Plus One

Problem Description

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 0s. Increment the large integer by one and return the resulting array of digits.

Key Insights

• The input is represented as an array of digits.
• Incrementing the number may cause a carry that needs to be propagated through the array.
• The most significant digit may change if there is a carry from the least significant digit (e.g., 999 becomes 1000).

Space and Time Complexity

Time Complexity: O(n), where n is the number of digits in the input array. We may need to traverse the entire array in the worst case. Space Complexity: O(1), since we are modifying the input array in place and not using any additional data structures that grow with the input size.

Solution

To solve this problem, we will:

1. Start from the last digit of the array and increment it by one.
2. If the resulting digit is less than 10, we can simply return the array as it is.
3. If the resulting digit is 10, we set it to 0 and carry over 1 to the next digit.
4. We continue this process until we either run out of digits or there is no more carry.
5. If we finish the loop and still have a carry, we prepend a 1 to the array.

The data structure used here is an array, and the algorithm follows a simple iterative approach to handle the carry.

Code Solutions