**π‘ Problem Formulation:** Given a list of strings, the task is to find the longest common prefix shared by all the strings. A prefix is a string that appears at the start of another string. For example, if the input list is `["flower","flow","flight"]`

, the longest common prefix is `"fl"`

. This common prefix is what we seek to programmatically determine.

## Method 1: Horizontal Scanning

This method involves comparing each string with the prefix found so far. The comparison starts with the first string as the initial prefix and iteratively shortens the prefix with each subsequent string until the common prefix is found or an empty string is reached.

Here’s an example:

def longest_common_prefix(strs): if not strs: return "" prefix = strs[0] for string in strs[1:]: while string[:len(prefix)] != prefix: prefix = prefix[:-1] if not prefix: return "" return prefix # Example usage: print(longest_common_prefix(["flower","flow","flight"]))

Output: `"fl"`

In this approach, we iterate over the list of strings, progressively chopping down the characters from the prefix until it matches with each string or results in an empty prefix. It uses a while loop inside a for loop to carry out the operation.

## Method 2: Vertical Scanning

This method examines each character position across all strings simultaneously, thus checking characters in vertical slices. As soon as a mismatch is encountered, the function returns the longest common prefix found up to that point.

Here’s an example:

def longest_common_prefix(strs): if not strs: return "" for i in range(len(strs[0])): char = strs[0][i] for string in strs: if i == len(string) or string[i] != char: return strs[0][:i] return strs[0] # Example usage: print(longest_common_prefix(["gadget", "gaudy", "gaze"]))

Output: `"ga"`

Vertical scanning optimizes comparisons based on characters at each index, stopping when a difference is encountered. This method could be more efficient when the strings have a large common prefix.

## Method 3: Divide and Conquer

The divide and conquer approach splits the list of strings into two halves and finds the longest common prefix for each half recursively. The final result is the common prefix between the two intermediate prefixes.

Here’s an example:

def common_prefix(str1, str2): min_len = min(len(str1), len(str2)) for i in range(min_len): if str1[i] != str2[i]: return str1[:i] return str1[:min_len] def longest_common_prefix(strs): if not strs: return "" if len(strs) == 1: return strs[0] mid = len(strs) // 2 lcp_left = longest_common_prefix(strs[:mid]) lcp_right = longest_common_prefix(strs[mid:]) return common_prefix(lcp_left, lcp_right) # Example usage: print(longest_common_prefix(["interview", "interrupt", "integrate", "integral"]))

Output: `"int"`

This method is efficient when dealing with a large set of strings, as it effectively reduces the problem size in each recursive call, allowing the function to quickly converge on the longest common prefix.

## Method 4: Binary Search

The binary search method applies the classic binary search algorithm to find the longest common prefix by treating the length of the prefix as a searchable space.

Here’s an example:

def is_common_prefix(strs, length): str1, strs = strs[0][:length], strs[1:] return all(s.startswith(str1) for s in strs) def longest_common_prefix(strs): if not strs: return "" min_length = min(len(s) for s in strs) low, high = 1, min_length while low <= high: middle = (low + high) // 2 if is_common_prefix(strs, middle): low = middle + 1 else: high = middle - 1 return strs[0][:(low + high) // 2] # Example usage: print(longest_common_prefix(["alpine", "alto", "almanac"]))

Output: `"al"`

Binary search is a highly efficient way to zero in on the exact length of the longest common prefix by comparing half of the remaining strings at each iteration, resulting in a logarithmic time complexity.

## Bonus One-Liner Method 5: Using Python’s Built-in Functions

A snappy one-liner approach employs a combination of Python’s built-in functions to find the longest common prefix. This makes the code concise but possibly less readable.

Here’s an example:

import os strs = ["sunlight", "sunflower", "suntan"] lcp = os.path.commonprefix(strs) print(lcp)

Output: `"sun"`

The one-liner uses the `os.path.commonprefix()`

function, designed for paths but also applicable to general string lists. It bypasses manual iteration and directly provides the result.

