Split a given binary string based on a given condition using C++ to maximize the sum

This article aims to solve a complex algorithmic problem involving splitting a binary string in a way that maximizes the cumulative sum obtained from the individual components. We will provide the reader with a comprehensive syntax outline for implementing the code and suggest two possible techniques to overcome this challenge. Furthermore, we will show two real complete executable codes based on the above method.

grammar

Before delving into the algorithm, it is crucial that we become familiar with the structure of the specified method that we will demonstrate through the upcoming code examples. This method takes a binary string as input and calculates its highest possible value by partitioning said input using predetermined conditions. Here's how this approach looks syntactically -

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

algorithm

Now we should discuss the stepwise algorithm to solve the problem of maximizing the sum by splitting a binary string.

Code snippet 1

• Initialize the 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', add it to the current substring.

  • If the character is '1' −

    • Update "maxSum" by adding the current "currentSum".

    • Reset `currentSum` to zero.

• After the traversal is completed, add the final "currentSum" and "maxSum".

• Return `maxSum` as the result.

method one

The first way to solve this problem involves implementing the above algorithm. Let’s look at 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

illustrate

• For convenience, the code first includes the necessary libraries ("iostream" and "string") and uses the "std" namespace.

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

• Two variables are initialized inside this function - `maxSum` and `currentSum`. The former keeps track of the maximum value reached so far, while the latter calculates the sum of each individual substring.

• Using a range-based for loop we iterate over each character "c" in the input "binaryString".

• If the current character "c" is "0", we multiply it by 10 and add the value "0" to update "currentSum". This effectively appends "0" to the current substring.

• If the current character "c" is "1", it means the current substring ends. We add `currentSum` to `maxSum` to update the maximum sum reached so far, then reset `currentSum` to zero to start a new substring.

• After completing the loop, it is calculated by adding the `currentSum` of the last substring to the previous `maxSum`. The `main` function provides a prompt that allows the user to enter a binary string.

• The "main" function provides a prompt that allows the user to enter 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.

Method 2

In the second approach, we will optimize the code by eliminating the need to perform integer multiplication. Instead, we will use bitwise operations to calculate the current sum. Let’s look at the code snippet of 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

illustrate

• Similar to the first method, the code first includes the necessary libraries and uses the `std` namespace.

• The definitions of function `maximizeSum` and function `main` are the same as those in the first method.

• In the `maximizeSum` function, use the bit left shift operator (`

• Equivalent to multiplying by 2. Then we add 0 to `currentSum` since the current character is "0".

• The rest of the code is the same in both methods. They receive a binary string as input. Use the `maximizeSum` function to calculate the maximum possible sum when splitting a string. This result is then presented to the user.

You can compile and run these codes in the C compiler. When a binary string is input, the program will output the maximum sum obtained by dividing the string according to the specified conditions.

in conclusion

In this article, we explore the problem of maximizing the sum by splitting a binary string based on a given condition. We provide the syntax of the method used in the code example and propose two ways to solve the problem. Initially, direct arithmetic was employed, while the following techniques optimize encoding through bitwise operations. Although both methods successfully solve the problem, the latter offers greater efficiency as it eliminates the need for integer multiplication. By understanding and implementing these algorithms, you can efficiently solve similar problems involving maximizing a sum by splitting a binary string.

The above is the detailed content of Split a given binary string based on a given condition using C++ to maximize the sum. For more information, please follow other related articles on the PHP Chinese website!