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Program to find how max score we can get by removing 10 or 01 from binary string in Python

Suppose we have a binary string s and two values zero_one and one_zero. Now let us consider an operation where we can delete any substring "01" and receive zero_one points. Or we can remove any substring "10" and receive one_zero points. We have to find the maximum number of points we can get after any number of operations.

So, if the input is like s = "10100101" zero_one = 3 one_zero = 2, then the output will be 11, as we can remove "01" three times to get 3*3 = 9 points. Then the remaining string is 10. By removing this we can get another 2 points so the total is 11.

To solve this, we will follow these steps −

  • A := a list of bits given as input string

  • if zero_one < one_zero, then

    • swap zero_one and one_zero

    • for i in range 0 to size of A, do

      • A[i] := A[i] XOR 1

  • ans := 0

  • stack := a new stack

  • for each x in A, do

    • if stack is not empty and stack top element < x, then

      • pop from stack

      • ans := ans + zero_one

    • otherwise,

      • push x into stack

  • ans := ans + one_zero * minimum of occurrence of 0 in stack and occurrence of 1 in stack

  • return ans

Example (Python)

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

class Solution:
   def solve(self, S, zero_one, one_zero):
      A = list(map(int, S))
      if zero_one < one_zero:
         zero_one, one_zero = one_zero, zero_one
         for i in range(len(A)):
            A[i] ^= 1
         ans = 0
         stack = []
         for x in A:
            if stack and stack[-1] < x:
               stack.pop()
               ans += zero_one
            else:
               stack.append(x)
         ans += one_zero * min(stack.count(0), stack.count(1))
         return ans
ob = Solution()
s = "10100101"
zero_one = 3
one_zero = 2
print(ob.solve(s, zero_one, one_zero))

Input

"10100101", 3, 2

Output

11