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Minimum String Length After Removing Substrings

Problem Overview

The task is to minimize a given string by repeatedly removing any occurrences of the substrings "AB" or "CD". After each removal, the string concatenates, and this may form new occurrences of "AB" or "CD". The goal is to find the minimum possible length of the string after performing all operations.

Approach (General)

  1. Stack-based Strategy:

    • A stack can be used to simulate the process of removing substrings.
    • Traverse the string character by character.
    • Push characters onto the stack unless they form "AB" or "CD" with the top element of the stack.
    • If a valid pair ("AB" or "CD") is formed, remove the top element of the stack (i.e., pop it).

  2. Final Length:

    • After processing the entire string, the remaining characters in the stack represent the minimized string.
    • The length of the minimized string is the size of the stack.

Step-by-Step Explanation

C++ Code

  1. Initialize an empty stack to keep track of characters that have not yet formed valid pairs for removal.
  2. Traverse the string from left to right.
  3. For each character, check the top of the stack:
    • If the top forms "AB" or "CD" with the current character, pop the top.
    • Otherwise, push the current character onto the stack.
  4. Repeat this process for every character in the string.
  5. After the entire traversal, the size of the stack is the minimized length of the string.

Java Code

  1. Create an empty stack to hold characters.
  2. Iterate over the string character by character.
  3. For each character:
    • If the stack is not empty and the top of the stack forms either "AB" or "CD" with the current character, pop the stack.
    • Otherwise, push the current character onto the stack.
  4. After the loop, the remaining elements in the stack form the minimized string.
  5. Return the size of the stack as the minimized length of the string.

JavaScript Code

  1. Create an empty array (which will act as a stack) to store characters.
  2. Loop through the string and check each character.
  3. For each character:
    • Check if the last element in the array forms "AB" or "CD" with the current character.
    • If a valid pair is found, remove the last element (pop the array).
    • If no valid pair is found, push the current character to the array.
  4. After the loop, the array contains the remaining characters of the minimized string.
  5. The length of the array is the minimized string length.

Python Code

  1. Initialize an empty list as the stack to hold the characters.
  2. Traverse the string character by character.
  3. For each character, check the last element of the list:
    • If it forms "AB" or "CD" with the current character, pop the last element.
    • If not, append the current character to the list.
  4. Continue this process until the entire string is processed.
  5. The length of the list at the end represents the minimized string length.

Go Code

  1. Use a slice as a stack to store characters.
  2. Iterate over the string one character at a time.
  3. For each character:
    • Check if the top of the stack (last element of the slice) forms "AB" or "CD" with the current character.
    • If a pair is found, pop the stack.
    • If no pair is found, push the current character onto the stack.
  4. After processing the entire string, the length of the slice is the minimized string length.

Final Thoughts

In each language, the core approach remains the same: using a stack (or stack-like structure) to remove valid substrings as they are encountered. The time complexity is linear with respect to the length of the string, making it efficient for the input size constraints.

This explanation provides a high-level overview of the logic without showing the actual code, guiding you through the problem-solving process in multiple programming languages.