Solving the LeetCode "Multiply Strings" Problem in Go

Difficulty: Medium | Tags: Math, String, Simulation

Introduction

Multiplying two large numbers represented as strings is a common problem in computer science, especially when dealing with numbers too large for standard data types. This problem tests our ability to simulate manual multiplication efficiently.

Problem Analysis

Given two non-negative integers represented as strings, we need to return their product as a string without converting them to integers directly. The challenge lies in handling large numbers and simulating the multiplication process digit by digit.

Solution Approach

We'll simulate the manual multiplication process we learned in school. The key steps are:

1. Initialize a result array to store intermediate products
2. Multiply each digit of the first number with each digit of the second number
3. Store the products in the correct positions in the result array
4. Handle carry values appropriately
5. Convert the result array to a string, removing leading zeros

Go Implementation

func multiply(num1 string, num2 string) string {
    if num1 == "0" || num2 == "0" {
        return "0"
    }
    m, n := len(num1), len(num2)
    res := make([]int, m+n)
    for i := m - 1; i >= 0; i-- {
        for j := n - 1; j >= 0; j-- {
            product := int(num1[i]-'0') * int(num2[j]-'0')
            sum := product + res[i+j+1]
            res[i+j+1] = sum % 10
            res[i+j] += sum / 10
        }
    }
    var result strings.Builder
    for i, val := range res {
        if i == 0 && val == 0 {
            continue
        }
        result.WriteString(strconv.Itoa(val))
    }
    return result.String()
}

Complexity Analysis

Time Complexity: O(m*n) where m and n are the lengths of the input strings. We perform a nested loop over both strings.

Space Complexity: O(m+n) for storing the result array. The output string can be at most m+n digits long.

Testing and Examples

Test cases to verify the implementation:

• "2" * "3" = "6"
• "123" * "456" = "56088"
• "0" * "1234" = "0"
• "999" * "999" = "998001"

Best Practices and Tips

Key takeaways for solving similar problems:

• Always handle the zero case separately for efficiency
• Use an array to store intermediate results for better performance
• Be careful with index calculations when placing digits in the result array
• Use a strings.Builder for efficient string concatenation
• Remember to skip leading zeros in the final result