Rabin Karp String Matching in DSA Python - Build from Scratch

Rabin Karp String Matching

📖 Scenario: You are building a simple text search tool that finds if a small pattern exists inside a larger text. This is like searching for a word in a book.

🎯 Goal: Implement the Rabin Karp algorithm to find the first position of a pattern string inside a text string using hashing.

📋 What You'll Learn

Create variables for the text and pattern strings

Set up variables for the hashing base and modulus

Calculate initial hash values for pattern and first window of text

Slide over the text to check for matching hash and then verify characters

Print the starting index of the first match or -1 if no match

💡 Why This Matters

🌍 Real World

Text search is used in search engines, editors, and DNA sequence analysis to quickly find patterns.

💼 Career

Understanding Rabin Karp helps in roles involving text processing, software development, and algorithm optimization.

1

Create the text and pattern strings

Create a variable called text and set it to the string "abracadabra". Create another variable called pattern and set it to the string "cada".

DSA Python

# Create variables text and pattern with given strings
# Your code here

Hint

Use simple string assignment like text = "abracadabra".

2

Set up hashing base and modulus

Create a variable called base and set it to 256. Create another variable called modulus and set it to 101. These will be used for hashing.

DSA Python

text = "abracadabra"
pattern = "cada"
# Create base and modulus variables for hashing
# Your code here

Hint

Use base = 256 and modulus = 101 exactly.

3

Calculate initial hashes and implement Rabin Karp logic

Create variables pattern_hash and text_hash and set them to 0. Create a variable h and set it to 1. Calculate h as (base ** (len(pattern) - 1)) % modulus. Use a for loop with variable i from 0 to len(pattern) - 1 to calculate the initial hash values for pattern_hash and text_hash. Then use a for loop with variable i from 0 to len(text) - len(pattern) + 1 to slide over the text, check if hashes match, and if so, verify characters one by one. If a match is found, set a variable result to the starting index i and break the loop. If no match is found, set result to -1.

DSA Python

text = "abracadabra"
pattern = "cada"
base = 256
modulus = 101
# Calculate initial hashes and implement Rabin Karp search
# Your code here

Hint

Calculate h first, then initial hashes, then slide over text checking hashes and characters.

4

Print the result index

Write a print statement to display the value of the variable result.

DSA Python

text = "abracadabra"
pattern = "cada"
base = 256
modulus = 101
pattern_hash = 0
text_hash = 0
h = 1
for i in range(len(pattern) - 1):
    h = (h * base) % modulus
for i in range(len(pattern)):
    pattern_hash = (base * pattern_hash + ord(pattern[i])) % modulus
    text_hash = (base * text_hash + ord(text[i])) % modulus
result = -1
for i in range(len(text) - len(pattern) + 1):
    if pattern_hash == text_hash:
        match = True
        for j in range(len(pattern)):
            if text[i + j] != pattern[j]:
                match = False
                break
        if match:
            result = i
            break
    if i < len(text) - len(pattern):
        text_hash = (base * (text_hash - ord(text[i]) * h) + ord(text[i + len(pattern)])) % modulus
        if text_hash < 0:
            text_hash += modulus
# Print the result variable
# Your code here

Hint

Use print(result) to show the index.

Practice

1. What is the main idea behind the Rabin Karp String Matching algorithm?

easy

A. It uses hashing to find pattern matches efficiently.

B. It compares each character one by one without hashing.

C. It sorts the text before searching for the pattern.

D. It uses recursion to find the pattern in the text.

Solution

1. Step 1: Understand Rabin Karp's approach

   The algorithm uses a hash function to convert the pattern and text substrings into numbers.

2. Step 2: Use hashing for efficient matching

   By comparing hash values instead of characters, it quickly finds potential matches.

3. Final Answer:

   It uses hashing to find pattern matches efficiently. -> Option A

4. Quick Check:

   Hashing = Efficient matching [OK]

Hint: Remember: Rabin Karp uses hashing for fast pattern search [OK]

Common Mistakes:

• Thinking it compares characters directly without hashing
• Confusing it with sorting-based algorithms
• Assuming it uses recursion

2. Which of the following is the correct way to compute the rolling hash in Rabin Karp for the next substring?

easy

A. new_hash = old_hash * old_char + new_char

B. new_hash = old_hash + old_char - new_char

C. new_hash = (old_hash - old_char * base^(m-1)) * base + new_char

D. new_hash = old_hash / base + new_char * base^(m-1)

Solution

1. Step 1: Recall rolling hash formula

   Rolling hash removes the old char's contribution and adds the new char's value.

