<p>You are given two arrays with <strong>positive</strong> integers <code>arr1</code> and <code>arr2</code>.</p>

<p>A <strong>prefix</strong> of a positive integer is an integer formed by one or more of its digits, starting from its <strong>leftmost</strong> digit. For example, <code>123</code> is a prefix of the integer <code>12345</code>, while <code>234</code> is <strong>not</strong>.</p>

<p>A <strong>common prefix</strong> of two integers <code>a</code> and <code>b</code> is an integer <code>c</code>, such that <code>c</code> is a prefix of both <code>a</code> and <code>b</code>. For example, <code>5655359</code> and <code>56554</code> have a common prefix <code>565</code> while <code>1223</code> and <code>43456</code> <strong>do not</strong> have a common prefix.</p>

<p>You need to find the length of the <strong>longest common prefix</strong> between all pairs of integers <code>(x, y)</code> such that <code>x</code> belongs to <code>arr1</code> and <code>y</code> belongs to <code>arr2</code>.</p>

<p>Return <em>the length of the <strong>longest</strong> common prefix among all pairs</em>.<em> If no common prefix exists among them</em>, <em>return</em> <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,10,100], arr2 = [1000]
<strong>Output:</strong> 3
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,2,3], arr2 = [4,4,4]
<strong>Output:</strong> 0
<strong>Explanation:</strong> 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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr1.length, arr2.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= arr1[i], arr2[i] &lt;= 10<sup>8</sup></code></li>
</ul>

import typing
class Trie:

    children: dict[str, typing.Self | str]

    def __init__(self):
        self.children = {}
    
    def add(self, string: str):

        if not string:
            self.children["."] = "."
            return

        if string[0] in self.children:
            self.children[string[0]].add(string[1:])
        else:
            self.children[string[0]] = Trie()
            self.children[string[0]].add(string[1:])
    
    def prefix_length(self, string: str):

        if not string:
            return 0
        count = 0 
        cur = self.children
        while string:
            if string[0] in cur:
                count += 1
                cur = cur[string[0]].children
                string = string[1:]
            else:
                break
        
        return count



class Solution:
    def longest_prefix(self, string_one: str, string_two: str):

        i = 0
        for a, b in zip(string_one, string_two):
            if a == b:
                i+=1
            else:
                break

        return i

    def longestCommonPrefix(self, arr1: List[int], arr2: List[int]) -> int:
        # arr1 = [str(val) for val in arr1]
        # arr2 = [str(val) for val in arr2]


        # biggest = 0

        # # O(n * m * k)
        # for v1 in arr1:
        #     for v2 in arr2:
        #         biggest = max(biggest, self.longest_prefix(v1, v2))
        
        # return biggest


        t = Trie()
        biggest = 0

        # t.add("554")
        # t.add("559")
        # print("pref length", t.prefix_length("559"))
        # print("pref length", t.prefix_length("55"))


        for num in arr2:
            t.add(str(num))

        for num in arr1:
            biggest = max(biggest, t.prefix_length(str(num)))
        

        return biggest
38731