Java Coding Test Course, Pebble Picking

Problem Description

You are assigned the task of collecting pebbles on the beach. You must extract pebbles according to specific rules.
The pebbles come in various colors, and there is a list of N pebbles given at the location.
Each pebble in this list has a unique color.
You can perform two operations repeatedly:
1. Take out a pebble
2. Put a pebble back.

What is the minimum number of operations (taking out or putting back) required to retrieve all the pebbles?
If it is impossible to retrieve all the pebbles, output ‘Impossible’.

Input Format

• The first line contains the number of pebbles N (1 ≤ N ≤ 100).
• The second line contains the colors of the N pebbles. The colors are given as integers from 1 to 100.

Output Format

Output the minimum number of operations required to retrieve all the pebbles. If it is impossible, print ‘Impossible’.

Problem Analysis

This problem involves managing the color palette of the pebbles and processing with minimal operations.
Each pebble can be grouped by color, and this grouping plays an important role in retrieving the desired pebbles.
It is necessary to have an approach that strategically combines taking out and putting back pebbles based on the rules.

Approach

To effectively solve the problem, we can approach it with the following steps.

1. Count the frequency of pebble colors: Count how many pebbles there are of each color.
2. Calculate the minimum number of operations: If the number of pebbles is odd, the operation of taking out should always take precedence, and final remaining operations should be considered additionally.
3. Validation: Check if it is possible to retrieve all the pebbles.

Sample Code

            
            import java.util.HashMap;
            import java.util.Scanner;

            public class PebbleRemoval {
                public static void main(String[] args) {
                    Scanner scanner = new Scanner(System.in);
                    int N = scanner.nextInt();
                    HashMap colorFrequency = new HashMap<>();
                    
                    for (int i = 0; i < N; i++) {
                        int color = scanner.nextInt();
                        colorFrequency.put(color, colorFrequency.getOrDefault(color, 0) + 1);
                    }
                    
                    int operations = 0;
                    int oddCount = 0;

                    for (int freq : colorFrequency.values()) {
                        if (freq % 2 != 0) {
                            oddCount++;
                        }
                        operations += freq;
                    }
                    
                    if (oddCount > 1) {
                        System.out.println("Impossible");
                    } else {
                        System.out.println(operations);
                    }

                    scanner.close();
                }
            }
            
        

Code Explanation

The above Java code demonstrates a basic structure for counting the frequency of pebble colors.

• It uses a HashMap to count the frequency of each color.
• It checks all frequencies to see if they are odd and tracks the take-out operations.
• Finally, it prints ‘Impossible’ if take-out operations are not feasible.