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7. Plus One

easyAsked at Spotify

Increment a large integer represented as a digit array by one.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given a non-empty array of digits representing a non-negative integer, increment one to the integer. Digits are stored such that the most significant digit is at the head; return the new digit array.

Constraints

  • 1 <= digits.length <= 100
  • 0 <= digits[i] <= 9
  • No leading zeros except value 0

Examples

Example 1

Input
digits=[1,2,3]
Output
[1,2,4]

Example 2

Input
digits=[9,9]
Output
[1,0,0]

Approaches

1. BigInt conversion

Convert to BigInt, add one, convert back to digits

Time
O(n)
Space
O(n)
const n = BigInt(digits.join('')) + 1n;
return n.toString().split('').map(Number);

Tradeoff:

2. Carry propagation

Walk right-to-left adding the carry; prepend 1 if it overflows. No allocations until needed.

Time
O(n)
Space
O(1)
function plusOne(digits) {
  for (let i = digits.length - 1; i >= 0; i--) {
    if (digits[i] < 9) {
      digits[i]++;
      return digits;
    }
    digits[i] = 0;
  }
  return [1, ...digits];
}

Tradeoff:

Spotify-specific tips

Spotify backend interviewers like the carry-propagation pattern because it mirrors how their stream-counter increments cascade through fixed-width counters in the listening-event ingestor.

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Output

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