Rabin Karp String Matching in DSA C - Execution Trace

Concept Flow - Rabin Karp String Matching

Start

↓

Calculate pattern hash

↓

Calculate initial text window hash

↓

For each window in text

↓

Compare pattern hash and window hash

Yes No↓

Check chars

↓

Match?

↓

Report

↓

End

The algorithm calculates hash of the pattern and text windows, compares hashes, and if equal, checks characters to find matches.

Execution Sample

DSA C

pattern = "abc";
text = "abdabcbabc";
for each window in text:
  if hash(window) == hash(pattern):
    check characters
  slide window and update hash

This code slides a window over the text, compares hash values with the pattern hash, and confirms matches by character check.

Execution Table

Step	Operation	Window Start Index	Pattern Hash	Window Hash	Hash Match?	Character Check	Match Found	Visual State
1	Calculate pattern hash	-	294	-	-	-	-	-
2	Calculate initial window hash (text[0..2])	0	294	294	Yes	Compare 'abc' with 'abd'	No	"a b d" -> ...
3	Slide window to text[1..3]	1	294	303	No	-	No	"b d a" -> ...
4	Slide window to text[2..4]	2	294	294	Yes	Compare 'abc' with 'dab'	No	"d a b" -> ...
5	Slide window to text[3..5]	3	294	294	Yes	Compare 'abc' with 'abc'	Yes	"a b c" -> ...
6	Slide window to text[4..6]	4	294	303	No	-	No	"b c b" -> ...
7	Slide window to text[5..7]	5	294	294	Yes	Compare 'abc' with 'cba'	No	"c b a" -> ...
8	Slide window to text[6..8]	6	294	294	Yes	Compare 'abc' with 'bab'	No	"b a b" -> ...
9	Slide window to text[7..9]	7	294	294	Yes	Compare 'abc' with 'abc'	Yes	"a b c" -> ...
10	Slide window to text[8..10]	-	294	-	-	-	-	-
11	End of text reached	-	294	-	-	-	-	-

💡 Reached end of text windows; no more windows to check.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	After Step 8	After Step 9	After Step 10	Final
pattern_hash	-	294	294	294	294	294	294	294	294	294	294
window_start_index	-	0	1	2	3	4	5	6	7	-	-
window_hash	-	294	303	294	294	303	294	294	294	-	-
match_found	-	No	No	No	Yes	No	No	No	Yes	-	-

Key Moments - 3 Insights

Why do we check characters even if the hashes match?

Because different strings can have the same hash (hash collision). The character check confirms the match, as shown in steps 2, 4, and 5 in the execution_table.

How is the window hash updated when sliding the window?

The hash is updated by removing the leftmost character's contribution and adding the new rightmost character's contribution, avoiding full recomputation. This is why window_hash changes between steps, e.g., step 3.

Why does the algorithm stop after the last window?

Because the window cannot slide beyond the text length minus pattern length. Step 11 shows the end of text windows reached.

Visual Quiz - 3 Questions

Look at the execution_table at step 5. What is the window start index and was a match found?

A Start index 3, match found Yes

B Start index 3, match found No

C Start index 2, match found Yes

D Start index 4, match found Yes

💡 Hint

Check the 'Window Start Index' and 'Match Found' columns in row for step 5.

At which step does the window hash first differ from the pattern hash?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look at the 'Window Hash' and 'Pattern Hash' columns in the execution_table rows.

If the pattern was "abd" instead of "abc", how would the match found at step 2 change?

A Match found would be Yes

B Match found would be No

C Window hash would not be calculated

D Algorithm would stop early

💡 Hint

Consider that the pattern hash would change and compare with window hash at step 2.

Concept Snapshot

Rabin Karp String Matching:
- Compute hash of pattern and initial text window
- Slide window over text, update hash efficiently
- If hashes match, check characters to confirm
- Handles collisions by verification
- Stops when window reaches text end

Full Transcript

Rabin Karp string matching works by calculating a hash value for the pattern and for each window of text of the same length. It slides the window one character at a time, updating the hash efficiently without recomputing from scratch. When the hash of the current window matches the pattern hash, it checks the characters one by one to confirm a real match, because different strings can have the same hash. The process continues until the window reaches the end of the text. This method speeds up searching by avoiding unnecessary character comparisons when hashes differ.