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Plus One – Solution & Complexity

Interview solutions
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Plus One

Solution Walkthrough

  1. Step 1: Add from the Least Significant Digit

    • The last array element is the ones place, so addition starts there.
    • If a digit is less than 9, adding one does not create a carry.
    • In that case, update the digit and return immediately.
    for i in range(len(digits) - 1, -1, -1):
    if digits[i] < 9:
        digits[i] += 1
        return digits

  2. Step 2: Propagate Carry Through Nines

    • A digit equal to 9 becomes 0 after adding one and carries to the next digit on the left.
    • Continue scanning left while digits are 9.
    • This mirrors elementary addition.
    for i in range(len(digits) - 1, -1, -1):
    if digits[i] == 9:
        digits[i] = 0
    else:
        digits[i] += 1
        return digits

  3. Step 3: Handle All-Nines Input

    • If every digit was 9, the loop turns them all into 0.
    • The result needs a new leading 1.
    • For example, [9, 9] becomes [1, 0, 0].
    return [1] + digits

  4. Step 4: Final Complete Solution

    • The algorithm mutates the input list in place when possible and only allocates a new leading digit for all-nines cases.
    • It scans from right to left once.
    • Time complexity is O(n), and extra space complexity is O(1) besides the returned list.
    def plus_one(digits: list[int]) -> list[int]:
    for i in range(len(digits) - 1, -1, -1):
        if digits[i] < 9:
            digits[i] += 1
            return digits
        digits[i] = 0

    return [1] + digits

FAQ

See also

Practice Plus One online (run code in the browser)Missing Number solution (easy)Pascal's Triangle solution (easy)3Sum solution (medium)3Sum Closest solution (medium)All coding interview problems
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