C++ Coding Test Course, Finding Parentheses Placement to Minimize Value

Problem Description

When a mathematical expression is given, we study how to appropriately place parentheses to create the minimum value of the expression. For example, assuming there is an expression “1+2-3+4”, this is a problem of finding the possible minimum value by placing parentheses.

Problem Definition

Given a string consisting of positive integers and operators (+, -), write an algorithm to find the minimum value of the expression by placing parentheses appropriately. The numbers range from 1 to 100, and there can be up to 100 operators.

Input Format

• The input is given as a single string. (e.g., “5-3+1-2”)

Output Format

• Output the minimum value as an integer.

Approach to the Problem

To solve this problem, it is necessary to understand the order of operations in the expression and the precedence of parentheses, adjusting the results of each operation to minimize the value. By using parentheses appropriately, we can adjust the order of calculations for addition and subtraction.

Idea

When analyzing the expression, the ‘+’ operator adds the numbers before and after it, while the ‘-‘ operator subtracts all the subsequent numbers, so this aspect should be well utilized. Thus, grouping the numbers following the “-” operator to subtract a larger value becomes a key strategy to achieve the minimum value.

Problem Solving Process

Step 1: Parsing the Expression

Split the input expression based on ‘+’ and ‘-‘, separating the numbers and operators. This prepares a basic data structure to adjust the order of operations.

Step 2: Handling Operators

Set the first number as the initial value and calculate by adding the next number for the ‘+’ operator and subtracting all subsequent numbers for the ‘-‘ operator.

Step 3: Calculating the Minimum Value

Finally, derive the minimum value from the final computed value based on all operation results.

C++ Code Implementation

Below is an example code implemented in C++ based on the above approach.

        
#include 
#include 
#include 
#include 

using namespace std;

int minValue(string expression) {
    vector numbers;
    vector operations;
    istringstream iss(expression);
    string temp;

    // Parsing the expression
    while (getline(iss, temp, '+')) {
        size_t pos = 0;
        while ((pos = temp.find('-')) != string::npos) {
            numbers.push_back(stoi(temp.substr(0, pos)));
            operations.push_back('+');
            temp = temp.substr(pos + 1);
        }
        numbers.push_back(stoi(temp));
        operations.push_back('-');
    }

    // Finding the position of '-' in the last operation to calculate the minimum value
    int result = numbers[0];
    bool subtractMode = false;

    for (int i = 1; i < numbers.size(); ++i) {
        if (operations[i - 1] == '-') {
            subtractMode = true;
        }
        if (subtractMode) {
            result -= numbers[i];
        } else {
            result += numbers[i];
        }
    }
    return result;
}

int main() {
    string expression;
    cout << "Enter the expression: ";
    cin >> expression;

    int result = minValue(expression);
    cout << "Minimum value: " << result << endl;
    return 0;
}
        
    

Code Explanation

The above code analyzes the input expression and performs operations to find the minimum value. It stores each number and operator in vectors, then computes according to the precedence of operators.

Results and Tests

For example, if "5-3+1-2" is provided as input, this code goes through the following steps to calculate the minimum value:

• 5 - 3 + 1 - 2 = 1

As a result, 1 is printed, which may vary based on the parameters. Testing through various expressions should be conducted.

Conclusion

To solve the parentheses placement problem, it is essential to understand the structure of the expression and fully utilize the effects of each operation. Especially, using the '-' operator to find the minimum value based on combinations of numbers is a useful strategy that can be applied to various problems.

Effectively utilizing the characteristics of the C++ language to solve problems and developing optimal solutions that reduce algorithmic complexity will greatly aid in job preparation. We hope this lesson contributes to your successful coding test preparation.