The basic case is easy enough, just increment the last digit.
Traverse the array from the least significant digit (rightmost) to the most significant, adding 1 and propagating any carry. If a carry remains after processing all digits, prepend a 1 to the array. Return the resulting array.
Pro tip: Mention that this problem is essentially a manual simulation of addition, and highlight that the only case where the array length increases is when all digits are 9. Also, discuss the time and space complexity upfront to show efficiency awareness.
Restate the problem to ensure understanding: the array represents a non-negative integer with no leading zeros except for zero itself. Confirm that in-place modification is acceptable or if a new array is preferred.
Iterate from the last index to the first. For each digit, if it is less than 9, increment it by 1 and return the array immediately. If it is 9, set it to 0 and continue to propagate the carry.
If the loop completes without returning, it means all digits were 9 and have been set to 0. Prepend a 1 to the array (or create a new array of length n+1 with 1 followed by zeros) and return it.
State that the time complexity is O(n) in the worst case (all 9s) and O(1) in the best case (last digit < 9). Space complexity is O(1) if modifying in-place, or O(n) if creating a new array for the all-9s case.
Walk through examples: [1,2,3] -> [1,2,4]; [9,9,9] -> [1,0,0,0]; [0] -> [1]; [9] -> [1,0]. Mention that the input array might be empty? (Usually not, but clarify).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.