From 704b518812163fba84307e697b00efd83f0700ac Mon Sep 17 00:00:00 2001
From: Baffin Lee <baffinlee@gmail.com>
Date: Tue, 24 Sep 2024 23:25:10 +0800
Subject: [PATCH] feat: solve No.3043

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+# 3043. Find the Length of the Longest Common Prefix
+
+- Difficulty: Medium.
+- Related Topics: Array, Hash Table, String, Trie.
+- Similar Questions: Longest Common Prefix, Longest Common Suffix Queries.
+
+## Problem
+
+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 a common prefix `565` 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`
+
+
+
+## Solution
+
+```javascript
+/**
+ * @param {number[]} arr1
+ * @param {number[]} arr2
+ * @return {number}
+ */
+var longestCommonPrefix = function(arr1, arr2) {
+    var trie = {};
+    for (var i = 0; i < arr1.length; i++) {
+        var str = `${arr1[i]}`;
+        var map = trie;
+        for (var j = 0; j < str.length; j++) {
+            if (!map[str[j]]) {
+                map[str[j]] = {};
+            }
+            map = map[str[j]];
+        }
+    }
+    var max = 0;
+    for (var i = 0; i < arr2.length; i++) {
+        var str = `${arr2[i]}`;
+        var map = trie;
+        var len = 0;
+        for (var j = 0; j < str.length; j++) {
+            if (!map[str[j]]) {
+                break;
+            }
+            len += 1;
+            map = map[str[j]];
+        }
+        max = Math.max(max, len);
+    }
+    return max;
+};
+```
+
+**Explain:**
+
+Trie.
+
+**Complexity:**
+
+* Time complexity : O(n * m).
+* Space complexity : O(n * m).