Find the Length of the Longest Common Prefix

Problem Description

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. A common prefix of two integers a and b is an integer c, such that c is a prefix of both a and b. 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.

Key Insights

• A common prefix is determined by comparing the digits of two integers from the two arrays.
• The length of the common prefix can be found by converting the integers to strings and comparing them character by character.
• The solution requires iterating through every integer in arr1 and arr2, resulting in a potentially large number of comparisons.

Space and Time Complexity

Time Complexity: O(n * m), where n is the length of arr1 and m is the length of arr2.
Space Complexity: O(1), as we are using a constant amount of space for storing lengths and temporary variables.

Solution

The approach to solve the problem involves iterating through each integer in arr1 and arr2, converting them to strings, and then comparing the digits to find the longest common prefix. The process involves:

1. For each integer in arr1, compare it with each integer in arr2.
2. Convert the integers to strings.
3. Compare the characters of both strings until they differ.
4. Keep track of the maximum length of the common prefixes found.

Code Solutions