Number of flips to make binary string alternate

This article elucidates the programming methodology using an input string outlining algorithmic steps and analyzing time and space complexity. It serves as a guide for effectively achieving the flips essential to converting a binary string into an alternate sequence. The strategies discussed can also be adapted to tackle challenges involving the manipulation of bit strings.

Binary strings are sequences containing 0s and 1s widely used in computing to represent bit vectors, sets and masking operations. An intriguing aspect of strings is alternating strings starting with 0 and having a pattern of alternating 0s and 1s like "010101010".

In this piece, we determine the number of bit flips needed to transform a given binary string into an alternating one. This concept finds applications such as encoding data for synchronization in data transmission or establishing an alternating heartbeat pattern among nodes in a distributed system for failure detection.

The optimal solution to this problem lies in employing programming. By creating a table where each entry indicates the flips required for the substring up to that point, we can efficiently determine the alterations by comparing current bits with expected alternating bits.

What is a Binary String?

A binary string is composed of only two symbols - 0 and 1. It can be thought of as a sequence of binary digits or bits. Binary strings are commonly used to represent data in computer systems and programming because computers operate on binary, using bits and bytes.

Some key properties of binary strings:

• A binary string can be any length - from empty to infinitely long. The length is the number of symbols (0s and 1s).
• The two symbols 0 and 1 are used to represent binary values or logical states. 0 typically means "off", "no", or "low". 1 means "on", "yes", or "high".
• The positions in a binary string are numbered starting from the leftmost bit as 0, 1, 2, etc. This position number is called the index.
• A binary string with n symbols has 2^n possible combinations. For example, a 3-bit binary string has 2^3 = 8 possible values from 000 to 111.
• Binary strings can represent integer values. The leftmost bit is the most significant bit (MSB).
• Bitwise operations like AND, OR, NOT, and XOR shifts can be performed on binary strings.
• Binary strings represent many data types in computing - numbers, characters, memory addresses, etc.
• In applications like communication, binary strings are used for digital signals, data compression, error detection and correction codes.

In summary, binary strings are simple but powerful data structures in computer science and information theory. Understanding binary string concepts and operations is useful for anyone in programming, algorithms, and digital systems.

Algorithm to Implement

1. Initialize
   • n = length of binary string
   • dp array of size n
   • dp[0] = 0
2. Iterate from i = 1 to n-1
   • Determine expected bit
     • If s[i-1] is '0', expected is '1'
     • Else expected is '0'
   • Compare s[i] with expected
     • If different:
       • dp[i] = dp[i-1] + 1
     • Else:
       • dp[i] = dp[i-1]
3. Return dp[n-1]

So, in summary:

• Initialize dp array
• Iterate over string
• Compare the current bit with the expected alternating bit
• If different, increment the previous dp value
• Else, copy the previous dp value
• Return final dp value

It implements a bottom-up dynamic programming approach to calculate the minimum flips required. We build the solution for longer substrings using the answers for shorter ones.

The key steps are comparing the current bit with an expected bit, updating the dp table accordingly, and returning the final value.

Output:

Explanation

• Define the getMinFlips function that takes the binary string
• Initialize n, dp array of size n, base case dp[0]=0
• Iterate over string from i=1 to n-1
• Determine expected bit based on the previous bit
• Compare s[i] with the expected bit
• If different, dp[i] = dp[i-1] + 1 (increment flip count)
• Else, dp[i] = dp[i-1] (copy flip count)
• Return the final dp value containing the result
• Driver code
• Call the function with an example string
• Print returned minimum flips

It implements the full dynamic programming solution to find the minimum flips required in O(n) time and O(n) space.