Plus One

Problem

https://leetcode.com/problems/plus-one/

You are given a large integer represented as an integer array digits, where each digits[i] is the i:sup:`th` 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.

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.

Pattern

Array, Math

Approaches

Right To Left Carry

Explanation

Add 1 to the end of the array. Start from the least signfinicant digit and carry any 1s to the next digit.

Code

def plusOne(digits: list[int]) -> list[int]:
    """Add 1 to the integer, represented in base 10, ``digits``."""
    n = len(digits)
    digits[-1] += 1
    for i in range(n - 1, -1, -1):
        if digits[i] == 10:
            digits[i] = 0
            if i == 0:
                digits.insert(0, 1)
            else:
                digits[i - 1] += 1
    return digits

Test

>>> from plus_one__right_to_left_carry import plusOne
>>> plusOne([4, 3, 2, 1])
[4, 3, 2, 2]
>>> plusOne([9])
[1, 0]

Complexity

\(n\) is the length of the input list

Measure	Complexity	Notes
Time	\(O(n)\)	single reverse pass
Auxiliary Space	\(O(1)\)

plus_one__right_to_left_carry.plusOne(digits: list[int]) → list[int]

Add 1 to the integer, represented in base 10, digits.