pythonstringalgorithmpattern-matching

# Python: Rabin-Karp algorithm hashing

I am implementing Rabin-Karp algorithm for fun. I came across this pseudocode:

``````    RABIN -KARP -MATCHER (T, P, d, q)
1 n = T.length
2 m = P.length
3 h = d^(m-1) mod q
4 p=0
5 t= 0
6 for i = 1 to m
/ preprocessing
/
7 p = (dp + P [i]) mod q
8 t = (dt + T [i]) mod q
9 for s = 0 to n-m
/ matching
/
10     if p == t
11         if P [1... m] == T [s + 1...s + m]
12             print “Pattern occurs with shift” s
13     if s < n-m
14         t  = (d(t-T[s + 1]h) + T [s + m + 1]) mod q
``````

I implemented in Python 2.7 like so:

``````def Rabin_Karp_Matcher(text, pattern, d, q):
n = len(text)
m = len(pattern)
h = pow(d,m-1)%q
p = 0
t =0
result = []
for i in range(m): # preprocessing
p = (d*p+ord(pattern[i]))%q
t = (d*t+ord(text[i]))%q
for s in range(n-m):
if p == t: # check character by character
match = True
for i in range(m):
if pattern[i] != text[s+i]:
match = False
break
if match:
result = result + [s]
if s < n-m:
t = (d*(t-ord(text[s+1])*h)+ord(text[s+m]))%q #index out of bounds here
return result
``````

where result is a list containing the index in text of pattern.

My code is failing to find the 26 in 3141592653589793 and I suspect it has something to do with my hashcode defined by line 14 of the pseudocode. Can anyone please help with this.

I passed in the following paramters:

P = "26" T = "3141592653589793" d = 257 q = 11

P and T must be strings/arrays of chars

Solution

• Here is a working version of your code:

``````def Rabin_Karp_Matcher(text, pattern, d, q):
n = len(text)
m = len(pattern)
h = pow(d,m-1)%q
p = 0
t = 0
result = []
for i in range(m): # preprocessing
p = (d*p+ord(pattern[i]))%q
t = (d*t+ord(text[i]))%q
for s in range(n-m+1): # note the +1
if p == t: # check character by character
match = True
for i in range(m):
if pattern[i] != text[s+i]:
match = False
break
if match:
result = result + [s]
if s < n-m:
t = (t-h*ord(text[s]))%q # remove letter s
t = (t*d+ord(text[s+m]))%q # add letter s+m
t = (t+q)%q # make sure that t >= 0
return result
print (Rabin_Karp_Matcher ("3141592653589793", "26", 257, 11))
print (Rabin_Karp_Matcher ("xxxxx", "xx", 40999999, 999999937))
``````

The output is:

``````[6]
[0, 1, 2, 3]
``````

On the first step, you check whether `text[0..m] == pattern`. On the second step, you want to check whether `text[1..m+1] == pattern`. Thus you remove `text[0]` from the hash (at the moment it is multiplied by your precomputed `h`): `t = (t-h*ord(text[s]))%q`. And then, add `text[m]` to it: `t = (t*d+ord(text[s+m]))%q`. On the next step, you remove `text[1]` and add `text[m+1]`, and so on. The `t = (t+q)%q` line is there because a negative number modulo `q` yields remainder in the range `(-q; 0]`, and we want it to be in the range `[0; q)`.

Note that you want to check a total of `n-m+1` substrings, not `n-m`, hence the correct loop is `for s in range(n-m+1)`. Checked by the second example (finding "xx" in "xxxxx").

Also worth noting:

1. The line `h = pow(d,m-1)%q` may be too slow if `m` is large. It is better to take the result modulo `q` after each of the `m-2` multiplications. Or just use the built-in way: `h = pow(d,m-1,q)`, as suggested by @oBrstisf8o in the comments.

2. This algorithm is still O(nm) in the worst case. With `text="a"*100000` and `pattern="a"*50000`, it will find 50001 positions where a substring of text matches the pattern, and it will check them all character-by-character. If you expect your code to work fast in such extreme cases, you should skip the character-by-character comparison and find a way to deal with false positives (i.e., hashes are equal but strings are not). Picking a large prime number `q` may help reduce the probability of a false positive to an acceptable level.