Plus One LeetCode

Key takeaways:
The Plus One problem requires adding one to an integer represented as an array of its digits.
The solution operates in $O(n)$ time complexity, where $n$ is the number of digits, as each digit is processed once from the end of the array. The space complexity can go to $O(n)$ in cases where the array length increases (e.g., [9, 9, 9, 9, 9]).
The problem helps understand and master array traversal and carry operations.

What is the LeetCode Plus One problem?

The Plus One problem involves an array representing a large integer, where each element corresponds to a digit of the integer. The task is to increment this integer by 1 and return the resulting array of digits. This problem is essential for your preparation for coding interviews as it tests your ability to manipulate arrays efficiently, handle arithmetic operations, and deal with edge cases such as carrying over digits in large integers.

Problem statement

You are given an integer array nums where each element corresponds to a digit of a large integer. The digits are ordered from most significant to least significant, and your task is to add 1 to the number and return the modified array.

Note: The The integer has no leading zeros.

Constraints:

$1\leq$ nums.length $\leq 10^{2}$
$0\leq$ nums[i] $\leq 9$

Let’s take a look at a few examples to get a better understanding of the problem statement:

Solution

The solution to the Plus One problem involves traversing an integer array from the last element to the first, managing carry operations as we increment the large integer represented by the array. The primary challenge arises when the array contains multiple trailing $9$ s, which results in carryovers. As we iterate through the array, we change each $9$ to a $0$ . Upon encountering a digit that is not $9$ , we increment it by $1$ and return the modified array immediately.

If we traverse the entire array and all digits are $9$ s, we set them to $0$ and prepend a $1$ to the beginning of the array. This approach ensures that the incremented value is accurately represented while operating in place.

Let’s look at the algorithm:

Traverse the nums array from the last element toward the first.
If the current digit is $9$ , change it to $0$ .
If a digit is found that is not $9$ , increment it by 1 and return the array.
If all digits are $9$ s, they will now be $0$ ’s. In this scenario, we prepend the digit $1$ to the array and return the result.

Let’s look at the following illustration to get a better understanding of the solution:

def plus_one(nums):
	n = len(nums) - 1
	# Traversing the array from end to start
	for i in range(n, -1, -1):
		# If the element of the nums array is 9, change it to 0
		if nums[i] == 9:
			nums[i] = 0
		# Otherwise, increment 1 and return the result
		else:
			nums[i] += 1
			return nums
	# Add 1 to the start of the array if all digits were 9
	return [1] + nums
# Driver code
def main():
	nums = [[1, 0, 5], [9, 9], [1, 9, 3, 2, 1], [6, 8], [1, 7, 6, 9]]
	for i in range(len(nums)):
		print(i+1, '.', '\tGiven array: ', nums[i], sep='')
		result = plus_one(nums[i])
		print('\n\tThe result: ', result)
		print('-' * 100)
if __name__ == '__main__':
	main()

Plus One

After discussing the solution to the given problem, we will now discuss its complexity analysis.

Time complexity

The time complexity of the solution is $O(n)$ , where $n$ is the length of nums array.

Space complexity

The space complexity is $O(n)$ even though the operations are done in-place. In the worst case, if all elements of the array are $9$ , we will need intermediate space to store the result, which will have $O(n+1)$ elements. Therefore, the overall space complexity is $O(n)$ .

Practice resources for LeetCode problems

To further strengthen your coding skills and boost your technical interview preparation, here are some more LeetCode problems to practice:

Moreover, you can explore these courses designed specifically to help you ace technical interviews. These courses are available in multiple programming languages, including Python, C++, C#, Java, JavaScript, and Go:

Moreover, if you’re confident in your preparation, consider trying Educative’s AI-powered mock interviews. Mock interviews are excellent for building confidence, sharpening problem-solving skills, and identifying areas to improve before the actual interview.

Happy learning!

Frequently asked questions

Haven’t found what you were looking for? Contact Us

What if all digits are 9?

If all digits are $9$ , the array will become $[0, 0, ..., 0]$ , and you prepend $1$ at the beginning to form the result.

How do you handle cases with trailing zeros?

The problem does not specify any need to handle trailing zeros differently since the array starts from the most significant digit.

What are the edge cases for this problem?

Edge cases include handling arrays with all nines, single-digit numbers, and empty arrays (though an empty array is not allowed based on the problem constraints).

Free Resources

Learn in-demand tech skills in half the time

PRODUCTS

Mock Interview

New

Courses

Skill Paths

Projects

Assessments