I was understanding the Rabin-Karp Algorithm from this website: https://www.geeksforgeeks.org/rabin-karp-algorithm-for-pattern-searching/
They had the following code in C++ for the algorithm:
#include <bits/stdc++.h>
using namespace std;
// d is the number of characters in the input alphabet
#define d 256
/* pat -> pattern
txt -> text
q -> A prime number
*/
void search(char pat[], char txt[], int q)
{
int M = strlen(pat);
int N = strlen(txt);
int i, j;
int p = 0; // hash value for pattern
int t = 0; // hash value for txt
int h = 1;
// The value of h would be "pow(d, M-1)%q"
for (i = 0; i < M - 1; i++)
h = (h * d) % q;
// Calculate the hash value of pattern and first
// window of text
for (i = 0; i < M; i++)
{
p = (d * p + pat[i]) % q;
t = (d * t + txt[i]) % q;
}
// Slide the pattern over text one by one
for (i = 0; i <= N - M; i++)
{
// Check the hash values of current window of text
// and pattern. If the hash values match then only
// check for characters on by one
if ( p == t )
{
/* Check for characters one by one */
for (j = 0; j < M; j++)
{
if (txt[i+j] != pat[j])
break;
}
// if p == t and pat[0...M-1] = txt[i, i+1, ...i+M-1]
if (j == M)
cout<<"Pattern found at index "<< i<<endl;
}
// Calculate hash value for next window of text: Remove
// leading digit, add trailing digit
if ( i < N-M )
{
t = (d*(t - txt[i]*h) + txt[i+M])%q;
// We might get negative value of t, converting it
// to positive
if (t < 0)
t = (t + q);
}
}
}
/* Driver code */
int main()
{
char txt[] = "GEEKS FOR GEEKS";
char pat[] = "GEEK";
// A prime number
int q = 101;
// Function Call
search(pat, txt, q);
return 0;
}
What I didn't understand was this block of code:
// We might get negative value of t, converting it
// to positive
if (t < 0)
t = (t + q);
How can t ever be negative? What we subtract from t is always less than t and then we add something to it so where does the possibility of t beign negative even come from?
I tested the code without this if statement and it didn't work properly. The exepected output was :
Pattern found at index 0
Pattern found at index 10
But I got:
Pattern found at index 0
