Unraveling the Enigma of Bead Challenge on InterviewBit: A Step-by-Step Guide

Are you one of the numerous programmers who can’t comprehend the logic of Bead Challenge on InterviewBit? Do the twisted strings and beads leave you bewildered, making you wonder how to approach this seemingly impossible problem? Fear not, dear coder, for we’re about to embark on a journey to unravel the mystery of the Bead Challenge, and by the end of this article, you’ll be well-equipped to tackle it head-on!

What is the Bead Challenge?

The Bead Challenge is a popular problem on InterviewBit, a platform known for its demanding coding challenges. In essence, the challenge presents you with a string of beads, where each bead is either red (R) or blue (B). The task is to find the minimum number of operations required to make the string alternating, i.e., starting with either R or B, followed by alternating colors.

Understanding the Problem Statement

Before we dive into the solution, let’s break down the problem statement to ensure we comprehend the requirements:

• String s: The input string consisting of R’s and B’s.
• Operations: The minimum number of operations required to make the string alternating.
• Operation: A single swap of two adjacent beads.

Approaching the Problem

To conquer the Bead Challenge, we’ll employ a combination of clever thinking and efficient algorithms. Buckle up, as we’re about to get started!

Step 1: Understand the Key Insight

One crucial observation is that the minimum number of operations is determined by the longest alternating subsequence within the input string. This realization is the foundation of our solution.

Step 2: Dynamic Programming to the Rescue

We’ll use dynamic programming to find the longest alternating subsequence. Create a 2D table dp of size (n+1) x 2, where:

dp[i][0] represents the length of the longest alternating subsequence ending at index i with the last bead being R.
dp[i][1] represents the length of the longest alternating subsequence ending at index i with the last bead being B.

Initialize the table with zeros, and then fill it up using the following recurrence relation:

dp[i][0] = max(dp[i-1][1], dp[i-2][0] + 1) if s[i-1] == 'R'
dp[i][1] = max(dp[i-1][0], dp[i-2][1] + 1) if s[i-1] == 'B'

This recurrence relation considers two possibilities for each bead:

• Either the current bead is part of the longest alternating subsequence, in which case we increment the corresponding value in the table.
• Or, the current bead is not part of the longest alternating subsequence, and we take the maximum value from the previous cells.

Step 3: Calculate the Minimum Operations

Once we’ve filled the dp table, the minimum number of operations is given by:

min_operations = n - max(dp[n][0], dp[n][1])

This calculation is based on the fact that the minimum number of operations is the difference between the total length of the string and the length of the longest alternating subsequence.

Example Walkthrough

Let’s consider an example to solidify our understanding:

Index	String s	dp[i][0]	dp[i][1]
0	R	1	0
1	B	1	2
2	R	2	2
3	B	2	3
4	R	3	3

In this example, the longest alternating subsequence is RBRBR, which has a length of 5. The minimum number of operations required is 5 - 5 = 0, as the string is already alternating.

Implementation in Code

Here’s the implementation in Python:

def min_operations(s):
    n = len(s)
    dp = [[0]*(2) for _ in range(n+1)]
    
    for i in range(1, n+1):
        if s[i-1] == 'R':
            dp[i][0] = max(dp[i-1][1], dp[i-2][0] + 1)
            dp[i][1] = dp[i-1][1]
        else:
            dp[i][0] = dp[i-1][0]
            dp[i][1] = max(dp[i-1][0], dp[i-2][1] + 1)
    
    return n - max(dp[n][0], dp[n][1])

Conclusion

Voilà! We’ve untangled the mystery of the Bead Challenge on InterviewBit. By employing dynamic programming and clever thinking, we’ve developed a solution that efficiently calculates the minimum number of operations required to make the string alternating. Remember, practice makes perfect, so be sure to try out this problem on InterviewBit and hone your coding skills!

With this comprehensive guide, you should now be well-equipped to tackle the Bead Challenge and other similar problems. Happy coding, and don’t let those beads get the better of you!

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