2. Step 2: Apply formula correctly

   It subtracts old_char * base^(m-1), multiplies by base, then adds new_char.

3. Final Answer:

   new_hash = (old_hash - old_char * base^(m-1)) * base + new_char -> Option C

4. Quick Check:

   Rolling hash formula = new_hash = (old_hash - old_char * base^(m-1)) * base + new_char [OK]

Hint: Subtract old char, multiply by base, add new char [OK]

Common Mistakes:

• Adding old_char instead of subtracting
• Dividing instead of multiplying by base
• Ignoring power of base for old_char

3. What will be the output of the following code snippet using Rabin Karp to find pattern 'abc' in text 'ababc'?

def rabin_karp(text, pattern):
    base = 256
    prime = 101
    m = len(pattern)
    n = len(text)
    pattern_hash = 0
    text_hash = 0
    h = 1

    for i in range(m-1):
        h = (h * base) % prime

    for i in range(m):
        pattern_hash = (base * pattern_hash + ord(pattern[i])) % prime
        text_hash = (base * text_hash + ord(text[i])) % prime

    for i in range(n - m + 1):
        if pattern_hash == text_hash:
            if text[i:i+m] == pattern:
                return i
        if i < n - m:
            text_hash = (base * (text_hash - ord(text[i]) * h) + ord(text[i + m])) % prime
            if text_hash < 0:
                text_hash += prime
    return -1

print(rabin_karp('ababc', 'abc'))

medium

A. 0

B. 1

C. -1

D. 2

Solution

1. Step 1: Calculate pattern and initial text hash

   Pattern 'abc' length 3, initial text substring 'aba'. Hashes differ, so move forward.

2. Step 2: Slide over text and compare hashes

   At index 1, substring 'bab' hash differs. At index 2, substring 'abc' hash matches pattern hash and strings match.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Pattern found at index 2 [OK]

Hint: Check hash then substring; match at index 2 [OK]

Common Mistakes:

• Returning first hash match without substring check
• Confusing index positions
• Ignoring negative hash adjustment

4. Identify the bug in this Rabin Karp implementation snippet:

text_hash = (base * (text_hash - ord(text[i]) * h) + ord(text[i + m])) % prime
if text_hash < 0:
    text_hash = text_hash - prime

medium

A. The negative hash correction should add prime, not subtract.

B. The subtraction of ord(text[i]) * h is incorrect.

C. The modulo operation should be done after adding prime.

D. The base should be added, not multiplied.

Solution

1. Step 1: Understand negative hash correction

   If hash is negative after modulo, add prime to make it positive.

2. Step 2: Identify incorrect operation

   Code subtracts prime instead of adding it, causing wrong hash values.

3. Final Answer:

   The negative hash correction should add prime, not subtract. -> Option A

4. Quick Check:

   Negative hash fix = add prime [OK]

Hint: Add prime if hash is negative, never subtract [OK]

Common Mistakes:

• Subtracting prime instead of adding
• Ignoring negative hash values
• Misplacing modulo operation

5. Given a large text and multiple patterns, which modification to Rabin Karp helps efficiently find all patterns in the text?

hard

A. Run Rabin Karp separately for each pattern without optimization.

B. Use a combined hash set of all patterns and check text substrings against it.

C. Sort all patterns and use binary search on text substrings.

D. Use recursion to search each pattern in the text.

Solution

1. Step 1: Understand multiple pattern search challenge

   Running Rabin Karp separately for each pattern is inefficient for many patterns.

2. Step 2: Use combined hashing approach

   Hash all patterns and store in a set. Then check each text substring's hash against this set for quick matches.

3. Final Answer:

   Use a combined hash set of all patterns and check text substrings against it. -> Option B

4. Quick Check:

   Combined hash set = efficient multi-pattern search [OK]

Hint: Hash all patterns once, check text hashes against set [OK]

Common Mistakes:

• Running separate searches for each pattern
• Sorting patterns instead of hashing
• Using recursion unnecessarily