"""

Problem Statement

=================

Given three strings A, B and C. Write a function that checks whether C is an interleaving of A and B. C is said to be

interleaving A and B, if it contains all characters of A and B and order of all characters in individual strings is

preserved.

http://www.geeksforgeeks.org/check-whether-a-given-string-is-an-interleaving-of-two-other-given-strings-set-2/

Video: https://www.youtube.com/watch?v=ih2OZ9-M3OM

"""

def is_interleaved_recursive(str1, str2, str3, pos1, pos2, pos3):

if pos1 == len(str1) and pos2 == len(str2) and pos3 == len(str3):

return True

if pos3 == len(str3):

return False

return (((pos1 < len(str1) and str1[pos1] == str3[pos3]) and is_interleaved_recursive(str1, str2, str3, pos1 + 1, pos2, pos3 + 1)) or

(pos2 < len(str2) and str2[pos2] == str3[pos3]) and is_interleaved_recursive(str1, str2, str3, pos1, pos2 + 1, pos3 + 1))

def is_interleaved(str1, str2, str3):

if len(str3) != (len(str1) + len(str2)):

return False

cols = len(str1) + 1

rows = len(str2) + 1

T = [[False for _ in range(cols)] for _ in range(rows)]

for row in range(rows):

for col in range(cols):

index = row + col - 1

if row == 0 and col == 0:

T[row][col] = True

elif row == 0:

if str3[index] == str1[col - 1]:

T[row][col] = True and T[row][col - 1]

elif col == 0:

if str3[index] == str2[row - 1]:

T[row][col] = True and T[row - 1][col]

else:

T[row][col] = ((T[row][col - 1] if str3[index] == str1[col - 1] else False) or

(T[row - 1][col] if str3[index] == str2[row - 1] else False))

return T[rows - 1][cols - 1]

if __name__ == '__main__':

str1 = "XXYM"

str2 = "XXZT"

str3 = "XXXZXYTM"

assert True == is_interleaved(str1, str2, str3)

assert True == is_interleaved_recursive(str1, str2, str3, 0, 0, 0)