Rectangular/lattice multiplication

Question

I am trying to implement the rectangular/lattice multiplication in Java. For those who don't know, this is a short tutorial.

I tried some methods wherein I used a single array to store multiplication of two digits and sigma-append zeroes to it. Once all the numbers are multiplied, I pick two elements from the array and then add the sigma value and fetch two more numbers and again perform the same thing until all the numbers are fetched.

The logic works fine but I am not able to find the exact number of zeroes that I should maintain, since for every different set of numbers (4 digits * 3 digits) I get different number of zeroes.

Could somebody please help?

Answer 1

I liked the tutorial, very neat. So I wanted to implement it, but not do your project work. So I came up with a lousy, quick and dirty implementation, violating many of the design rules I practice myself. I used arrays to save the digit by digit multiplication results, and pretty much followed what the tutorial said. I never have had to count the number of 0's, and I am not sure what is sigma-appending, so I cannot answer that. Lastly, there is a bug in the code which shows up when the 2 numbers have a different count of digits. Here is the source code - feel free to edit and use any part. I think an easy fix would be to prepend 0's to the smaller number to make the digit count the same for the 2 numbers, and not to display the corresponding row/columns. More bookkeeping, but thats up to you.

import java.util.*;
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

public class Lattice extends JPanel implements ActionListener {

protected Font  axisFont, rectFont, carrFont;

protected Color boxColor = new Color (25, 143, 103),    gridColor = new Color (78, 23, 211),
        diagColor = new Color (93, 192, 85),    fontColor = new Color (23, 187, 98),
        carrColor = new Color (162, 34, 19);

protected int   nDigitP, nDigitQ, dSize = 60,
        m1, m2, lastCarry, iResult[],
        xDigits[], yDigits[], prodTL[][], prodBR[][];

public Lattice (int p, int q, Font font) {
    nDigitP = (int) Math.ceil (Math.log10 (p)); xDigits = new int[nDigitP];
    nDigitQ = (int) Math.ceil (Math.log10 (q)); yDigits = new int[nDigitQ];

    prodTL = new int[nDigitP][nDigitQ];     prodBR = new int[nDigitP][nDigitQ];

    m1 = p; m2 = q;                 // To display in report
    int np = p, nq = q, size = font.getSize();  // Save the digits in array

    for (int i = 0 ; i < nDigitP ; i++) {
        xDigits[i] = np % 10;
        np /= 10;
    }
    for (int i = 0 ; i < nDigitQ ; i++) {
        yDigits[i] = nq % 10;
        nq /= 10;
    }

    for (int i = 0 ; i < nDigitP ; i++) {       // Cell products as upper/lower matrix
        for (int j = 0 ; j < nDigitQ ; j++) {
            int prod = xDigits[i] * yDigits[j];
            prodTL[i][j] = prod / 10;
            prodBR[i][j] = prod % 10;
    }}

    axisFont = font.deriveFont (Font.PLAIN, size+8.0f);
    rectFont = font.deriveFont (Font.PLAIN, size+4.0f);
    carrFont = font.deriveFont (Font.PLAIN);

    setPreferredSize (new Dimension ((nDigitP+2)*dSize, (nDigitQ+2)*dSize));
}

public void paint (Graphics g) {
    int w = getWidth(), h = getHeight();
    Graphics2D g2 = (Graphics2D) g;         // To make diagonal lines smooth
    g2.setPaint (Color.white);
    g2.fillRect (0,0,w,h);

    int dx = (int) Math.round (w/(2.0+nDigitP)),    // Grid spacing to position
        dy = (int) Math.round (h/(2.0+nDigitQ));    // the lines and the digits

    g2.setRenderingHint (RenderingHints.KEY_ANTIALIASING,
                                            RenderingHints.VALUE_ANTIALIAS_ON);
    g2.setRenderingHint (RenderingHints.KEY_INTERPOLATION,
                                    RenderingHints.VALUE_INTERPOLATION_BILINEAR);

