Minimum Recolors to Get K Consecutive Black Blocks

class Solution {
public:
    int minRecolorOperations(string blockLine, int width) {
        int start = 0, whiteCount = 0, minRecolors = INT_MAX;
    
        // Traverse with the end index
        for (int end = 0; end < blockLine.size(); end++) {
            // Count white blocks at the current end index
            if (blockLine[end] == 'W') {
                whiteCount++;
            }
    
            // When we have a window of size 'width'
            if (end - start + 1 == width) {
                // Compare and update the minimum recolor needed
                minRecolors = min(minRecolors, whiteCount);
    
                // Reduce white count when exceeding window size
                if (blockLine[start] == 'W') whiteCount--;
    
                // Slide the window
                start++;
            }
        }
        return minRecolors;
    }
};

The provided C++ solution is designed to find the minimum number of recolor operations needed to transform a given segment of blocks into a segment consisting entirely of black blocks (denoted by 'B') in a string, where white blocks are denoted by 'W'. The goal is to have at least 'k' consecutive black blocks. The string representing the blocks and the desired length of consecutive black blocks, k, are passed as inputs to the function.

Here’s how the solution works:

• Initiate a sliding window approach with two pointers, start and end, to represent the current window of blocks being assessed.
• Initialize whiteCount to track the number of white blocks in the current sliding window and minRecolors to store the minimum recolor operations found.
• Traverse the string using the end pointer. For each block at position end, if the block is white, increment the whiteCount.
• Check if the size of the window between start and end matches the desired width k. If it does:
  • Update minRecolors with the smaller value between the current minRecolors and whiteCount.
  • If the block at position start is white, decrement whiteCount (since the block will be excluded from the window in the next step).
  • Increment the start pointer to slide the window forward.
• The loop ends when end has moved past the last block in the string.
• Finally, return minRecolors, which now holds the minimum number of recolors needed to achieve at least k consecutive black blocks within any segment of the input block string.

This approach efficiently minimizes the number of color changes required by dynamically adjusting the assessment window and counting only the necessary changes for each possible segment.

class Solution {
    
    public int minRecolorsNeeded(String blockSequence, int k) {
        int start = 0, whiteCount = 0, minRecolors = Integer.MAX_VALUE;
    
        for (int end = 0; end < blockSequence.length(); end++) {
            if (blockSequence.charAt(end) == 'W') {
                whiteCount++;
            }
    
            if (end - start + 1 == k) {
                minRecolors = Math.min(minRecolors, whiteCount);
    
                if (blockSequence.charAt(start) == 'W') whiteCount--;
    
                start++;
            }
        }
        return minRecolors;
    }
}

The given solution is a Java program designed to solve the problem of determining the minimum number of recolors needed to get exactly 'k' consecutive black blocks in a given string sequence of blocks colored either black ('B') or white ('W').

The program follows these steps:

1. Initialize three variables: start to mark the beginning of the sliding window, whiteCount to keep track of the number of white blocks within the current window, and minRecolors set to the maximum possible value (infinity in practical scenarios).

2. Iterate over each character in the string with a variable end that represents the end of the sliding window.

3. As the window slides (increment end), update the whiteCount if a white block ('W') is found.

4. Check if the window size has reached 'k'. If it has:

   • Update minRecolors to the minimum of its current value or the whiteCount.
   • If the block at the start position of the window is white, decrement whiteCount because the window is about to exclude that block in the next step.
   • Move the start forward by one position to slide the window.

5. Return minRecolors as the result which gives the minimum recolors needed.

The algorithm effectively uses a sliding window technique to examine each possible sequence of 'k' blocks in the string. By keeping a tally of white blocks within each window and updating the counters correctly with each slide, it minimizes the number of recalculations needed, resulting in an efficient solution.

class Solution:
    def minRecolorings(self, blockLine: str, length: int) -> int:
        start = 0
        countWhite = 0
        leastRecolors = float("inf")
    
        for end in range(len(blockLine)):
            if blockLine[end] == "W":
                countWhite += 1
            if end - start + 1 == length:
                leastRecolors = min(leastRecolors, countWhite)
                if blockLine[start] == "W":
                    countWhite -= 1
                start += 1
    
        return leastRecolors

The problem requires finding the minimum number of times you need to recolor white blocks to black in order to have k consecutive black blocks in a given string representation of blocks. The solution is implemented in Python using a sliding window approach.

• Initialize start to zero, which marks the beginning of the sliding window.
• Utilize countWhite to track the number of white blocks ('W') within the current window.
• Use leastRecolors to keep track of the minimum recolors required, starting its value at infinity to ensure it will be updated during the process.

Follow the steps below to solve the problem:

1. Iterate through each block in the blockLine string using a variable end which marks the end of the sliding window.
2. Check if the current block is white ('W') and increment countWhite accordingly.
3. When the window size matches the desired length k:
   • Update leastRecolors with the minimum of its current value or countWhite.
   • If the block at the start of the window is white, decrement countWhite.
   • Move the start of the window forward by 1.
4. The loop continues until every possible window of size k has been examined.
5. Return leastRecolors, which now contains the minimum number of recolors required to achieve at least one sequence of k consecutive black blocks.

This method efficiently uses a sliding window technique to check each possible sequence of k blocks in the string, ensuring optimal performance by only requiring a single pass through the blockLine. The conditionals within the loop handle the adjustment of the window and the count of white blocks efficiently.