String Pattern Matching Naive in DSA C# - Time & Space Complexity

Time Complexity: String Pattern Matching Naive

O(n * m)

Understanding Time Complexity

We want to understand how long it takes to find a pattern inside a text using a simple method.

How does the time needed grow when the text or pattern gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public static int NaivePatternMatch(string text, string pattern)
{
    int n = text.Length;
    int m = pattern.Length;
    for (int i = 0; i <= n - m; i++)
    {
        int j;
        for (j = 0; j < m; j++)
        {
            if (text[i + j] != pattern[j])
                break;
        }
        if (j == m)
            return i; // pattern found at index i
    }
    return -1; // pattern not found
}
    

This code checks every possible position in the text to see if the pattern matches starting there.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing characters of the pattern with the text.
• How many times: For each position in the text (about n - m + 1 times), it compares up to m characters.

How Execution Grows With Input

As the text and pattern get longer, the number of comparisons grows roughly by multiplying their lengths.

Input Size (n)	Approx. Operations
10 (text), 3 (pattern)	About 8 * 3 = 24 comparisons
100 (text), 5 (pattern)	About 96 * 5 = 480 comparisons
1000 (text), 10 (pattern)	About 991 * 10 = 9,910 comparisons

Pattern observation: Doubling the text or pattern length roughly doubles the work, so the total work grows like the product of their sizes.

Final Time Complexity

Time Complexity: O(n * m)

This means the time needed grows proportionally to the text length times the pattern length.

Common Mistake

[X] Wrong: "The search always takes time proportional to the text length only."

[OK] Correct: Because for each position in the text, the pattern characters are also checked, so the pattern length matters too.

Interview Connect

Understanding this simple search method helps build a foundation for more efficient algorithms and shows you can analyze how code scales with input size.

Self-Check

"What if we used a more advanced algorithm like KMP instead of naive search? How would the time complexity change?"

Practice

1. What is the main idea behind the naive string pattern matching algorithm?

easy

A. Check every possible position in the text to find the pattern

B. Use a hash function to find the pattern quickly

C. Build a prefix table to skip unnecessary comparisons

D. Sort the text and pattern before matching

Solution

1. Step 1: Understand naive matching approach

   The naive algorithm tries to match the pattern starting at every position in the text.

2. Step 2: Compare with other methods

   Other methods like hashing or prefix tables are not used in naive matching.

3. Final Answer:

   Check every possible position in the text to find the pattern -> Option A

4. Quick Check:

   Naive = Check all positions [OK]

Hint: Naive means try all positions one by one [OK]

Common Mistakes:

• Confusing naive with hashing or prefix methods
• Thinking naive skips positions
• Assuming sorting is involved

2. Which of the following is the correct syntax to start a loop for naive pattern matching in C# if text length is n and pattern length is m?

easy

A. for (int i = 0; i <= n; i++)

B. for (int i = 0; i < n; i++)

C. for (int i = 0; i < m; i++)

D. for (int i = 0; i <= n - m; i++)

Solution

1. Step 1: Determine loop range for pattern matching

   The loop must run from 0 to n - m inclusive to avoid overflow when matching pattern of length m.

2. Step 2: Check each option

   for (int i = 0; i <= n - m; i++) correctly uses i <= n - m. Others either go beyond or are too short.

3. Final Answer:

   for (int i = 0; i <= n - m; i++) -> Option D

4. Quick Check:

   Loop till n - m inclusive [OK]

Hint: Loop till n - m to fit pattern fully [OK]

Common Mistakes:

• Looping till n causes index out of range
• Looping till m is too short
• Using < instead of <= misses last position

3. What will be the output of the following C# code snippet?

string text = "abcabcabc";
string pattern = "abc";
int count = 0;
for (int i = 0; i <= text.Length - pattern.Length; i++) {
    int j;
    for (j = 0; j < pattern.Length; j++) {
        if (text[i + j] != pattern[j])
            break;
    }
    if (j == pattern.Length)
        count++;
}
Console.WriteLine(count);

medium

A. 1

B. 2

C. 3

D. 0

Solution

1. Step 1: Identify pattern occurrences in text

   The pattern "abc" appears at positions 0, 3, and 6 in the text "abcabcabc".

2. Step 2: Count matches in the loop

   The inner loop confirms full matches at these positions, so count increments 3 times.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Pattern occurs 3 times [OK]

Hint: Count full matches by checking all pattern chars [OK]

Common Mistakes:

• Counting partial matches
• Off-by-one errors in loop limits
• Breaking early without counting

4. The following code tries to implement naive pattern matching but does not work correctly. What is the bug?

string text = "hellohello";
string pattern = "lo";
int count = 0;
for (int i = 0; i < text.Length - pattern.Length; i++) {
    int j;
    for (j = 0; j < pattern.Length; j++) {
        if (text[i + j] != pattern[j])
            break;
    }
    if (j == pattern.Length)
        count++;
}
Console.WriteLine(count);

medium

A. The outer loop should use <= instead of < to include last position

B. The inner loop should start from 1 instead of 0

C. The pattern length is not used correctly

D. The count variable is not initialized

Solution

1. Step 1: Analyze loop boundary

   The outer loop runs from 0 to text.Length - pattern.Length - 1, missing the last valid start position.

2. Step 2: Correct loop condition

   Changing < to <= ensures the last possible position is checked for pattern match.

3. Final Answer:

   The outer loop should use <= instead of < to include last position -> Option A

4. Quick Check:

   Loop boundary off by one [OK]

Hint: Use <= to cover last possible start index [OK]

Common Mistakes:

• Using < causes missing last match
• Changing inner loop start breaks matching
• Ignoring initialization of count

5. Given a text "ababababab" and a pattern "abab", how many times will the naive pattern matching algorithm find the pattern if overlapping matches are counted?

hard

A. 2

B. 4

C. 3

D. 5

Solution

1. Step 1: Identify all overlapping matches

   The pattern "abab" appears starting at indices 0, 2, 4, and 6 in the text "ababababab".

2. Step 2: Count total matches including overlaps

   Counting all these positions gives 4 matches.

3. Final Answer:

   4 -> Option B

4. Quick Check:

   Overlapping matches counted = 4 [OK]

Hint: Check every position, count overlaps too [OK]

Common Mistakes:

• Ignoring overlapping matches
• Counting only non-overlapping occurrences
• Miscounting start indices