Add longest common substring

dynamic_programming/longest_common_substring.py

@@ -0,0 +1,74 @@
+"""
+Longest Common Substring Problem Statement: Given two sequences, find the length
+of longest common substring present in both of them. A substring is
+necessarily continuous.
+Example:"abcdef", "xabded" have the length of longest common substring 2 ("ab" or "de").
+"""
+
+
+def longest_common_substring(t1: str, t2: str) -> int:
+ """
+ Finds the length of longest common substring between two strings.
+
+ Parameters
+ ----------
+ t1: str, one of the strings
+ t2: str, the other string
+
+ Returns
+ -------
+ ans: int, the length of the longest common substring.
+
+ >>> longest_common_substring("", "")
+ 0
+
+ >>> longest_common_substring("a","")
+ 0
+
+ >>> longest_common_substring("", "a")
+ 0
+
+ >>> longest_common_substring("a", "a")
+ 1
+
+ >>> longest_common_substring("abcdef", "bcd")
+ 3
+
+ >>> longest_common_substring("abcdef", "xabded")
+ 2
+
+ >>> longest_common_substring("GeeksforGeeks", "GeeksQuiz")
+ 5
+
+ >>> longest_common_substring("abcdxyz", "xyzabcd")
+ 4
+
+ >>> longest_common_substring("zxabcdezy", "yzabcdezx")
+ 6
+
+ >>> longest_common_substring("OldSite:GeeksforGeeks.org", "NewSite:GeeksQuiz.com")
+ 10
+ """
+
+ assert t1 is not None
+ assert t2 is not None
+
+ t1_length = len(t1)
+ t2_length = len(t2)
+
+ dp = [[0] * (t2_length + 1) for _ in range(t1_length + 1)]
+ ans = 0
+
+ for i in range(1, t1_length + 1):
+ for j in range(1, t2_length + 1):
+ if t1[i - 1] == t2[j - 1]:
+ dp[i][j] = 1 + dp[i - 1][j - 1]
+ ans = max(ans, dp[i][j])
+
+ return ans
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()