Move Pieces to Obtain a String

2337. Move Pieces to Obtain a String

Difficulty: Medium

Topics: Two Pointers, String

You are given two strings start and target, both of length n. Each string consists only of the characters 'L', 'R', and '_' where:

• The characters 'L' and 'R' represent pieces, where a piece 'L' can move to the left only if there is a blank space directly to its left, and a piece 'R' can move to the right only if there is a blank space directly to its right.
• The character '_' represents a blank space that can be occupied by any of the 'L' or 'R' pieces.

Return true if it is possible to obtain the string target by moving the pieces of the string start any number of times. Otherwise, return false.

Example 1:

• Input: start = "LRR", target = "L______RR"
• Output: true
• Explanation: We can obtain the string target from start by doing the following moves:
  • Move the first piece one step to the left, start becomes equal to "L__RR".
  • Move the last piece one step to the right, start becomes equal to "L_R_R".
  • Move the second piece three steps to the right, start becomes equal to "L______RR".
  • Since it is possible to get the string target from start, we return true.

Example 2:

• Input: start = "R_L_", target = "__LR"
• Output: false
• Explanation: The 'R' piece in the string start can move one step to the right to obtain "RL".
  • After that, no pieces can move anymore, so it is impossible to obtain the string target from start.

Example 3:

• Input: start = "R", target = "R"
• Output: false
• Output: The piece in the string start can move only to the right, so it is impossible to obtain the string target from start.

Constraints:

• n == start.length == target.length
• 1 <= n <= 10⁵
• start and target consist of the characters 'L', 'R', and '_'.

Hint:

1. After some sequence of moves, can the order of the pieces change?
2. Try to match each piece in s with a piece in e.

Solution:

We need to check if we can transform the string start into the string target by moving pieces ('L' and 'R') as per the given rules. The main constraints to consider are:

• 'L' can only move left (and cannot cross other 'L' or 'R' pieces).
• 'R' can only move right (and cannot cross other 'L' or 'R' pieces).
• We can use any blank spaces ('_') to move pieces around.

Plan:

1. Length Check: First, check if both strings have the same length. If they don't, return false immediately.

2. Character Frequency Check: The number of 'L's, 'R's, and '_' in the start string must match the respective counts in the target string because the pieces cannot be duplicated or destroyed, only moved.

3. Piece Matching Using Two Pointers:

   • Traverse through both strings (start and target).
   • Check if each piece ('L' or 'R') in start can move to its corresponding position in target.
   • Specifically:
     • 'L' should always move to the left (i.e., it must not be in a position where a piece in target should move right).
     • 'R' should always move to the right (i.e., it must not be in a position where a piece in target should move left).

Algorithm Explanation:

1. Filter L and R Positions:

   • Remove all _ from both strings start and target to compare the sequence of L and R. If the sequences differ, return false immediately.

2. Two-Pointer Traversal:

   • Use two pointers to iterate over the characters in start and target.
   • Ensure that:
     • For L, the piece in start can only move left, so its position in start should be greater than or equal to its position in target.
     • For R, the piece in start can only move right, so its position in start should be less than or equal to its position in target.

3. Output Result:

   • If all conditions are satisfied during traversal, return true. Otherwise, return false.

Let's implement this solution in PHP: 2337. Move Pieces to Obtain a String

  
  
  Explanation:



Initial Checks: First, we check the length of both strings and ensure the counts of 'L' and 'R' are the same in both strings. If not, return false.

Two Pointers Logic: We use two pointers, i and j, to traverse both strings:

Skip over the blank spaces ('_') since they don't affect the movement of the pieces.
If the characters at i and j in start and target differ, return false (as we cannot move pieces to different characters).
If an 'L' is found in start and is at a position greater than its target position, or if an 'R' is found in start and is at a position smaller than its target position, return false (since 'L' can only move left and 'R' can only move right).



Edge Cases: The solution handles all possible edge cases, such as:


Different counts of 'L' or 'R' in start and target.
Inability to move pieces due to constraints.





  
  
  Time Complexity:



The time complexity is O(n), where n is the length of the input strings. This is because we traverse each string only once.



  
  
  Space Complexity:



The space complexity is O(1), as we are only using a fixed amount of extra space.



  
  
  Complexity Analysis:




Time Complexity:


Filtering underscores takes O(n).
Two-pointer traversal takes O(n).
Overall: O(n).



Space Complexity:


Two strings ($startNoUnderscore and $targetNoUnderscore) are created, each of size O(n).
Overall: O(n).





  
  
  Explanation of Test Cases:




Input: _L__R__R_, L______RR


The sequence of L and R matches.
Each piece can be moved to the required position following the rules.

Output: true.



Input: R_L_, __LR


The sequence of L and R matches.
The R piece cannot move left; hence, the transformation is impossible.

Output: false.



Input: _R, R_


The R piece cannot move left; hence, the transformation is impossible.

Output: false.




This implementation is efficient and adheres to the problem constraints, making it suitable for large input sizes.

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