manacher's algorithm to find palindromic string (#676)

manacher's algorithm to find palindromic string in linear time complexity

strings/manacher.py

@@ -0,0 +1,52 @@
+# calculate palindromic length from center with incresmenting difference
+def palindromic_length( center, diff, string):
+    if center-diff == -1 or center+diff == len(string) or string[center-diff] != string[center+diff] :
+        return 0
+    return 1 + palindromic_length(center, diff+1, string)
+
+def palindromic_string( input_string ):
+    """
+    Manacher’s algorithm which finds Longest Palindromic Substring in linear time.
+
+    1. first this conver input_string("xyx") into new_string("x|y|x") where odd positions are actual input
+        characters.
+    2. for each character in new_string it find corresponding length and store,
+        a. max_length
+        b. max_length's center
+    3. return output_string from center - max_length to center + max_length and remove all "|"   
+    """
+    max_length = 0
+    
+    # if input_string is "aba" than new_input_string become "a|b|a"
+    new_input_string = ""
+    output_string = ""
+
+    # append each character + "|" in new_string for range(0, length-1)
+    for i in input_string[:len(input_string)-1] :
+        new_input_string += i + "|"
+    #append last character
+    new_input_string += input_string[-1]
+
+
+    # for each character in new_string find corresponding palindromic string
+    for i in range(len(new_input_string)) :
+
+        # get palindromic length from ith position
+        length = palindromic_length(i, 1, new_input_string)
+
+        # update max_length and start position
+        if max_length < length :
+            max_length = length
+            start = i
+    
+    #create that string
+    for i in new_input_string[start-max_length:start+max_length+1] :
+        if i != "|":
+            output_string += i
+    
+    return output_string
+
+
+if __name__ == '__main__':
+    n = input()
+    print(palindromic_string(n))