Longest Common Prefix in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Longest Common Prefix (LCP) in a list of strings?

The Longest Common Prefix is the longest starting substring that is common to all strings in the list.

beginner

How do you find the LCP by comparing characters vertically?

Check each character position across all strings. Stop when a mismatch or end of any string is found. The matched characters so far form the LCP.

intermediate

What is the time complexity of the vertical scanning method for LCP?

O(S) where S is the sum of all characters in all strings, because each character is checked at most once.

beginner

Why is it important to handle empty strings or empty list when finding LCP?

Because if the list is empty or contains empty strings, the LCP is empty. Handling these avoids errors and incorrect results.

intermediate

What is a simple Python code snippet to find the LCP using horizontal scanning?

Start with the first string as prefix. Compare prefix with each string and shorten prefix until it matches. Return prefix at the end.

What does the Longest Common Prefix represent?

A The longest substring common anywhere in all strings

B The longest substring common at the end of all strings

C The longest substring common at the start of all strings

D The shortest string in the list

The LCP is the longest starting substring shared by all strings.

If the input list is empty, what should the LCP be?

A Empty string

B None

C First string in the list

D Error

With no strings, the longest common prefix is empty.

Which approach compares characters column by column across all strings?

A Binary search

B Horizontal scanning

C Divide and conquer

D Vertical scanning

Vertical scanning checks each character position across all strings.

What happens if one string is empty in the list?

A LCP is the longest string

B LCP is empty string

C LCP is the shortest non-empty string

D LCP is the first string

An empty string means no common prefix beyond empty string.

What is the time complexity of checking all characters in all strings for LCP?

A O(S), where S is total characters

B O(N), where N is number of strings

C O(1)

D O(log N)

Each character in all strings is checked at most once, so O(S).

Explain how you would find the Longest Common Prefix in a list of strings using vertical scanning.

Think about comparing characters column by column.

Describe edge cases to consider when implementing Longest Common Prefix.

What if no strings or some strings are empty?

Practice

1. What does the Longest Common Prefix (LCP) problem ask you to find given a list of strings?

easy

A. The total number of strings in the list

B. The longest starting substring common to all strings

C. The longest substring common to any two strings

D. The longest ending substring common to all strings

Solution

1. Step 1: Understand the problem definition

   The Longest Common Prefix means the longest substring at the start of all strings that is the same.

2. Step 2: Compare options with the definition

   Only The longest starting substring common to all strings matches this definition exactly.

3. Final Answer:

   The longest starting substring common to all strings -> Option B

4. Quick Check:

   Longest Common Prefix = longest starting substring [OK]

Hint: Focus on the start of strings, not anywhere else [OK]

Common Mistakes:

• Confusing prefix with suffix
• Thinking about any substring instead of prefix
• Counting total strings instead of prefix length

2. Which of the following Python code snippets correctly initializes a variable to store the longest common prefix as an empty string?

easy

A. lcp = None

B. lcp = []

C. lcp = ''

D. lcp = 0

Solution

1. Step 1: Identify the correct data type for prefix storage

   The longest common prefix is a string, so it should be initialized as an empty string.

2. Step 2: Match initialization with data type

   lcp = '' initializes lcp as an empty string, which is correct.

3. Final Answer:

   lcp = '' -> Option C

4. Quick Check:

   Prefix is a string, so empty string initialization [OK]

Hint: Use empty string '' to start prefix, not list or number [OK]

Common Mistakes:

• Using list [] instead of string
• Using None which is not a string
• Using 0 which is a number, not string

3. What will be the output of the following Python code?

def longest_common_prefix(strs):
    if not strs:
        return ''
    prefix = strs[0]
    for s in strs[1:]:
        while not s.startswith(prefix):
            prefix = prefix[:-1]
            if not prefix:
                return ''
    return prefix

print(longest_common_prefix(['flower', 'flow', 'flight']))

medium

A. fl

B. flow

C. f

D. flower

Solution

1. Step 1: Initialize prefix and iterate over strings

   Prefix starts as 'flower'. Check 'flow': 'flow' does not start with 'flower', so remove last char to 'flowe', then 'flow', which matches.

2. Step 2: Check next string 'flight'

   'flight' does not start with 'flow', remove last char to 'flo', no match; then 'fl', which matches.

3. Final Answer:

   fl -> Option A

4. Quick Check:

   Common start of all strings = 'fl' [OK]

Hint: Shrink prefix until all strings start with it [OK]

Common Mistakes:

• Returning first string without checking others
• Not shrinking prefix correctly
• Confusing substring anywhere with prefix

4. The following code is intended to find the longest common prefix but has a bug. What is the bug?

def longest_common_prefix(strs):
    prefix = strs[0]
    for s in strs:
        while not s.startswith(prefix):
            prefix = prefix[:-1]
    return prefix

print(longest_common_prefix(['dog', 'racecar', 'car']))

medium

A. No return statement inside the loop

B. Loop starts from first string causing incorrect prefix update

C. Using s.startswith(prefix) instead of prefix.startswith(s)

D. Missing check for empty prefix causing infinite loop

Solution

1. Step 1: Analyze loop and prefix shrinking

   The code shrinks prefix until s starts with prefix, but does not check if prefix becomes empty.

2. Step 2: Identify infinite loop risk

   If no common prefix exists, prefix will shrink to empty string, then prefix[:-1] stays empty, causing infinite loop.

3. Final Answer:

   Missing check for empty prefix causing infinite loop -> Option D

4. Quick Check:

   Empty prefix check needed to stop loop [OK]

Hint: Always check if prefix is empty to avoid infinite loops [OK]

Common Mistakes:

• Not checking prefix empty condition
• Looping over all strings including first
• Confusing startswith arguments

5. Given a list of strings, how would you efficiently find the longest common prefix using a vertical scanning approach? Which of the following best describes the method?

hard

A. Compare characters column by column across all strings until a mismatch is found

B. Sort the strings and compare only the first and last strings completely

C. Use a hash map to count character frequencies at each position

D. Concatenate all strings and find the longest substring

Solution

1. Step 1: Understand vertical scanning

   Vertical scanning means checking each character position across all strings one by one.

2. Step 2: Identify stopping condition

   Stop when a mismatch or end of any string is found at that position.

3. Final Answer:

   Compare characters column by column across all strings until a mismatch is found -> Option A

4. Quick Check:

   Vertical scanning = column-wise character comparison [OK]

Hint: Check characters by columns, stop at first mismatch [OK]

Common Mistakes:

• Confusing vertical scanning with sorting
• Using hash maps unnecessarily
• Concatenating strings instead of comparing