Plus One Leetcode Problem 66 [Python Solution]

In this blog post, we’re going to tackle a relatively straightforward LeetCode problem – the Plus One Leetcode Problem.

This problem falls under the “Math & Geometry” category and is classified as “Easy.” It’s often a go-to problem for those starting with algorithmic challenges.

The question revolves around incrementing a large integer represented as an array of digits.

So, let’s dive into it.

Problem Overview

Question: You are given a large integer represented as an integer array digits, where each digits[i] is the ith digit of the integer.

The digits are ordered from most significant to least significant in left-to-right order.

The large integer does not contain any leading 0’s.

Your task is to increment the large integer by one and return the resulting array of digits.

Example 1:

Input: digits = [1, 2, 3]
Output: [1, 2, 4]
Explanation: The array represents the integer 123. Incrementing by one gives 123 + 1 = 124. Thus, the result should be [1, 2, 4].

Example 2:

Input: digits = [4, 3, 2, 1]
Output: [4, 3, 2, 2]
Explanation: The array represents the integer 4321. Incrementing by one gives 4321 + 1 = 4322. Thus, the result should be [4, 3, 2, 2].

Example 3:

Input: digits = [9]
Output: [1, 0]
Explanation: The array represents the integer 9. Incrementing by one gives 9 + 1 = 10. Thus, the result should be [1, 0].

Constraints:

• 1 <= digits.length <= 100
• 0 <= digits[i] <= 9
• digits does not contain any leading 0’s.

Now that we understand the problem, let’s explore the various aspects of solving it efficiently.

Understanding the Constraints

Before diving into the solution, it’s crucial to understand the constraints imposed by the problem.

These constraints help us determine the range of inputs we need to consider and design our solution accordingly.

1. Size of the digits array (digits.length): The array can have a minimum length of 1 and a maximum length of 100. This means we need a solution that can handle arrays of varying sizes.
2. Value of each digit (digits[i]): Each digit can range from 0 to 9, inclusive.

We’ll need to consider the impact of this range on our solution, especially when dealing with the digit 9.

3. Leading Zeros: The problem specifies that the integer does not contain any leading 0’s.

This means that we don’t have to worry about removing leading zeros from the result, which simplifies our solution.

Now that we have a good grasp of the problem and its constraints, let’s explore the solution strategies.

Plus One LeetCode Problem Solution

1. Bruteforce Approach

The first approach that comes to mind is a straightforward bruteforce method.

We’ll start from the least significant digit (rightmost digit) and add 1 to it.

If the result is 10, we set that digit to 0 and move to the next digit to the left, carrying over the 1. We continue this process until we either finish processing all digits or don’t have a carry anymore.

Here’s the Python code for this approach:

def plusOne(self, digits: List[int]) -> List[int]:
        carry = 1  # Start with a carry of 1
        i = 0  # Initialize the index for the rightmost digit
        digits = digits[::-1]  # Reverse the array to start from the right

        while carry:
            if i < len(digits):
                if digits[i] == 9:
                    digits[i] = 0
                else:
                    digits[i] += 1
                    carry = 0
            else:
                digits.append(carry)
                carry = 0
            i += 1

        return digits[::-1]  # Reverse the array back to the original order

This code takes care of the problem by incrementing the digits while handling carry as needed.

It’s a simple and intuitive solution, which makes it a good choice for beginners.

The time complexity of this approach is O(n), where n is the length of the digits array, and the space complexity is O(1).

Time and Space Complexity

Let’s analyze the time and space complexity of our bruteforce solution:

• Time Complexity: The time complexity of this solution is O(n), where n is the length of the digits array.

We iterate through the array once, performing constant-time operations, making it a linear time solution.

• Space Complexity: The space complexity is O(1) because we only use a constant amount of extra space, regardless of the size of the input array.

We modify the digits array in place without using any additional data structures.

Reasoning Behind Our Approach

The reasoning behind this approach is relatively straightforward.

We start from the rightmost digit, which is the least significant digit, and work our way to the left.

At each step, we consider the current digit, add the carry (which starts as 1), and update the digit and carry accordingly.

If the current digit is 9, we set it to 0 and carry over 1, just like how you’d carry over in manual addition.

If the current digit is not 9, we simply add 1 to it, set the carry to 0, and stop because we don’t need to carry anymore.

If we run out of digits before the carry becomes 0, we append the carry as a new digit.

Finally, we reverse the array to restore the original order of digits, and we have our result.

This approach is efficient and covers all edge cases, including the case where the input contains only 9s, leading to the creation of a new digit.

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Conclusion

In this blog post, we’ve explored the LeetCode problem Plus One We’ve walked through the problem statement, understood the constraints, and presented a Python solution using a bruteforce approach.

This solution efficiently handles various scenarios and edge cases, making it suitable for solving the problem.

If you’re a beginner in the world of algorithmic challenges, this problem is a great starting point.

It not only tests your coding skills but also reinforces your understanding of addition and carrying over in a digital number system.

Feel free to check out the question on LeetCode and try the solution for yourself.

Don’t forget to practice and explore more problems to enhance your problem-solving skills.

If you have any questions or suggestions, please share them in the comments section below.

Happy coding!