KMP Pattern Matching Algorithm in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does KMP stand for in the KMP Pattern Matching Algorithm?

KMP stands for Knuth-Morris-Pratt, the last names of the three people who created this efficient pattern searching algorithm.

beginner

What is the main advantage of the KMP algorithm over the naive pattern matching approach?

KMP avoids rechecking characters that have already been matched by using a precomputed table, making it faster especially for large texts and patterns.

intermediate

What is the purpose of the 'lps' (Longest Prefix Suffix) array in KMP?

The 'lps' array stores the length of the longest proper prefix of the pattern that is also a suffix for each prefix of the pattern. It helps decide where to continue matching after a mismatch.

intermediate

In KMP, what happens when a mismatch occurs after some matches?

Instead of starting over, KMP uses the 'lps' array to skip characters and continue matching from the longest prefix that matches a suffix, saving time.

intermediate

What is the time complexity of the KMP Pattern Matching Algorithm?

The time complexity is O(n + m), where n is the length of the text and m is the length of the pattern, because each character is processed at most twice.

What does the 'lps' array in KMP represent?

A Longest prefix which is also suffix for pattern prefixes

B Length of the pattern

C Positions of pattern matches in text

D Number of mismatches found

The 'lps' array stores the length of the longest proper prefix which is also a suffix for each prefix of the pattern.

What is the main benefit of using KMP over naive pattern matching?

A It uses less memory

B It finds all substrings in constant time

C It works only on small texts

D It avoids rechecking characters after mismatch

KMP avoids rechecking characters by using the 'lps' array, making it more efficient than naive matching.

If a mismatch occurs at pattern index 3, where does KMP jump next?

A Back to pattern start

B To the index given by lps[2]

C To the next character in text

D To the end of the pattern

KMP uses the lps value of the previous index (3-1=2) to decide where to continue matching.

What is the worst-case time complexity of KMP?

A O(n*m)

B O(n^2)

C O(n + m)

D O(m^2)

KMP runs in linear time relative to text and pattern lengths, O(n + m).

Which step is NOT part of the KMP algorithm?

A Restart matching from the beginning after mismatch

B Precompute the lps array

C Compare characters of text and pattern

D Use lps to skip unnecessary comparisons

KMP does NOT restart from the beginning after mismatch; it uses lps to skip ahead.

Explain how the 'lps' array is constructed and how it helps in pattern matching.

Think about prefixes and suffixes in the pattern.

Describe the steps KMP takes when a mismatch happens during pattern matching.

Focus on how KMP avoids rechecking characters.

Practice

1. What is the main purpose of the KMP (Knuth-Morris-Pratt) algorithm in pattern matching?

easy

A. To efficiently find occurrences of a pattern in a text without rechecking characters

B. To sort the characters of the pattern alphabetically

C. To reverse the text before searching

D. To count the total number of characters in the text

Solution

1. Step 1: Understand KMP's goal

   KMP algorithm is designed to find all occurrences of a pattern in a text efficiently.

2. Step 2: Identify how KMP works

   It avoids rechecking characters by using a prefix table to skip unnecessary comparisons.

3. Final Answer:

   To efficiently find occurrences of a pattern in a text without rechecking characters -> Option A

4. Quick Check:

   KMP = Efficient pattern search [OK]

Hint: KMP skips repeated checks using prefix info [OK]

Common Mistakes:

• Thinking KMP sorts or reverses strings
• Confusing KMP with simple substring search
• Assuming KMP counts characters only

2. Which of the following correctly declares the prefix (lps) array in C for KMP algorithm of size m?

easy

A. int *lps = malloc(m * sizeof(int));

B. int lps = new int[m];

C. int lps[m];

D. int lps[] = {m};

Solution

1. Step 1: Understand array declaration in C

   Static arrays like int lps[m]; require constant size or C99 support; dynamic allocation uses malloc.

2. Step 2: Identify correct dynamic allocation

   int *lps = malloc(m * sizeof(int)); correctly allocates memory for m integers dynamically.

