Introduction

In this blog post, we will explore how to solve the LeetCode problem "3043" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given two arrays with positive integers arr1 and arr2. A prefix of a positive integer is an integer formed by one or more of its digits, starting from its leftmost digit. For example, 123 is a prefix of the integer 12345, while 234 is not. A common prefix of two integers a and b is an integer c, such that c is a prefix of both a and b. For example, 5655359 and 56554 have common prefixes 565 and 5655 while 1223 and 43456 do not have a common prefix. You need to find the length of the longest common prefix between all pairs of integers (x, y) such that x belongs to arr1 and y belongs to arr2. Return the length of the longest common prefix among all pairs. If no common prefix exists among them, return 0. Example 1: Input: arr1 = [1,10,100], arr2 = [1000] Output: 3 Explanation: There are 3 pairs (arr1[i], arr2[j]): - The longest common prefix of (1, 1000) is 1. - The longest common prefix of (10, 1000) is 10. - The longest common prefix of (100, 1000) is 100. The longest common prefix is 100 with a length of 3. Example 2: Input: arr1 = [1,2,3], arr2 = [4,4,4] Output: 0 Explanation: There exists no common prefix for any pair (arr1[i], arr2[j]), hence we return 0. Note that common prefixes between elements of the same array do not count. Constraints: 1 <= arr1.length, arr2.length <= 5 * 104 1 <= arr1[i], arr2[i] <= 108

Explanation

Here's a breakdown of the solution:

• Convert to Strings: Transform the integer arrays into arrays of strings. This simplifies prefix comparisons.
• Find Minimum Length: Determine the shortest possible length of a common prefix by finding the minimum length string across all elements in both arrays.

• Iterative Comparison: Iterate from index 0 up to the minimum length. In each iteration, check if the characters at the current index are the same across all pairs of strings from arr1 and arr2. If they are not, the longest common prefix is the length found in the previous iteration.

• Runtime Complexity: O(N M L) where N is the length of arr1, M is the length of arr2, and L is the length of the shortest string.

• Storage Complexity: O(N + M), to store the string representations of the arrays.

Code

    def longest_common_prefix(arr1, arr2):
    """
    Finds the length of the longest common prefix between all pairs of integers (x, y)
    such that x belongs to arr1 and y belongs to arr2.

    Args:
        arr1: A list of positive integers.
        arr2: A list of positive integers.

    Returns:
        The length of the longest common prefix among all pairs.
    """

    str_arr1 = [str(x) for x in arr1]
    str_arr2 = [str(x) for x in arr2]

    min_len = float('inf')
    for s in str_arr1:
        min_len = min(min_len, len(s))
    for s in str_arr2:
        min_len = min(min_len, len(s))

    if min_len == float('inf'):
        return 0

    lcp_len = 0
    for i in range(min_len):
        char = None
        valid = True

        for s1 in str_arr1:
            for s2 in str_arr2:
                if char is None:
                    char = s1[i]
                if i >= len(s1) or i >= len(s2) or s1[i] != s2[i] or s1[i] != char:
                    valid = False
                    break
            if not valid:
                break
        if valid:
            lcp_len += 1
        else:
            break

    return lcp_len