Minimum Length of String After Operations

Problem Statement

In this task, you receive a string ( s ). You are tasked to repeatedly modify the string by performing a defined process that primarily involves choosing a character in the string and removing certain instances of this character based on specific conditions. The process can be carried out an unlimited number of times, with the goal of reducing the length of the string to its minimum possible value through these operations.

Here's a detailed breakdown of the operation:

1. You select an index ( i ) in the string. This index must fulfill the condition where the character at index ( i ) (( s[i] )) has at least one identical character somewhere to its left and also to its right within the string.
2. Once an appropriate index ( i ) has been chosen, you remove the closest identical character to the left and the closest identical character to the right of ( s[i] ).

The outcome to be determined is the minimal length the string ( s ) can be reduced to, after applying the above operation optimally any number of times.

Examples

Example 1

Input:

s = "abaacbcbb"

Output:

5

Explanation:

* Choose index 2, then remove the characters at indices 0 and 3. The resulting string is `s = "bacbcbb"`.
* Choose index 3, then remove the characters at indices 0 and 5. The resulting string is `s = "acbcb"`.

Example 2

Input:

s = "aa"

Output:

2

Explanation:

Constraints

• 1 <= s.length <= 2 * 105
• s consists only of lowercase English letters.

Approach and Intuition

The goal given the problem is to reduce the string to its minimal length by removing characters according to specified rules. Looking at the examples:

• For s = "abaacbcbb":
  1. The character 'a' at index 2 is selected (s[2] = 'a'). The character 'a' also exists at index 1 to the left and index 3 to the right of index 2. The closest occurrences on both sides are removed, resulting in s = "bacbcbb".
  2. The character 'b' at index 3 is then selected (s[3] = 'b'). It has occurrences at indices 0 to its left and 5 to its right, which are then eliminated. The string further reduces to s = "acbcb".
• For s = "aa":
  1. There is no valid position where a character has duplicates on both sides that are different from themselves, so no operation can be performed.

Analyzing the constraints and the operations, the task involves several challenges:

• Efficiently identifying valid indices ( i ) for the operation.
• Managing the removal of elements in a way that still allows for quick identification of new valid indices in potentially large-scale strings (up to ( 200,000 ) characters).
• Direct removal from and manipulation of strings isn't efficient in Python due to strings being immutable. Instead, an approach involving data structures that support efficient removal and insertion, like linked lists or using additional arrays to manage active indices of characters, may be required.

The minimum length result is dependent on how effectively the operations are utilized to cluster and remove repeating characters while adhering to the rules provided. An efficient algorithm might thus involve a strategic selection of indices for the operation to maximize removals in each step.

Solutions

class Solution {
public:
    int minLen(string str) {
        int visible = 0;
        int bitMask = 0;
        int bitPos;
    
        // Loop over characters to modify bit masks
        for (int idx = 0; idx < str.length(); idx++) {
            bitPos = 1 << (str[idx] - 'a');
            visible |= bitPos;
            bitMask ^= bitPos;
        }
    
        int minLength = 0;
    
        // Calculate required minimum total length
        while (visible) {
            bitPos = visible & (visible - 1);
            minLength += 2 - ((bitMask & (visible - bitPos)) != 0);
            visible = bitPos;
        }
    
        return minLength;
    }
};