## Summary/Discussion

**Method 1:**Horizontal Scanning. Simplicity is a plus. Small strings work well, but the method could be slow for long strings with short common prefixes.**Method 2:**Vertical Scanning. Helps save time by focusing on character positions. Potentially more efficient for large common prefixes.**Method 3:**Divide and Conquer. Scalability and efficiency for a large number of strings. Overhead may be a concern with smaller lists.**Method 4:**Binary Search. Optimal for long strings with varying lengths. May be overkill for simple or small sets of strings.**Method 5:**One-liner with`os.path.commonprefix()`

. Elegance and ease of writing. May lack performance tuning specific to problem context.

In this approach, we iterate over the list of strings, progressively chopping down the characters from the prefix until it matches with each string or results in an empty prefix. It uses a while loop inside a for loop to carry out the operation.

## Method 2: Vertical Scanning

This method examines each character position across all strings simultaneously, thus checking characters in vertical slices. As soon as a mismatch is encountered, the function returns the longest common prefix found up to that point.

Here’s an example:

def longest_common_prefix(strs): if not strs: return "" for i in range(len(strs[0])): char = strs[0][i] for string in strs: if i == len(string) or string[i] != char: return strs[0][:i] return strs[0] # Example usage: print(longest_common_prefix(["gadget", "gaudy", "gaze"]))

Output: `"ga"`

Vertical scanning optimizes comparisons based on characters at each index, stopping when a difference is encountered. This method could be more efficient when the strings have a large common prefix.

## Method 3: Divide and Conquer

The divide and conquer approach splits the list of strings into two halves and finds the longest common prefix for each half recursively. The final result is the common prefix between the two intermediate prefixes.

Here’s an example:

def common_prefix(str1, str2): min_len = min(len(str1), len(str2)) for i in range(min_len): if str1[i] != str2[i]: return str1[:i] return str1[:min_len] def longest_common_prefix(strs): if not strs: return "" if len(strs) == 1: return strs[0] mid = len(strs) // 2 lcp_left = longest_common_prefix(strs[:mid]) lcp_right = longest_common_prefix(strs[mid:]) return common_prefix(lcp_left, lcp_right) # Example usage: print(longest_common_prefix(["interview", "interrupt", "integrate", "integral"]))

Output: `"int"`

This method is efficient when dealing with a large set of strings, as it effectively reduces the problem size in each recursive call, allowing the function to quickly converge on the longest common prefix.

## Method 4: Binary Search

The binary search method applies the classic binary search algorithm to find the longest common prefix by treating the length of the prefix as a searchable space.

Here’s an example:

def is_common_prefix(strs, length): str1, strs = strs[0][:length], strs[1:] return all(s.startswith(str1) for s in strs) def longest_common_prefix(strs): if not strs: return "" min_length = min(len(s) for s in strs) low, high = 1, min_length while low <= high: middle = (low + high) // 2 if is_common_prefix(strs, middle): low = middle + 1 else: high = middle - 1 return strs[0][:(low + high) // 2] # Example usage: print(longest_common_prefix(["alpine", "alto", "almanac"]))

Output: `"al"`

Binary search is a highly efficient way to zero in on the exact length of the longest common prefix by comparing half of the remaining strings at each iteration, resulting in a logarithmic time complexity.

## Bonus One-Liner Method 5: Using Python’s Built-in Functions

A snappy one-liner approach employs a combination of Python’s built-in functions to find the longest common prefix. This makes the code concise but possibly less readable.

Here’s an example:

import os strs = ["sunlight", "sunflower", "suntan"] lcp = os.path.commonprefix(strs) print(lcp)

Output: `"sun"`

The one-liner uses the `os.path.commonprefix()`

function, designed for paths but also applicable to general string lists. It bypasses manual iteration and directly provides the result.

## Summary/Discussion

**Method 1:**Horizontal Scanning. Simplicity is a plus. Small strings work well, but the method could be slow for long strings with short common prefixes.**Method 2:**Vertical Scanning. Helps save time by focusing on character positions. Potentially more efficient for large common prefixes.**Method 3:**Divide and Conquer. Scalability and efficiency for a large number of strings. Overhead may be a concern with smaller lists.**Method 4:**Binary Search. Optimal for long strings with varying lengths. May be overkill for simple or small sets of strings.**Method 5:**One-liner with`os.path.commonprefix()`

. Elegance and ease of writing. May lack performance tuning specific to problem context.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.