3. Final Answer:

   int *lps = malloc(m * sizeof(int)); -> Option A

4. Quick Check:

   Dynamic array = malloc usage [OK]

Hint: Use malloc for dynamic arrays in C [OK]

Common Mistakes:

• Using Java-style array allocation in C
• Incorrect static array size syntax
• Misusing array initialization syntax

3. What will be the output of the following C code snippet using KMP prefix array computation for pattern "ABABC"?

int main() {
    char pattern[] = "ABABC";
    int m = 5, i = 1, len = 0;
    int lps[5] = {0};
    while (i < m) {
        if (pattern[i] == pattern[len]) {
            len++;
            lps[i] = len;
            i++;
        } else {
            if (len != 0) {
                len = lps[len - 1];
            } else {
                lps[i] = 0;
                i++;
            }
        }
    }
    for (int j = 0; j < m; j++) {
        printf("%d ", lps[j]);
    }
    return 0;
}

medium

A. 0 0 1 2 1

B. 0 1 0 1 2

C. 0 1 2 3 4

D. 0 0 1 2 0

Solution

1. Step 1: Compute lps array step-by-step for "ABABC"

   Index 0: 0; i=1: 'B' != 'A' (len=0) -> lps[1]=0, i=2; i=2: 'A' == 'A' -> len=1, lps[2]=1, i=3; i=3: 'B' == 'B' -> len=2, lps[3]=2, i=4; i=4: 'C' != 'A' (len=2) -> len=lps[1]=0, 'C' != 'A' -> lps[4]=0.

2. Step 2: Final lps array values

   The lps array is [0, 0, 1, 2, 0]. Output: 0 0 1 2 0

3. Final Answer:

   0 0 1 2 0 -> Option D

4. Quick Check:

   lps for "ABABC" = 0 0 1 2 0 [OK]

Hint: Trace lps step-by-step for each pattern char [OK]

Common Mistakes:

• Miscomputing fallback index in lps
• Confusing pattern characters during comparison
• Assuming lps always increases

4. Identify the bug in this KMP prefix array computation snippet and select the fix:

int i = 1, len = 0;
while (i <= m) {
    if (pattern[i] == pattern[len]) {
        len++;
        lps[i] = len;
        i++;
    } else {
        if (len != 0) {
            len = lps[len - 1];
        } else {
            lps[i] = 0;
            i++;
        }
    }
}

medium

A. Remove i++ inside else block

B. Initialize len to 1 instead of 0

C. Change loop condition to i < m

D. Use pattern[len+1] instead of pattern[len]

Solution

1. Step 1: Analyze loop boundary

   The loop runs while i <= m, but array indices go from 0 to m-1, so i == m causes out-of-bounds access.

2. Step 2: Correct loop condition

   Changing condition to i < m prevents accessing beyond array size.

3. Final Answer:

   Change loop condition to i < m -> Option C

4. Quick Check:

   Loop index must be less than array size [OK]

Hint: Loop till less than array size, not equal [OK]

Common Mistakes:

• Using <= instead of < causing overflow
• Incorrect initialization of len
• Misplacing increment statements

5. Given text "ABABDABACDABABCABAB" and pattern "ABABCABAB", how many times does the KMP algorithm find the pattern in the text?

hard

A. 1

B. 2

C. 3

D. 0

Solution

1. Step 1: Understand pattern occurrences

   Check the text for exact matches of pattern "ABABCABAB" (length 9).

2. Step 2: Locate matches in text

   Pattern matches fully at index 10 ("ABABCABAB" from positions 10-18) and also at index 0 ("ABABDABAC" partial mismatch at 4th char but KMP finds overlapping matches). Actually, KMP finds the pattern twice: once starting at index 0 (partial mismatch but KMP continues) and once at index 10 fully matching. The correct count is 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Pattern found twice in text [OK]

Hint: Count full pattern matches in text using KMP [OK]

Common Mistakes:

• Counting partial matches as full
• Misidentifying additional matches (e.g., at index 14)
• Overlooking text length boundaries