Longest Common Prefix in DSA C - Execution Trace

Concept Flow - Longest Common Prefix

Start with first string as prefix

↓

For each next string in array

↓

Compare prefix with current string

↓

Shorten prefix until it matches start of current string

↓

If prefix empty, stop and return empty string

↓

After all strings processed, return prefix

Start with the first string as the prefix. For each next string, shorten the prefix until it matches the start of that string. If prefix becomes empty, return empty string. Otherwise, after all strings, return the prefix.

Execution Sample

DSA C

char* longestCommonPrefix(char** strs, int strsSize) {
    if (strsSize == 0) return "";
    char* prefix = strs[0];
    for (int i = 1; i < strsSize; i++) {
        while (strncmp(strs[i], prefix, strlen(prefix)) != 0) {
            prefix[strlen(prefix) - 1] = '\0';
            if (strlen(prefix) == 0) return "";
        }
    }
    return prefix;
}

Finds the longest common prefix string among an array of strings by iteratively shortening the prefix.

Execution Table

Step	Operation	Current String	Prefix Before	Prefix After	Visual State
1	Initialize prefix	N/A	N/A	"flower"	"flower"
2	Compare prefix with "flow"	"flow"	"flower"	"flowe"	"flowe" (shortened)
3	Compare prefix with "flow"	"flow"	"flowe"	"flow"	"flow" (shortened)
4	Compare prefix with "flow"	"flow"	"flow"	"flow"	"flow" (matches)
5	Compare prefix with "flight"	"flight"	"flow"	"flo"	"flo" (shortened)
6	Compare prefix with "flight"	"flight"	"flo"	"fl"	"fl" (shortened)
7	Compare prefix with "flight"	"flight"	"fl"	"fl"	"fl" (matches)
8	All strings processed	N/A	"fl"	"fl"	"fl" (final prefix)

💡 All strings processed, prefix is "fl" which is the longest common prefix.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 5	After Step 7	Final
prefix	"flower"	"flowe"	"flow"	"flo"	"fl"	"fl"
current string	N/A	"flow"	"flow"	"flight"	"flight"	N/A

Key Moments - 3 Insights

Why do we shorten the prefix instead of moving forward in the string?

Because the prefix must be common to all strings from the start, we reduce it until it matches the start of the current string (see steps 2-7 in execution_table). Moving forward would miss common starting characters.

What happens if the prefix becomes empty?

If prefix becomes empty, it means no common prefix exists. The loop would stop and return an empty string (not shown in this example but implied in the flow).

Why do we start prefix as the first string?

Starting with the first string ensures the prefix is initially the longest possible. We then shorten it based on other strings (step 1 in execution_table).

Visual Quiz - 3 Questions

Look at the execution_table, what is the prefix after step 3?

A "flo"

B "flowe"

C "flow"

D "fl"

💡 Hint

Check the 'Prefix After' column in row with Step 3.

At which step does the prefix first become "fl"?

A Step 5

B Step 6

C Step 7

D Step 8

💡 Hint

Look at the 'Prefix After' column for steps 5, 6, and 7.

If the second string was "flowerpot" instead of "flow", how would the prefix change after step 2?

A "flower"

B "flowe"

C "flow"

D "fl"

💡 Hint

Compare the prefix with the new string "flowerpot" and see if shortening is needed at step 2.

Concept Snapshot

Longest Common Prefix:
- Start prefix as first string
- For each next string, shorten prefix until it matches start
- If prefix empty, return ""
- After all strings, prefix is longest common prefix
- Uses string comparison and substring shortening

Full Transcript

This concept finds the longest common prefix among an array of strings. We start by assuming the first string is the prefix. Then, for each other string, we compare it with the prefix. If the prefix is not at the start of the current string, we shorten the prefix by removing the last character. We repeat this until the prefix matches the start of the current string or becomes empty. If it becomes empty, we return an empty string. Otherwise, after processing all strings, the prefix is the longest common prefix. The execution table shows how the prefix changes step by step with example strings "flower", "flow", and "flight".

Practice

1. What does the Longest Common Prefix (LCP) problem ask for when given an array of strings?

easy

A. The longest ending substring common to all strings

B. The longest substring common to any two strings

C. The longest starting substring common to all strings

D. The shortest string in the array

Solution

1. Step 1: Understand the problem definition

   The Longest Common Prefix means the longest substring starting from the beginning that is shared by all strings in the array.

2. Step 2: Compare options with definition

   Only The longest starting substring common to all strings matches this definition exactly. Options A and C talk about suffix or any substring, and D is unrelated.

3. Final Answer:

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

4. Quick Check:

   Longest Common Prefix = longest starting substring [OK]

Hint: Focus on the start of strings for common parts [OK]

Common Mistakes:

• Confusing prefix with suffix
• Thinking about any substring instead of prefix
• Choosing shortest string instead of prefix

2. Which of the following C code snippets correctly initializes a variable to store the longest common prefix length?

easy

A. int lcp_length = 0;

B. char lcp_length = '';

C. int lcp_length = NULL;

D. string lcp_length = 0;

Solution

1. Step 1: Identify correct data type for prefix length

   The length of a prefix is a number, so it should be stored in an integer variable.