    g2.setFont (axisFont);
    FontMetrics fm = g2.getFontMetrics();
    for (int i = 0 ; i < nDigitP ; i++) {       // Grid || Y-axis and labels on axis
        int px = w - (i+1)*dx;
        g2.setPaint (gridColor);
        if (i > 0)
            g2.drawLine (px, dy, px, h-dy);
        String str = /*i + */"" + xDigits[i];
        int strw = fm.stringWidth (str);
        g2.setPaint (fontColor);
        g2.drawString (str, px-dx/2-strw/2, 4*dy/5);
    }

    for (int i = 0 ; i < nDigitQ ; i++) {       // Grid || X-axis and labels on axis
        int py = h - (i+1)*dy;
        g2.setPaint (gridColor);
        if (i > 0)
            g2.drawLine (dx, py, w-dx, py);
        String str = /*i + */"" + yDigits[i];
        int strw = fm.stringWidth (str);
        g2.setPaint (fontColor);
        g2.drawString (str, w-dx+2*dx/5-strw/2, py-dy/2+10);
    }

    g2.setFont (rectFont);
    fm = g2.getFontMetrics();           // Upper/Lower traingular product matrix
    for (int i = 0 ; i < nDigitP ; i++) {
        for (int j = 0 ; j < nDigitQ ; j++) {
            int px = w - (i+1)*dx;
            int py = h - (j+1)*dy;

            String strT = "" + prodTL[i][j];
            int strw = fm.stringWidth (strT);
            g2.drawString (strT, px-3*dx/4-strw/2, py-3*dy/4+5);

            String strB = "" + prodBR[i][j];
            strw = fm.stringWidth (strB);
            g2.drawString (strB, px-dx/4-strw/2, py-dy/4+5);
    }}

    g2.setFont (axisFont);
    fm = g2.getFontMetrics();
    int carry = 0;
    Vector cVector = new Vector(), iVector = new Vector();
    for (int k = 0 ; k < 2*Math.max (nDigitP, nDigitQ) ; k++) {
        int dSum = carry, i = k/2, j = k/2;
        //System.out.println ("k="+k);
        if ((k % 2) == 0) {             // even k
            if (k/2 < nDigitP && k/2 < nDigitQ)
                dSum += prodBR[k/2][k/2];
            // go right and top
            for (int c = 0 ; c < k ; c++) {
                if (--i < 0)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodTL[i][j];
                    //System.out.println (" >> TL (i,j) = (" + i+","+j+")");
                if (++j == nDigitQ)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodBR[i][j];
                    //System.out.println (" >> BR (i,j) = (" + i+","+j+")");
            }
            // go bottom and left
            i =  k/2; j = k/2;
            for (int c = 0 ; c < k ; c++) {
                if (--j < 0)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodTL[i][j];
                    //System.out.println (" >> TL (i,j) = (" + i+","+j+")");
                if (++i == nDigitP)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodBR[i][j];
                    //System.out.println (" >> BR (i,j) = (" + i+","+j+")");
        }} else {                   // odd k
            if (k/2 < nDigitP && k/2 < nDigitQ)
                dSum += prodTL[k/2][k/2];
            // go top and right
            for (int c = 0 ; c < k ; c++) {
                if (++j == nDigitQ)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodBR[i][j];
                    //System.out.println (" >> BR (i,j) = (" + i+","+j+")");
                if (--i < 0)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodTL[i][j];
                    //System.out.println (" >> TL (i,j) = (" + i+","+j+")");
            }
            i =  k/2; j = k/2;
            // go left and bottom
            for (int c = 0 ; c < k ; c++) {
                if (++i == nDigitP)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodBR[i][j];
                    //System.out.println (" >> BR (i,j) = (" + i+","+j+")");
                if (--j < 0)
                    break;
                if (i < nDigitP && j < nDigitQ)
                    dSum += prodTL[i][j];
                    //System.out.println (" >> TL (i,j) = (" + i+","+j+")");
        }}

        int digit = dSum % 10;  carry = dSum / 10;
        cVector.addElement (new Integer (carry));
        iVector.addElement (new Integer (digit));
        String strD = "" + digit;
        int strw = fm.stringWidth (strD);
        if (k < nDigitP) {
            int px = w - (k+1)*dx - 4*dx/5, py = h-dy + fm.getHeight();
            g2.drawString (strD, px-strw/2, py);
        } else {
            int px = dx - 12, py = h - (k-nDigitP+1)*dy - dy/4;
            g2.drawString (strD, px-strw/2, py+5);
    }} // End k-loop

    g2.setPaint (diagColor);
    for (int i = 0 ; i < nDigitP ; i++) {
        int xt = (i+1) * dx,
            yb = (i+2) * dy;
        g2.drawLine (xt, dy, 0, yb);
    }
    for (int i = 0 ; i < nDigitQ ; i++) {
        int xb = (i + nDigitP - nDigitQ) * dx,
            yr = (i+1) * dy;
        g2.drawLine (w-dx, yr, xb, h);
    }

