Program to find length of subsequence that can be removed still t is subsequence of s in Python

PythonServer Side ProgrammingProgramming

Suppose we have a string s and another string t. And t is a subsequence of s. We have to find the maximum length of a substring that we can remove from s so that, t is still a subsequence of s.

So, if the input is like s = "xyzxyxz" t = "yz", then the output will be 4, as We can remove the substring "abca"

To solve this, we will follow these steps −

  • left := a new list, right := also a new list

  • c1 := -1, c2 := -1, c3 := -1

  • j := 0

  • for i in range 0 to size of s, do

    • if s[i] is same as t[j], then

      • insert i at the end of left

      • j := j + 1

    • if j is same as size of t , then

      • c1 := size of s - i - 1

      • come out from the loop

  • j := size of t - 1

  • for i in range size of s - 1 to 0, decrease by 1, do

    • if s[i] is same as t[j], then

      • insert i into right at position 0

      • j := j - 1

    • if j is same as -1, then

      • c2 := i

      • come out from the loop

  • for i in range 0 to size of t - 1, do

    • c3 := maximum of c3 and (right[i + 1] - left[i] - 1)

  • return maximum of c1, c2 and c3

Example (Python)

Let us see the following implementation to get a better understanding −

 Live Demo

class Solution:
   def solve(self, s, t):
      left = []
      right = []
      c1 = -1
      c2 = -1
      c3 = -1
      j = 0
      for i in range(len(s)):
         if s[i] == t[j]:
            left.append(i)
            j += 1
         if j == len(t):
            c1 = len(s) - i - 1
            break
      j = len(t) - 1
      for i in range(len(s) - 1, -1, -1):
         if s[i] == t[j]:
            right.insert(0, i)
            j -= 1
         if j == -1:
            c2 = i
            break
      for i in range(len(t) - 1):
         c3 = max(c3, right[i + 1] - left[i] - 1)
      return max(c1, c2, c3)
ob = Solution()
s = "xyzxyxz"
t = "yz"
print(ob.solve(s, t))

Input

"xyzxyxz", "yz"

Output

4
raja
Published on 21-Dec-2020 13:51:43
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