#author: Pankaj Kumar
#time complexity: O(length(string) + length(pattern))
#space complexity: O(length(string) + length(pattern))
#Link to theory: http://www.geeksforgeeks.org/z-algorithm-linear-time-pattern-searching-algorithm/
def z_algo(arr):
z = [0 for i in range(len(arr))]
left , right = 0 , 0
for k in range(1 , len(arr)):
if k > right:
left = k
right = k
while right < len(arr) and arr[right] == arr[right-left]:
right += 1
z[k] = right - left
right -= 1
else:
k1 = k - left
if z[k1] < right - k + 1:
z[k] = z[k1]
else:
left = k
while right < len(arr) and arr[right] == arr[right-left]:
right += 1
z[k] = right - left
right -= 1
return z
def makepattern(string , pattern):
n , m = len(string) , len(pattern)
str_arr = []
for i in range(m):
str_arr.append(pattern[i])
str_arr.append('$')
for i in range(n):
str_arr.append(string[i])
z_values = z_algo(str_arr)
result = []
for i in range(len(z_values)):
if z_values[i] == m:
result.append(i - m - 1)
print result
if __name__ == '__main__':
string = 'abcdeabcd'
pattern = 'abc'
makepattern(string , pattern)