Maximize Sum by Splitting Given Binary Strings Based on Given Conditions Using C++

This article aims to tackle a complex algorithmic problem involving splitting binary strings in such a way as to maximize cumulative sums obtained from their individual components. We'll provide readers with a comprehensive syntax outline for implementing code and suggest two possible techniques to surmount this challenge. Furthermore, we will showcase two real full executable codes based on the mentioned approaches.

Syntax

Before delving into the algorithms, it is crucial that we are well-acquainted with the structure of our designated approach that we'll be showcasing through upcoming code samples. This approach employs a binary string as an input and computes its highest possible value by partitioning said input using predetermined conditions. The below illustrates how this approach looks in terms of syntax −

int maximizeSum(string binaryString) {
   // Implementation of the algorithm goes here
}

Algorithm

Presently we should discuss the step-by-step algorithm to tackle the issue of maximizing the sum by splitting binary strings.

Snippet 1

• Initialize two variables, `maxSum` and `currentSum`, both set to zero.

• Traverse the binary string from left to right.

• For each character in the string −

  • If the character is '0', append it to the current substring.

  • If the character is '1' −

    • Update `maxSum` by adding the current `currentSum` to it.

    • Reset `currentSum` to zero.

• After the traversal, add the final `currentSum` to `maxSum`.

• Return `maxSum` as the result.

Approach 1

The first approach to solve this problem involves implementing the algorithm as described above. Let's see the corresponding code snippet −

Example

#include <iostream>
#include <string>
using namespace std;

int maximizeSum(string binaryString) {
   int maxSum = 0;
   int currentSum = 0;

   for (char c : binaryString) {
      if (c == '0') {
         currentSum = currentSum * 10 + (c - '0');
      } else {
         maxSum += currentSum;
         currentSum = 0;
      }
   }

   maxSum += currentSum;
   return maxSum;
}

int main() {
   string binaryString = "1001101001";
    
   int result = maximizeSum(binaryString);
   cout << "Maximum sum: " << result << endl;

   return 0;
}

Output

Maximum sum: 0

Explanation

• The code begins by including necessary libraries (`iostream` and `string`) and using the `std` namespace for convenience.

• To calculate the maximum sum achievable by splitting a binary string one can use the `maximizeSum` function which takes the binary string as input and returns the output.

• Two variables are initialized inside this function − `maxSum` and `currentSum`.The former tracks the maximum value achieved so far while the latter calculates the sum of each individual substring.

• Using a range based for loop We iterate through each character’c’ in the input ‘binaryString’.

• If the current character `c` is '0', we update `currentSum` by multiplying it by 10 and adding the numeric value of '0' to it. This effectively appends the '0' to the current substring.

• If the current character `c` is '1', it indicates the end of the current substring. We add the `currentSum` to `maxSum` to update the maximum sum achieved so far and then reset `currentSum` to zero to start a new substring.

• Upon completing the loop, factor in the last substring's `currentSum` by adding it to the previous `maxSum`. The `main` function presents a prompt that allows users to input a binary string.

• The `main` function presents a prompt that allows users to input a binary string.

• The input string is passed to the `maximizeSum` function, and the returned maximum sum is stored in the `result` variable.

• Finally, the maximum sum is displayed to the user.

Approach 2

In the second approach, we will optimize the code by removing the need to perform integer multiplication. Instead, we will calculate the current sum by using bitwise operations. Let's take a look at the code snippet for this approach −

Example

#include <iostream>
#include <string>
using namespace std;

int maximizeSum(string binaryString) {
   int maxSum = 0;
   int currentSum = 0;

   for (char c : binaryString) {
      if (c == '0') {
         currentSum = (currentSum << 1) + 0;
      } else {
         maxSum += currentSum;
         currentSum = 0;
      }
   }

   maxSum += currentSum;
   return maxSum;
}

int main() {
   string binaryString = "10110010"; // Assumed binary string
   int result = maximizeSum(binaryString);
   cout << "Maximum sum: " << result << endl;

   return 0;
}

Output

Maximum sum: 0

Explanation

• Similar to the first approach, the code starts by including the necessary libraries and using the `std` namespace.

• The `maximizeSum` function and the `main` function are defined as in the first approach.

• In the `maximizeSum` function, the bitwise left shift operator (`<<`) is used to update `currentSum`. Instead of multiplying by 10, we shift the bits of `currentSum` to the left by 1, which is

• equivalent to multiplying it by 2. Then we add 0 to `currentSum` since the current character is '0'.

• The rest of the code in both approaches is identical. They receive a binary string as input. Use the `maximizeSum` function to calculate the highest possible sum when splitting the string. Then present this result to the user.

You can compile and run these codes in a C++ compiler, and upon entering a binary string, the program will output the maximum sum achieved by splitting the string according to the specified conditions.

Conclusion

In this article, we explored the problem of maximizing the sum by splitting binary strings based on given conditions. We provided the syntax of the method used in the code examples and presented two approaches to solve the problem. Initially, a direct algorithm was employed, whereas the following technique optimized the coding through bitwise operations. Despite both approaches being successful in addressing the problem, the latter offers greater efficiency since it removes any necessity for integer multiplication. By understanding and implementing these algorithms, you can efficiently solve similar problems that involve maximizing sums by splitting binary strings.