A two-dimensional array of integers in which most elements are zero is called a sparse array. Because most elements have a value of zero, memory can be saved by storing only the non-zero values along with their row and column indexes. The following complete SparseArrayEntry class is used to represent non-zero elements in a sparse array. A SparseArrayEntry object cannot be modified after it has been constructed.

import java.util.*;

public class SparseArrayEntry {
    private int row;
    private int col;
    private int value;

    public SparseArrayEntry(int r, int c, int v) {
        this.row = r;
        this.col = c;
        this.value = v;
    }

    public int getRow() {
        return row;
    }

    public int getCol() {
        return col;
    }

    public int getValue() {
        return value;
    }
}

public class SparseArray {
    private int numRows;
    private int numCols;
    private List<SparseArrayEntry> entries;

    public SparseArray(int numRows, int numCols) {
        this.numRows = numRows;
        this.numCols = numCols;
        this.entries = new ArrayList<>();
    }

    public void addEntry(int row, int col, int value) {
        entries.add(new SparseArrayEntry(row, col, value));
    }
    
    public void removeColumn(int col) {
        List<SparseArrayEntry> newEntries = new ArrayList<>();
        for (SparseArrayEntry entry : entries) {
            if (entry.getCol() != col) {
                if (entry.getCol() > col) {
                    newEntries.add(new SparseArrayEntry(entry.getRow(), entry.getCol() - 1, entry.getValue()));
                } else {
                    newEntries.add(entry);
                }
            }
        }
        entries = newEntries;
        numCols--;
    }
    

    public void printArray() {
        for (SparseArrayEntry entry : entries) {
            System.out.println("Row: " + entry.getRow() + ", Col: " + entry.getCol() + ", Value: " + entry.getValue());
        }
    }

    public static void main(String[] args) {
        SparseArray sparseArray = new SparseArray(5, 5);
        sparseArray.addEntry(0, 1, 1);
        sparseArray.addEntry(0, 2, 2);
        sparseArray.addEntry(0, 3, 3);
        sparseArray.addEntry(1, 1, 4);
        sparseArray.addEntry(1, 2, 5);
        sparseArray.addEntry(1, 3, 6);
        sparseArray.addEntry(2, 1, 7);
        sparseArray.addEntry(2, 2, 8);
        sparseArray.addEntry(2, 3, 9);
        sparseArray.addEntry(3, 1, 10);
        sparseArray.addEntry(3, 2, 11);
        sparseArray.addEntry(3, 3, 12);
        sparseArray.addEntry(4, 1, 13);
        sparseArray.addEntry(4, 2, 14);
        sparseArray.addEntry(4, 3, 15);

        System.out.println("Before removing column:");
        sparseArray.printArray();

        sparseArray.removeColumn(1);

        System.out.println("After removing column:");
        sparseArray.printArray();
    }
}

SparseArray.main(new String[0]);

Before removing column:
Row: 0, Col: 1, Value: 1
Row: 0, Col: 2, Value: 2
Row: 0, Col: 3, Value: 3
Row: 1, Col: 1, Value: 4
Row: 1, Col: 2, Value: 5
Row: 1, Col: 3, Value: 6
Row: 2, Col: 1, Value: 7
Row: 2, Col: 2, Value: 8
Row: 2, Col: 3, Value: 9
Row: 3, Col: 1, Value: 10
Row: 3, Col: 2, Value: 11
Row: 3, Col: 3, Value: 12
Row: 4, Col: 1, Value: 13
Row: 4, Col: 2, Value: 14
Row: 4, Col: 3, Value: 15
After removing column:
Row: 0, Col: 1, Value: 2
Row: 0, Col: 2, Value: 3
Row: 1, Col: 1, Value: 5
Row: 1, Col: 2, Value: 6
Row: 2, Col: 1, Value: 8
Row: 2, Col: 2, Value: 9
Row: 3, Col: 1, Value: 11
Row: 3, Col: 2, Value: 12
Row: 4, Col: 1, Value: 14
Row: 4, Col: 2, Value: 15

Question 3