Longest Common Prefix in DSA Python - Execution Trace

Concept Flow - Longest Common Prefix

Start with first string as prefix

↓

Compare prefix with next string

↓

Reduce prefix length until it matches

↓

Move to next string

↓

All strings checked?

No→Repeat comparison

Yes↓

Return prefix

Start with the first string as the prefix. Compare it with each next string, reducing prefix length until it matches. Repeat for all strings, then return the prefix.

Execution Sample

DSA Python

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

Finds the longest common prefix string among an array of strings by shrinking the prefix until it matches all strings.

Execution Table

Step	Operation	Current String	Prefix Before	Prefix After	Visual State
1	Initialize prefix	N/A	N/A	flower	prefix = 'flower'
2	Compare prefix with 'flow'	flow	flower	flow	prefix reduced to 'flow' because 'flow' does not start with 'flower'
3	Compare prefix with 'flight'	flight	flow	fl	prefix reduced to 'fl' because 'flight' does not start with 'flow' or 'flo'
4	All strings checked	N/A	fl	fl	Final prefix is 'fl'

💡 All strings checked, prefix 'fl' matches all strings

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
prefix	flower	flow	fl	fl
current string	N/A	flow	flight	N/A

Key Moments - 3 Insights

Why do we reduce the prefix instead of increasing it?

Because we start with the first string as the longest possible prefix. We reduce it only when the next string does not start with it, as shown in steps 2 and 3 of the execution_table.

What happens if the prefix becomes empty?

If the prefix becomes empty, it means there is no common prefix among the strings. The loop stops and returns an empty string. This is implied in the while loop in step 3.

Why do we check 's.startswith(prefix)' inside a while loop?

Because the prefix may need to be shortened multiple times until it matches the start of the current string, as shown in step 3 where prefix shrinks from 'flow' to 'fl'.

Visual Quiz - 3 Questions

Look at the execution_table, what is the prefix after comparing with the second string?

A flower

B flow

C fl

D flight

💡 Hint

Check Step 2 in the execution_table where prefix changes after comparing with 'flow'

At which step does the prefix become 'fl'?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look at the prefix after Step 3 in the execution_table

If the input strings were ['dog', 'racecar', 'car'], what would happen to the prefix?

A It would become empty ''

B It would become 'd'

C It would remain 'dog'

D It would become 'car'

💡 Hint

Think about prefix reduction when no common start exists, as explained in key_moments

Concept Snapshot

Longest Common Prefix:
- Start with first string as prefix
- Compare prefix with each string
- While prefix not matching start, reduce prefix
- Return prefix after all strings checked
- Empty prefix means no common prefix

Full Transcript

The longest common prefix algorithm starts by assuming the first string is the prefix. It then compares this prefix with each subsequent string. If the current string does not start with the prefix, the prefix is shortened by removing the last character. This process repeats until the prefix matches the start of the current string or becomes empty. After checking all strings, the remaining prefix is returned as the longest common prefix. If the prefix becomes empty, it means no common prefix exists among the strings.

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