PLEASE Modify the addCol(j) and removeCol(j) operations only so it runs O(row() + col()-j) instead of O(row() *(col() -j)) time. 

 import java.util.List; import java.util.ArrayList; import java.util.Random; import java.util.Collections;  public class FasterTable implements Table { List> tab; int nrows, ncols; public FasterTable(Class t) { nrows = 0; ncols = 0; tab = new ArrayList>(); } public int rows() { return nrows; } public int cols() { return ncols; } public T get(int i, int j) { if (i  rows() - 1 || j  cols()-1) throw new IndexOutOfBoundsException(); return tab.get(i).get(j); } public T set(int i, int j, T x) { if (i  rows() - 1 || j  cols()-1) throw new IndexOutOfBoundsException(); return tab.get(i).set(j, x); } public void addRow(int i) { if (i  rows()) throw new IndexOutOfBoundsException(); nrows++; List row = new ArrayList(); for (int j = 0; j null); tab.add(i, row); } public void removeRow(int i) { if (i  rows() - 1) throw new IndexOutOfBoundsException(); nrows--; tab.remove(i); } public void addCol(int j) { // this method is too slow!  if (j  cols()) throw new IndexOutOfBoundsException(); ncols++; // this loop takes O( rows*(cols()-j) ) time  for (int i = 0; i null); // O( cols()-j ) time  } public void removeCol(int j) { // this method is too slow!  if (j  cols() - 1) throw new IndexOutOfBoundsException(); ncols--; // this loop takes O( rows*(cols()-j) ) time  for (int i = 0; i // O( cols()-j ) time  } public String toString() { StringBuilder sb = new StringBuilder(); for (int i = 0; i for (int j = 0; j " "); } sb.append(" "); } return sb.toString(); } public static void main(String[] args) { Tester.testTable(new FasterTable(Integer.class)); } } 

Hint 1: To make addCol(i) fast enough, you have to avoid calling add(i,nul1) for each row in your table. You can, however, afford to call add (null) for each each row. Hint 2: To make removeCol(i) fast enough, you have to avoid calling remove(i) for each row in your table. You can, however, afford to call set(i,null) for each row