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Algomap/Longest_Common_Prefix/README.md

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+# 14. Longest Common Prefix (Easy)
+
+## Table of Contents
+
+- [Problem Statement](#problem-statement)
+- [Examples](#examples)
+- [Constraints](#constraints)
+- [Approach](#approach)
+- [Solutions](#solutions)
+  - [Solution 1: Sorting and Comparing](#solution-1-sorting-and-comparing)
+  - [Solution 2: Character-by-Character Comparison](#solution-2-character-by-character-comparison)
+- [Complexity Analysis](#complexity-analysis)
+- [Code Explanation](#code-explanation)
+- [Related Resources](#related-resources)
+
+## Problem Statement
+
+[Longest Common Prefix](https://leetcode.com/problems/longest-common-prefix/description/)
+
+Write a function to find the longest common prefix string amongst an array of strings.
+
+If there is no common prefix, return an empty string `""`.
+
+## Examples
+
+### Example 1:
+
+```
+Input: strs = ["flower","flow","flight"]
+Output: "fl"
+```
+
+### Example 2:
+
+```
+Input: strs = ["dog","racecar","car"]
+Output: ""
+Explanation: There is no common prefix among the input strings.
+```
+
+## Constraints
+
+- $1 \leq strs.length \leq 200$
+- $0 \leq strs[i].length \leq 200$
+- `strs[i]` consists of only lowercase English letters.
+
+## Approach
+
+We'll explore two different approaches to solve this problem:
+
+1. Sorting and comparing the first and last strings.
+2. Character-by-character comparison of all strings.
+
+## Solutions
+
+### Solution 1: Sorting and Comparing
+
+```python
+class Solution(object):
+    def longestCommonPrefix(self, strs):
+        ans = ""
+        strs = sorted(strs)
+        min_len, max_len = strs[0], strs[-1]
+        for i in range(min(len(min_len), len(max_len))):
+            if min_len[i] != max_len[i]:
+                return ans
+            ans += min_len[i]
+        return ans
+```
+
+### Solution 2: Character-by-Character Comparison
+
+```python
+class Solution(object):
+    def longestCommonPrefix(self, strs):
+        min_length = float('inf')
+        for s in strs:
+            if len(s) < min_length:
+                min_length = len(s)
+
+        i = 0
+        while i < min_length:
+            for s in strs:
+                if s[i] != strs[0][i]:
+                    return s[:i]
+            i += 1
+
+        return strs[0][:i]
+```
+
+## Complexity Analysis
+
+### Solution 1:
+- Time Complexity: $O(N \log N + M)$, where N is the number of strings and M is the length of the shortest string.
+- Space Complexity: $O(1)$ (excluding the space used for sorting)
+
+### Solution 2:
+- Time Complexity: $O(S)$, where S is the sum of all characters in all strings.
+- Space Complexity: $O(1)$
+
+## Code Explanation
+
+### Solution 1: Sorting and Comparing
+1. Sort the input array of strings lexicographically.
+2. Compare the first (lexicographically smallest) and last (lexicographically largest) strings.
+3. Build the common prefix until a mismatch is found or we reach the end of either string.
+
+### Solution 2: Character-by-Character Comparison
+1. Find the length of the shortest string in the array.
+2. Compare characters at each position for all strings.
+3. If a mismatch is found, return the common prefix up to that point.
+4. If no mismatch is found, return the entire shortest string.
+
+## Related Resources
+
+- [YouTube Explanation](https://www.youtube.com/watch?v=8C6F8_nM0qs)
+- [GitHub Solution](https://github.com/gahogg/Leetcode-Solutions/blob/main/Longest%20Common%20Prefix%20-%20Leetcode%2014/Longest%20Common%20Prefix%20-%20Leetcode%2014.py)
+- [LeetCode Solution](https://leetcode.com/problems/longest-common-prefix/solutions/5684830/solution/)
+- [Personal Submission](https://leetcode.com/submissions/detail/1366878699/)
+
+> [!NOTE]
+> This problem is part of a larger collection following the roadmap on [algomap.io](https://algomap.io/). For more details and related problems, please refer to the AlgoMap website.