Merge pull request prabhupant#341 from erithwik/longest-palindromic-substring

Add Longest Palindromic Substring

Author: prabhupant

algorithms/dynamic_programming/longest_palindromic_substring.py

@@ -0,0 +1,57 @@
+def longest_palindromic_substring_DP(s):
+
+    S = [[False for i in range(len(s))] for j in range(len(s))]
+
+    max_palindrome = ""
+
+    for i in range(len(s))[::-1]:
+        for j in range(i, len(s)):
+            # if j - 1 < 3, then there is one or two characters between these
+            # two positions, implying that if s[i] == s[j]
+            # then that small string is a palindrome
+            # We check if the above cases is valid or i
+            # they are larger, we use DP to check the substring
+            # in between j and i
+            S[i][j] = s[i] == s[j] and (j - i < 3 or S[i+1][j-1])
+            if S[i][j] and j - i + 1 > len(max_palindrome):
+                max_palindrome = s[i:j+1]
+
+    return max_palindrome
+
+
+def longest_palindromic_substring_expansion(s):
+    max_palindrome = ""
+
+    for i in range(len(s) * 2 - 1):
+        if i % 2 == 0:
+            # This is when you are "on" an actual character
+            # o = offset, ind = current character
+            o = 0
+            ind = i // 2
+            while ind + o < len(s) and ind - o >= 0:
+                if(s[ind + o] != s[ind - o]):
+                    break
+                if ind + o - (ind - o) + 1 > len(max_palindrome):
+                    max_palindrome = s[ind-o:ind+o + 1]
+                o += 1
+        else:
+            # This is when you are "in the middle of" two characters
+            # o = offset, sind = start char, eind = end char
+            o = 0
+            sind = i // 2
+            eind = i // 2 + 1
+            while sind - o >= 0 and eind + o < len(s):
+                if(s[sind - o] != s[eind + o]):
+                    break
+                if eind + o - (sind - o) + 1 > len(max_palindrome):
+                    max_palindrome = s[sind - o:eind + o + 1]
+                o += 1
+
+    return max_palindrome
+
+
+input_string = "abbbacdcaacdca"
+
+ans_DP = longest_palindromic_substring_DP(input_string)
+ans_expansion = longest_palindromic_substring_expansion(input_string)
+print("DP Solution: {}, Expansion Solution: {}".format(ans_DP, ans_expansion))