66 Plus One Leetcode Solution In Java Explained Step by Step

Plus One Problem in Java (Complete Explanation)

The Plus One problem is a common array-based question frequently asked in coding interviews and competitive programming platforms. It tests your understanding of array traversal, carry propagation, and edge case handling.

Problem Description – What is "Plus One"?

The Plus One problem asks you to increment a large integer represented as an array of digits by 1. Each element in the array represents a single digit, with the most significant digit at the front.

The challenge arises when digits result in a carry, such as when a digit is 9, which requires updating multiple positions or even expanding the array.

Example 1:

Input: [1, 2, 3]

Output: [1, 2, 4]

Explanation: The array represents 123, and adding 1 results in 124.

Example 2:

Input: [9, 9, 9]

Output: [1, 0, 0, 0]

Explanation: 999 + 1 becomes 1000, so the array size increases.

Key Challenges

• Carry propagation: Handling cases where digits become 10.
• Edge cases: Expanding the array when all digits are 9.
• Efficiency: Solving the problem in linear time.

Optimal Java Solution for Plus One

The most efficient approach is to traverse the array from right to left, handling carry as needed.

private static int[] getPlusOne(int[] digits) {

    for (int i = digits.length - 1; i >= 0; i--) {

        if (digits[i] < 9) {
            digits[i]++;
            return digits;
        }

        digits[i] = 0;
    }

    int[] newNumber = new int[digits.length + 1];
    newNumber[0] = 1;

    return newNumber;
}

Step-by-Step Breakdown

1. Traverse from Right to Left

We start from the least significant digit because that’s where the increment happens.

2. Digit Less Than 9

If a digit is less than 9, increment it and return the array immediately. No further carry is required.

3. Digit Equals 9

If the digit is 9, set it to 0 and carry the increment to the next digit.

4. All Digits Are 9

If all digits become 0, create a new array with one extra digit and set the first element to 1.

Time and Space Complexity

Time Complexity: O(n), where n is the number of digits.

Space Complexity: O(n) in the worst case when a new array is created.

Why This Solution Is Optimal

This solution minimizes unnecessary operations by stopping early when no carry is needed. It efficiently handles both normal and edge cases, making it ideal for coding interviews.

Conclusion

The Plus One problem may look simple, but it teaches essential concepts like carry handling and array manipulation. Mastering such problems improves your problem-solving skills and prepares you for more complex interview questions.

Practice similar variations to strengthen your understanding and build confidence for technical interviews.

Happy coding!