Java Coding Test Course, Grouping Numbers to Create Maximum Value

Recent algorithm problems are becoming increasingly important in technical interviews. In particular, the ability to solve problems using programming languages such as Java is required by many companies. In this post, we will solve a problem based on the topic “Forming the Maximum Value by Grouping Numbers.” This problem is very interesting because it can be approached using dynamic programming and greedy algorithms.

Problem Definition

Problem: Given an array of integers, group the numbers appropriately to form the maximum value. The numbers can be grouped in two ways:
1) By multiplying two numbers.
2) By adding two numbers.
However, multiplication can only be done when both numbers are greater than 1.

For example, if the given array is [1, 2, 3, 4, 5], the maximum value can be 5*(4*(3+2)) = 30. The goal is to find the maximum value possible by grouping the numbers in various ways.

Problem Analysis

To solve this problem, it is important to understand two basic rules:

  • Grouping and multiplying numbers greater than 1 always creates the maximum value.
  • Additions may be more beneficial for 1 or 0.

Approach

To solve this problem, we can approach it with the following steps:

  1. Sort the given array.
  2. Multiply as many numbers greater than 1 as possible, and add 1s and 0s appropriately.
  3. Calculate the maximum value considering all cases.

Java Code Implementation

Below is a Java code example based on the above approach:

        
        import java.util.Arrays;
        
        public class MaxValueFormation {
            public static void main(String[] args) {
                int[] numbers = {1, 2, 3, 0, 5};
                System.out.println("Maximum Value: " + maxValue(numbers));
            }
            
            public static int maxValue(int[] numbers) {
                Arrays.sort(numbers);
                int maxValue = 0;
                int n = numbers.length;
                
                for (int i = n - 1; i >= 0; i--) {
                    if (numbers[i] <= 1 || maxValue == 0) {
                        maxValue += numbers[i];
                    } else {
                        maxValue *= numbers[i];
                    }
                }
                return maxValue;
            }
        }

Code Explanation

The code above performs the following operations to calculate the maximum value from the given integer array:

  • First, it sorts the array in ascending order.
  • It initializes the maximum value and accesses the largest number in the array one by one.
  • If the number is less than or equal to 1, it adds it to reflect in the maximum value. If the number is greater than 1, it multiplies it to update the maximum value.

Example Execution

When executing the above code, the maximum value 15 is output for the input array [1, 2, 3, 0, 5].

Complexity Analysis

The time complexity of this algorithm is O(n log n). This is the time required to sort the array. The space complexity is O(1), meaning it does not require additional space.

Conclusion

In this post, we were able to address the algorithm problem of “Forming the Maximum Value by Grouping Numbers.” We learned how to efficiently solve problems using various mathematical principles and algorithms. Even if you encounter similar problems in future coding tests, you will be able to solve them using the principles learned in this course. I hope you continue to practice with other algorithm problems to further enhance your skills!