Java Coding Test Course, Finding the Arrangement of Parentheses that Creates the Minimum Value

Problem Definition

You need to find a way to create the minimum value using the given numbers and parentheses. For example, when a string containing numbers and operators is given, the problem involves calculating the possible minimum value by placing parentheses appropriately. This problem aims to optimize an expression that can yield different results depending on the placement of parentheses.

Example Problem

Approach to the Problem

To create the minimum value, you need to try all possible arrangements of parentheses and compare the results. The algorithm that can be used here is “divide and conquer.” The expression is partially divided, and each result is compared to derive the final result.

Step 1: Parsing the Expression

First, parse the input string to separate the numbers and operators. Then, prioritize each operation and calculate the results accordingly.

Step 2: Recursive Calculation

Recursively split the expression to calculate the results of each part. Each operator branches into child nodes, allowing the calculation of values for all combinations.

Step 3: Minimum Value Comparison

After calculating all possible cases, compare them to find the minimum value. During this process, results can be stored to prevent duplicate calculations.

Python Code Example

def minValue(expression):
    import re

    # Separate the expression into numbers and operators
    tokens = re.findall(r'\d+|[+*/-]', expression)
    
    # Function to search all combinations
    def dfs(tokens):
        if len(tokens) == 1:
            return int(tokens[0])
        
        min_result = float('inf')
        
        for i in range(1, len(tokens), 2):
            operator = tokens[i]
            left = tokens[:i]
            right = tokens[i + 1:]

            for left_result in dfs(left):
                for right_result in dfs(right):
                    if operator == '+':
                        result = left_result + right_result
                    elif operator == '-':
                        result = left_result - right_result
                    elif operator == '*':
                        result = left_result * right_result
                    elif operator == '/':
                        result = left_result // right_result
                    
                    min_result = min(min_result, result)
        
        return min_result
    
    return dfs(tokens)

# Example usage
print(minValue("1+2*3-4/2"))

Conclusion

This problem serves as practice in understanding how the placement of parentheses affects results and in finding the minimum value through recursive thinking. The process of optimizing while considering various conditions is a commonly used approach in coding tests. Implement the code and test various cases in practice.

Tips for Coding Test Preparation

• Understand the problem and accurately grasp its requirements.
• Generate various cases through examples.
• Learn and practice recursive approaches.
• Experiment with multiple ideas to find the optimal solution.

Additional Resources

Find and study materials describing various algorithm problems and solutions. By solidifying the basics of algorithms, you will be able to achieve good results in coding tests.