<Integer> visit = new HashSet<Integer>();


    while (!visit.contains(n)) {
        visit.add(n);

        n = sumOfSquare(n);

        if (n == 1) return true;
    }

    return false;
}

public int sumOfSquare(int n) {
    int output = 0;

    while (n != 0) {
        int digit = n % 10;
        digit = digit * digit;
        output += digit;
        n = n / 10;
    }

    return output;
}

Java reference adapted from neetcode-gh/leetcode · MIT license

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