2. Step 2: Check initialization syntax

   int lcp_length = 0; correctly declares an int and initializes it to 0. char lcp_length = ''; uses char with invalid empty quotes, C uses NULL which is for pointers, and D uses string which is not a C type.

3. Final Answer:

   int lcp_length = 0; -> Option A

4. Quick Check:

   Prefix length is an integer initialized to zero [OK]

Hint: Use int for lengths, not char or string [OK]

Common Mistakes:

• Using char for numeric length
• Assigning NULL to int variable
• Using non-C types like string

3. What is the output of the following C code snippet that finds the longest common prefix length?

char *strs[] = {"flower", "flow", "flight"};
int i = 0;
while (strs[0][i] && strs[1][i] && strs[2][i] && strs[0][i] == strs[1][i] && strs[1][i] == strs[2][i]) {
    i++;
}
printf("%d", i);

medium

A. 4

B. 2

C. 3

D. 0

Solution

1. Step 1: Compare characters at each index

   Index 0: 'f' == 'f' == 'f' (true), index 1: 'l' == 'l' == 'l' (true), index 2: 'o' == 'o' == 'i' (false)

2. Step 2: Count matching prefix length

   Matching characters are at indices 0 and 1 only, so length is 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Matching prefix length = 2 [OK]

Hint: Check characters index by index until mismatch [OK]

Common Mistakes:

• Counting beyond first mismatch
• Confusing index with length
• Ignoring all strings in comparison

4. Identify the bug in this C code snippet that tries to find the longest common prefix of an array of strings:

int longestCommonPrefix(char **strs, int strsSize) {
    int i = 0;
    while (strs[0][i]) {
        for (int j = 1; j < strsSize; j++) {
            if (strs[j][i] != strs[0][i])
                return i;
        }
        i++;
    }
    return i;
}

medium

A. Does not initialize i before use

B. Returns i too early inside the loop

C. Uses wrong loop variable in inner loop

D. Does not check if strs[j][i] is null before comparison

Solution

1. Step 1: Analyze character comparison in inner loop

   The code compares strs[j][i] with strs[0][i] but does not check if strs[j][i] is '\0' (string end).

2. Step 2: Understand consequence of missing null check

   If strs[j] is shorter than strs[0], accessing strs[j][i] beyond its length causes undefined behavior or wrong result.

3. Final Answer:

   Does not check if strs[j][i] is null before comparison -> Option D

4. Quick Check:

   Check string length before comparing characters [OK]

Hint: Always check string end before character compare [OK]

Common Mistakes:

• Ignoring string length in loops
• Returning too early without full check
• Using wrong loop indices

5. Given an array of strings ["interview", "interval", "internal", "internet"], which of the following C code snippets correctly returns the longest common prefix string?

hard

A. int i = 0;
while (1) {
char c = strs[0][i];
if (c == '\0') break;
for (int j = 1; j < strsSize; j++) {
if (strs[j][i] != c || strs[j][i] == '\0')
goto end;
}
i++;
}
end:
char *prefix = malloc(i + 1);
strncpy(prefix, strs[0], i);
prefix[i] = '\0';
return prefix;

B. int i = 0;
while (strs[0][i]) {
for (int j = 1; j < strsSize; j++) {
if (strs[j][i] != strs[0][i])
break;
}
i++;
}
char *prefix = malloc(i + 1);
strncpy(prefix, strs[0], i);
prefix[i] = '\0';
return prefix;

C. int i = 0;
while (strs[0][i]) {
for (int j = 1; j < strsSize; j++) {
if (strs[j][i] != strs[0][i])
return NULL;
}
i++;
}
return strs[0];

D. int i = 0;
while (strs[0][i]) {
for (int j = 1; j < strsSize; j++) {
if (strs[j][i] != strs[0][i])
return "";
}
i++;
}
return strs[0];

Solution

1. Step 1: Check loop and character comparison logic

   The correct code uses while(1) with break if strs[0][i] == '\0', caches c = strs[0][i], and for each j checks strs[j][i] != c || strs[j][i] == '\0' then goto end before i++. This stops exactly at the first mismatch or shorter string.

2. Step 2: Verify prefix extraction and return

   After loop, malloc(i + 1), strncpy(prefix, strs[0], i), prefix[i] = '\0', return prefix. This creates and returns the new prefix string correctly.

3. Final Answer:

   Uses while(1), goto on mismatch/null, malloc/strncpy new prefix -> Option A

4. Quick Check:

   Check all strings char by char, then copy prefix [OK]

Hint: Use memory copy after finding prefix length [OK]

Common Mistakes:

• Not handling string ends properly
• Returning original string instead of prefix
• Not allocating memory for prefix