Add Numbers Written as Text

EasyMath & Geometry

Problem

An accounting export stores amounts as decimal strings that can be thousands of digits long, too long for any built-in integer type.

Given two non-negative integers first and second as strings, return their sum as a string. Do not convert the whole strings to numbers.

Example 1

Input:
first = "456", second = "77"
Output:
"533"

6 + 7 = 13 (write 3, carry 1), 5 + 7 + 1 = 13 (write 3, carry 1), 4 + 1 = 5.

Example 2

Input:
first = "999", second = "1"
Output:
"1000"

The carry ripples all the way and adds a new leading digit.

Example 3

Input:
first = "0", second = "0"
Output:
"0"

Constraints

  • 1 ≤ first.length, second.length ≤ 10^4
  • Both contain digits only and have no leading zeros, except the number "0" itself

Hint

Show the first hint

Do it the way you add on paper: from the rightmost digit to the left.

Walkthrough

How to approach it

01Clarify before coding

  • Can the inputs have different lengths? Yes; treat the missing digits of the shorter one as 0.
  • Are there signs or decimal points? No, only non-negative integers.
  • Can I just use a big-integer library? No: the point is the digit-by-digit algorithm.

02Brute force

Convert both strings to numbers and add them.

Cost: Fails outright: 10^4 digits overflow every fixed-width type. Prepending each digit to a string instead of reversing once also makes it O(n²).

The rest of the walkthrough is in the app

The full walkthrough (key insight, step-by-step, dry run, complexity, edge cases, pitfalls, follow-ups) and solutions in Python and JavaScript are in the app, next to an editor and a terminal that runs your code against the tests.

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This problem is part of Pro.