Problem statement

Given two non-negative integers num1 and num2 represented as strings, return their sum as a string.

You must solve the problem without converting the inputs to integers directly and without using any big-integer library.

Example 1

Input: num1 = "11", num2 = "123"
Output: 134

Example 2

Input: num1 = "456", num2 = "77"
Output: 533

Example 3

Input: num1 = "0", num2 = "0"
Output: 0

Constraints

• 1 <= num1.length, num2.length <= 20
• num1 and num2 consist of digits only.
• Neither has a leading zero, except the value 0 itself.

Hints for Add Strings

1. Hint 1

   Column addition from the right, carrying as you go.

2. Hint 2

   Treat a missing digit in the shorter string as 0 rather than special-casing the lengths.

3. Hint 3

   The loop must survive a final carry — "9" + "1" is "10", one character longer than either input.

How to solve Add Strings

Schoolbook addition from the right with a carry, treating a missing digit in the shorter string as zero.

Approach

1. Set i, j to the last indices of the two strings and carry = 0.
2. While i >= 0 or j >= 0 or carry: sum the carry and the available digits, append sum % 10, set carry = sum // 10.
3. Reverse the collected digits and join.

Why it works

Each column produces a digit in 0…9 and a carry of 0 or 1. Processing columns right to left with the carry threaded through is the definition of decimal addition, and the loop condition ensures a leading carry is emitted.

Complexity

• Time — O(max(len a, len b))
• Space — O(max(len a, len b))

Pitfalls

• Use ord(ch) - 48 (or the language's equivalent) rather than parsing each character.
• "9" + "1" is "10" — the result can be longer than both inputs.

Reference solution

Python

def addStrings(num1: str, num2: str) -> str:
    i, j, carry = len(num1) - 1, len(num2) - 1, 0
    out = []
    while i >= 0 or j >= 0 or carry:
        total = carry
        if i >= 0:
            total += ord(num1[i]) - 48
            i -= 1
        if j >= 0:
            total += ord(num2[j]) - 48
            j -= 1
        out.append(str(total % 10))
        carry = total // 10
    return "".join(reversed(out))

Java

public static String addStrings(String num1, String num2) {
    int i = num1.length() - 1, j = num2.length() - 1, carry = 0;
    StringBuilder sb = new StringBuilder();
    while (i >= 0 || j >= 0 || carry > 0) {
        int total = carry;
        if (i >= 0) { total += num1.charAt(i) - '0'; i--; }
        if (j >= 0) { total += num2.charAt(j) - '0'; j--; }
        sb.append((char) ('0' + total % 10));
        carry = total >= 10 ? 1 : 0;
    }
    return sb.reverse().toString();
}

C++

string addStrings(string num1, string num2) {
    int i = (int) num1.size() - 1, j = (int) num2.size() - 1, carry = 0;
    string out = "";
    while (i >= 0 || j >= 0 || carry > 0) {
        int total = carry;
        if (i >= 0) { total += num1[i] - '0'; i--; }
        if (j >= 0) { total += num2[j] - '0'; j--; }
        out += (char) ('0' + total % 10);
        carry = total >= 10 ? 1 : 0;
    }
    reverse(out.begin(), out.end());
    return out;
}

JavaScript

var addStrings = function(num1, num2) {
    let i = num1.length - 1, j = num2.length - 1, carry = 0, out = "";
    while (i >= 0 || j >= 0 || carry > 0) {
        let total = carry;
        if (i >= 0) { total += num1.charCodeAt(i) - 48; i--; }
        if (j >= 0) { total += num2.charCodeAt(j) - 48; j--; }
        out = String(total % 10) + out;
        carry = total >= 10 ? 1 : 0;
    }
    return out;
};

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