Longest Common Prefix in DSA C - Time & Space Complexity

Time Complexity: Longest Common Prefix

O(n * m)

Understanding Time Complexity

We want to understand how the time needed to find the longest common prefix changes as we add more words or longer words.

How does the work grow when the input list or word length grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code finds the longest common prefix among an array of strings by comparing characters one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Nested loops comparing characters of each string at the same position.
• How many times: Outer loop runs up to the length of the shortest string; inner loop runs for each string in the array.

How Execution Grows With Input

As we add more strings or longer strings, the comparisons increase.

Input Size (n = number of strings)	Approx. Operations
10 strings, each length 5	About 50 character comparisons
100 strings, each length 5	About 500 character comparisons
100 strings, each length 100	Up to 10,000 character comparisons

Pattern observation: The work grows roughly with the product of the number of strings and the length of the shortest string.

Final Time Complexity

Time Complexity: O(n * m)

This means the time grows with the number of strings (n) times the length of the shortest string (m).

Common Mistake

[X] Wrong: "The time depends only on the number of strings, not their length."

[OK] Correct: We must check characters one by one, so longer strings mean more work even if the number of strings stays the same.

Interview Connect

Understanding this helps you explain how your solution scales and shows you can analyze nested loops clearly.

Self-Check

"What if we sorted the strings first and only compared the first and last strings? How would the time complexity change?"

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