KMP Pattern Matching Algorithm in DSA Python - 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 computer scientists who created this efficient pattern matching 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 'Longest Prefix Suffix' (LPS) 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 characters have matched?

Instead of restarting from the next character in the text, KMP uses the LPS array to shift the pattern to the right position, skipping unnecessary comparisons.

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 Length of the pattern

B Positions of pattern matches in text

C Number of mismatches found

D Length of longest prefix which is also suffix for pattern prefixes

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

Why is KMP faster than naive pattern matching?

A It uses a precomputed table to avoid rechecking characters

B It checks all characters twice

C It uses random guessing

D It only works on small texts

KMP uses the LPS array to skip unnecessary comparisons, avoiding rechecking characters.

What is the worst-case time complexity of KMP?

A O(n + m)

B O(n * m)

C O(n^2)

D O(m^2)

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

When a mismatch occurs in KMP, what does the algorithm do?

A Stops the search

B Restarts matching from the next character in text

C Uses LPS array to shift pattern without rechecking matched characters

D Skips the entire pattern

KMP uses the LPS array to shift the pattern smartly, avoiding rechecking matched characters.

What is the first step in the KMP algorithm?

A Reverse the pattern

B Compute the LPS array for the pattern

C Search the pattern in the text directly

D Sort the text

KMP first computes the LPS array to know how to shift the pattern during matching.

Explain how the LPS array is constructed in the KMP algorithm and why it is important.

Think about matching prefixes and suffixes within the pattern itself.

Describe the process of pattern matching in KMP when a mismatch occurs after some characters matched.

Focus on how KMP shifts the pattern smartly instead of naive restarting.

Practice

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

easy

A. To calculate the factorial of a number recursively

B. To sort an array of numbers in ascending order

C. To reverse a string in linear time

D. To find occurrences of a pattern string within a text efficiently

Solution

1. Step 1: Understand the goal of KMP algorithm

   KMP is designed to search for a pattern inside a larger text efficiently without rechecking characters unnecessarily.

2. Step 2: Compare with other options

   Sorting, reversing strings, and factorial calculations are unrelated to pattern searching.

3. Final Answer:

   To find occurrences of a pattern string within a text efficiently -> Option D

4. Quick Check:

   KMP = Pattern search [OK]

Hint: KMP is about fast pattern search in text [OK]

Common Mistakes:

• Confusing KMP with sorting algorithms
• Thinking KMP reverses strings
• Assuming KMP calculates mathematical functions

2. Which of the following is the correct way to initialize the prefix table (lps array) in KMP algorithm in Python?

easy

A. lps = [0] * len(pattern)

B. lps = []

C. lps = [1] * len(pattern)

D. lps = None

Solution

1. Step 1: Understand the prefix table initialization

   The prefix table (lps array) stores lengths of longest proper prefix which is also suffix for each prefix of the pattern. It must be initialized with zeros for all positions.

2. Step 2: Check each option

   lps = [0] * len(pattern) correctly initializes lps with zeros for the entire pattern length. lps = [] is empty list, which is incomplete. lps = [1] * len(pattern) initializes with ones, which is incorrect. lps = None sets None, which is invalid.

3. Final Answer:

   lps = [0] * len(pattern) -> Option A

4. Quick Check:

   Prefix table starts with zeros [OK]

Hint: Prefix table starts with zeros for all pattern chars [OK]

Common Mistakes:

• Initializing lps with ones instead of zeros
• Leaving lps empty
• Assigning None to lps

3. What will be the output of the following Python code snippet using KMP algorithm?

def compute_lps(pattern):
    lps = [0] * len(pattern)
    length = 0
    i = 1
    while i < len(pattern):
        if pattern[i] == pattern[length]:
            length += 1
            lps[i] = length
            i += 1
        else:
            if length != 0:
                length = lps[length - 1]
            else:
                lps[i] = 0
                i += 1
    return lps

pattern = "ABABC"
lps = compute_lps(pattern)
print(lps)

medium

A. [1, 0, 1, 0, 1]

B. [0, 0, 1, 2, 0]

C. [0, 1, 2, 3, 4]

D. [0, 0, 0, 0, 0]

Solution

1. Step 1: Compute lps array for pattern "ABABC"

   Index 0: lps[0] = 0 (always zero)
   Index 1: pattern[1] = 'B' != pattern[0] = 'A', lps[1] = 0
   Index 2: pattern[2] = 'A' == pattern[0] = 'A', lps[2] = 1
   Index 3: pattern[3] = 'B' == pattern[1] = 'B', lps[3] = 2
   Index 4: pattern[4] = 'C' != pattern[2] = 'A', lps[4] = 0

2. Step 2: Final lps array

   The computed lps array is [0, 0, 1, 2, 0].

3. Final Answer:

   [0, 0, 1, 2, 0] -> Option B

4. Quick Check:

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

Hint: Match prefix and suffix lengths stepwise [OK]

Common Mistakes:

• Confusing lps values with pattern indices
• Assuming all zeros or all increasing values
• Mixing up characters when comparing

4. Identify the error in the following KMP prefix table computation code snippet:

def compute_lps(pattern):
    lps = [0] * len(pattern)
    length = 0
    i = 0
    while i < len(pattern):
        if pattern[i] == pattern[length]:
            length += 1
            lps[i] = length
            i += 1
        else:
            if length != 0:
                length = lps[length - 1]
            else:
                lps[i] = 0
                i += 1
    return lps

medium

A. The loop should start with i = 1, not i = 0

B. The lps array should be initialized with ones

C. The length variable should start at 1

D. The function should return pattern instead of lps

Solution

1. Step 1: Analyze the loop initialization

   In KMP prefix table computation, the first character's lps is always zero and we start comparing from the second character, so i should start at 1.

2. Step 2: Check the given code

   The code starts with i = 0, which causes comparing pattern[0] with pattern[0] immediately, leading to incorrect lps values and infinite loop risk.

3. Final Answer:

   The loop should start with i = 1, not i = 0 -> Option A

4. Quick Check:

   Start i at 1 for prefix table [OK]

Hint: Start prefix loop from second character (i=1) [OK]

Common Mistakes:

• Starting loop at zero causing wrong comparisons
• Initializing lps with ones instead of zeros
• Returning wrong variable

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

hard

A. 2

B. 3

C. 1

D. 0

Solution

1. Step 1: Understand the pattern and text

   The pattern "ABABCABAB" is searched inside the text "ABABDABACDABABCABAB" using KMP which efficiently finds all occurrences.

2. Step 2: Identify pattern occurrences

   By scanning the text:
   - Occurrence starts at index 10 (substring "ABABCABAB")
   So pattern appears 1 time.

3. Final Answer:

   1 -> Option C

4. Quick Check:

   Pattern appears once in text [OK]

Hint: Count all pattern matches including overlaps [OK]

Common Mistakes:

• Counting only first occurrence
• Ignoring overlapping matches
• Misreading pattern or text