Multiply Strings

LeetCode 43 | Difficulty: Medium

Medium

Problem Description

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Note: You must not use any built-in BigInteger library or convert the inputs to integer directly.

Example 1:

Input: num1 = "2", num2 = "3"
Output: "6"

Example 2:

Input: num1 = "123", num2 = "456"
Output: "56088"

Constraints:

- `1 <= num1.length, num2.length <= 200`

- `num1` and `num2` consist of digits only.

- Both `num1` and `num2` do not contain any leading zero, except the number `0` itself.

Topics: Math, String, Simulation

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

Solution 1: C# (Best: 159 ms)

Metric	Value
Runtime	159 ms
Memory	N/A
Date	2017-10-29

Solution

public class Solution {
    public string Multiply(string num1, string num2) {
        int[] sum = new int[num1.Length + num2.Length];
     
    for (int i = num1.Length-1; i>=0; i--)
    {
        int carry = 0;
        for (int j = num2.Length-1; j>=0; j--)
        {
            int tmp = (sum[i + j + 1]) + (num1[i] - '0') * (num2[j] - '0') + carry;
            sum[i + j + 1] = tmp%10;
            carry = tmp / 10;
        }
        sum[i] += carry;
    }
    var result = string.Join("",sum).TrimStart('0');
    return string.IsNullOrEmpty(result) ? "0" : result;
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.