Implementations of z array and algorithm for string matching

pydatastructs/miscellaneous_data_structures/tests/test_stack.py

@@ -3,6 +3,7 @@
 from pydatastructs.utils.raises_util import raises
 from pydatastructs.utils.misc_util import _check_type
 
+
 def test_Stack():
     s = Stack(implementation='array')
     s1 = Stack()
@@ -12,6 +13,7 @@ def test_Stack():
     assert _check_type(s2, LinkedListStack) is True
     assert raises(NotImplementedError, lambda: Stack(implementation=''))
 
+
 def test_ArrayStack():
     s = Stack(implementation='array')
     s.push(1)
@@ -23,11 +25,12 @@ def test_ArrayStack():
     assert s.pop() == 2
     assert s.pop() == 1
     assert s.is_empty is True
-    assert raises(IndexError, lambda : s.pop())
+    assert raises(IndexError, lambda: s.pop())
     _s = Stack(items=[1, 2, 3])
     assert str(_s) == '[1, 2, 3]'
     assert len(_s) == 3
 
+
 def test_LinkedListStack():
     s = Stack(implementation='linked_list')
     s.push(1)
@@ -39,16 +42,17 @@ def test_LinkedListStack():
     assert s.pop().key == 2
     assert s.pop().key == 1
     assert s.is_empty is True
-    assert raises(IndexError, lambda : s.pop())
+    assert raises(IndexError, lambda: s.pop())
     assert str(s) == '[]'
-    _s = Stack(implementation='linked_list',items=[1, 2, 3])
+    _s = Stack(implementation='linked_list', items=[1, 2, 3])
     assert str(_s) == "['(1, None)', '(2, None)', '(3, None)']"
     assert len(_s) == 3
 
-    s = Stack(implementation='linked_list',items=['a',None,type,{}])
+    s = Stack(implementation='linked_list', items=['a', None, type, {}])
     assert len(s) == 4
     assert s.size == 4
 
     peek = s.peek
     assert peek.key == s.pop().key
-    assert raises(TypeError, lambda: Stack(implementation='linked_list', items={0, 1}))
+    assert raises(TypeError, lambda: Stack(
+        implementation='linked_list', items={0, 1}))

pydatastructs/strings/Z_function.py

@@ -0,0 +1,93 @@
+
+# from pydatastructs.utils.misc_util import (
+#   Backend, raise_if_backend_is_not_python)
+
+
+"""Suppose we are given a string s of length n. The Z-function for this string is an array 
+of length n where the i-th element is equal to the greatest number of characters starting 
+from the position i that coincide with the first characters of s.
+
+In other words, z[i] is the length of the longest string that is, at the same time, a 
+prefix of s and a prefix of the suffix of s starting at i."""
+
+
+def search(text, pattern):
+
+    # Create concatenated string "P$T"
+    concat = pattern + "$" + text
+    l = len(concat)
+
+    # Construct Z array
+    z = [0] * l
+    Z_Array(concat, z)
+
+    # now looping through Z array for matching condition
+    for i in range(l):
+
+        # if Z[i] (matched region) is equal to pattern
+        # length we got the pattern
+        if z[i] == len(pattern):
+            return i - len(pattern) - 1
+
+
+def Z_Array(string, z):
+    n = len(string)
+
+    # [L,R] make a window which matches
+    # with prefix of s
+    l, r, k = 0, 0, 0
+    for i in range(1, n):
+
+        # if i>R nothing matches so we will calculate.
+        # Z[i] using naive way.
+        if i > r:
+            l, r = i, i
+
+            # R-L = 0 in starting, so it will start
+            # checking from 0'th index. For example,
+            # for "ababab" and i = 1, the value of R
+            # remains 0 and Z[i] becomes 0. For string
+            # "aaaaaa" and i = 1, Z[i] and R become 5
+            while r < n and string[r - l] == string[r]:
+                r += 1
+            z[i] = r - l
+            r -= 1
+        else:
+
+            # k = i-L so k corresponds to number which
+            # matches in [L,R] interval.
+            k = i - l
+
+            # if Z[k] is less than remaining interval
+            # then Z[i] will be equal to Z[k].
+            # For example, str = "ababab", i = 3, R = 5
+            # and L = 2
+            if z[k] < r - i + 1:
+                z[i] = z[k]
+
+            # For example str = "aaaaaa" and i = 2,
+            # R is 5, L is 0
+            else:
+
+                # else start from R and check manually
+                l = i
+                while r < n and string[r - l] == string[r]:
+                    r += 1
+                z[i] = r - l
+                r -= 1
+
+
+"""If the programmer only needs the values of Z array for other appllications of this algorithm
+such as String compression
+"""
+
+
+def Z_function(pattern, text):
+    concat = pattern + "$" + text
+
+    l = len(concat)
+
+    # Construct Z array
+    z = [0] * l
+    Z_Array(concat, z)
+    return z