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Separate Black and White Balls Solution

In this problem, the goal is to group all black balls (represented by 1s) to the right and all white balls (represented by 0s) to the left, using the fewest adjacent swaps. Below is the step-by-step breakdown of how the solution is approached and implemented in various languages, including C++, Java, JavaScript, Python, and Go.

C++ Solution Explanation

  1. Initialization:

    • We start by initializing two variables: one to count the number of black balls (1s) encountered, and another to track the total number of swaps needed.

  2. Traverse the String:

    • Loop through each character in the input string.
    • When we find a white ball (0), it will need to swap with all the black balls to its left. So, we add the number of black balls encountered so far to the total swap count.
    • When we find a black ball (1), increment the black ball count.

  3. Return Result:

    • After iterating through the entire string, return the accumulated swap count as the minimum number of steps required.

Java Solution Explanation

  1. Initialize Variables:

    • We define a variable to keep track of the total swaps needed (res) and a counter for the number of black balls (i).

  2. Loop Through String:

    • Loop through each character in the string.
    • For each white ball (0), calculate how far it needs to move left by subtracting the current index from the number of black balls encountered, and add this value to the total result.
    • When a black ball (1) is found, increment the black ball counter.

  3. Final Result:

    • Return the total count of swaps as the answer.

JavaScript Solution Explanation

  1. Set Up Variables:

    • We start by initializing two variables: one for counting the number of black balls (1s), and another to accumulate the total number of swaps required.

  2. Iterate Over the String:

    • Traverse through each character in the string.
    • If the character is a white ball (0), add the number of black balls encountered so far to the total number of swaps.
    • If the character is a black ball (1), increment the black ball counter.

  3. Output Result:

    • Once the loop is complete, return the total number of swaps as the result.

Python Solution Explanation

  1. Initialize Variables:

    • We initialize two variables: blackCount to track the number of black balls, and ans to store the total number of swaps required.

  2. Process Each Character:

    • Traverse the input string character by character.
    • If we find a white ball (0), we add the number of black balls already encountered (blackCount) to the total swap count.
    • If a black ball (1) is found, increment the black ball counter.

  3. Return the Answer:

    • After the traversal is finished, return the total swap count stored in ans.

Go Solution Explanation

  1. Initialize Counters:

    • Declare two variables: one to track the number of black balls encountered (blackCount), and another to store the total number of swaps required (ans).

  2. Traverse the String:

    • Iterate through each character in the string.
    • For each white ball (0), add the number of black balls encountered so far to the total number of swaps.
    • For each black ball (1), increment the black ball counter.

  3. Return Result:

    • After processing all the characters, return the accumulated number of swaps as the result.

Conclusion

Each solution, whether written in C++, Java, JavaScript, Python, or Go, follows the same logic:

  1. Count the number of black balls encountered.
  2. For each white ball encountered, add the number of black balls on its left to the total number of swaps.
  3. Return the total number of swaps at the end.

These solutions are optimized for performance, running in linear time, ( O(n) ), where ( n ) is the length of the string. They also use constant space, ( O(1) ), making them efficient for large inputs.