Find All Distinct Palindromic Substrings of a Given String in Python

Suppose we have a string with lowercase ASCII characters, we have to find all distinct continuous palindromic substrings of it.

So, if the input is like "bddaaa", then the output will be [a, aa, aaa, b, d, dd]

To solve this, we will follow these steps −

• m := a new map
• n := size of s
• matrix := make two rows of n number of 0s
• s := "@" concatenate s concatenate "#"
• for j in range 0 to 1, do
  • temp := 0
  • matrix[j, 0] := 0
  • i := 1
  • while i <= n, do
    • while s[i - temp - 1] is same as s[i + j + temp], do
      • temp := temp + 1
    • matrix[j, i] := temp
    • k := 1
    • while (matrix[j, i - k] is not same as temp - k) and k < temp, do
      • matrix[j,i+k] := minimum of matrix[j, i-k]
      • k := k + 1
    • temp := maximum of temp - k, 0
    • i := i + k
• s := s from index 1 to end
• m[s[0]] := 1
• for i in range 1 to n, do
  • for j in range 0 to 1, do
    • for temp in range, do
      • m[substring of s from (i - temp - 1) to (i - temp - 1 + 2 * temp + j)] = 1
    • 
      
  • m[s[i]] := 1
• for each i in m, do
  • display i

Example

Let us see the following implementation to get better understanding −

 Live Demo

def find_substr(s):
   m = dict()
   n = len(s)
   matrix = [[0 for x in range(n+1)] for x in range(2)]
   s = "@" + s + "#"
   for j in range(2):
      temp = 0
      matrix[j][0] = 0
      i = 1
      while i <= n:
         while s[i - temp - 1] == s[i + j + temp]:
            temp += 1
         matrix[j][i] = temp
         k = 1
         while (matrix[j][i - k] != temp - k) and (k < temp):
            matrix[j][i+k] = min(matrix[j][i-k], temp - k)
            k += 1
         temp = max(temp - k, 0)
         i += k
   s = s[1:len(s)-1]
   m[s[0]] = 1
   for i in range(1,n):
      for j in range(2):
         for temp in range(matrix[j][i],0,-1):
            m[s[i - temp - 1 : i - temp - 1 + 2 * temp + j]] = 1
      m[s[i]] = 1
   for i in m:
      print (i)
find_substr("bddaaa")

Input

bddaaa

Output

a
aa
b
aaa
d
dd