    // System.out.println ("carry Vector has " + cVector.size() + " elements");
    g2.setFont (carrFont);
    g2.setPaint (carrColor);
    fm = g2.getFontMetrics();
    for (int k = 0 ; k < 2*Math.max (nDigitP, nDigitQ) ; k++) {
        carry = ((Integer) cVector.elementAt (k)).intValue();
        lastCarry = carry;  // To display
        if (carry == 0)
            continue;
        String strC = "" + carry;
        int strw = fm.stringWidth (strC),
            px = w-dx-5-strw/2,         // Const X while going Up
            py = dy + fm.getHeight();       // Const Y while going Left
        if (k < (nDigitQ-1))
            py = h-(k+3)*dy + dy/5 + fm.getHeight();
        else
            px = w - (k-nDigitQ+2) * dx - dx/2 - strw/2;
        g2.drawString (strC, px, py);
    }

    int n = iVector.size();     // Save the vector content to display later
    iResult = new int[n];
    for (int i = 0 ; i < n ; i++)
        iResult[i] = ((Integer) iVector.elementAt (n-i-1)).intValue();
    g2.setPaint (boxColor);     g2.drawRect (dx, dy, w-2*dx, h-2*dy);
}

private void displayResults () {
    StringBuffer sb = new StringBuffer ("Lattice: " + m1 + " \u00D7 " + m2 + " = " + 
                        ((lastCarry == 0) ? "" : (""+lastCarry)));
    for (int k = 0 ; k < iResult.length ; k++)
        sb.append ("" + iResult[k]);
    // System.out.println (sb.toString());
    JOptionPane.showMessageDialog (null, sb.toString(), "Lattice Multiplier",
                            JOptionPane.INFORMATION_MESSAGE);
}

public JPanel getButtonPanel () {
    JPanel bp = new JPanel(new GridLayout (1,bNames.length));
    for (int i = 0 ; i < bNames.length ; i++) {
        JButton b = new JButton (bNames[i]);
        b.addActionListener (this);
        bp.add (b);
    }
    return bp;
}

private final static String[] bNames = {"Close", "Result"};

public void actionPerformed (ActionEvent e) {
    String cmd = e.getActionCommand();
    if (cmd.equals (bNames[0]))     System.exit (0);
    else if (cmd.equals (bNames[1]))    displayResults();
}

public static void main (String[] args) {
    JTextField tf1 = new JTextField (), tf2 = new JTextField();
    JPanel num2m = new JPanel(new GridBagLayout());
    GridBagConstraints gbc = new GridBagConstraints();
    gbc.insets = new Insets (2,2,2,2);

    gbc.fill = GridBagConstraints.HORIZONTAL;
    gbc.gridx = 0;
    gbc.gridy = GridBagConstraints.RELATIVE;
    gbc.anchor = GridBagConstraints.EAST;

    JLabel
    label = new JLabel ("Multiplicand", JLabel.TRAILING);   num2m.add (label, gbc);
    label = new JLabel ("Multiplier", JLabel.TRAILING); num2m.add (label, gbc);
    gbc.gridx++;
    gbc.weightx = 1.0f;     num2m.add (tf1, gbc);   num2m.add (tf2, gbc);

    JFrame lf = new JFrame ("Lattice Multiplication");
    if (JOptionPane.showConfirmDialog (lf, num2m, "Enter numbers to multiply",
                JOptionPane.OK_CANCEL_OPTION,
                JOptionPane.QUESTION_MESSAGE ) == JOptionPane.OK_OPTION) {
        try {
            int m = Integer.parseInt (tf1.getText()), n = Integer.parseInt (tf2.getText());
            Lattice lattice = new Lattice (m, n, label.getFont());
            lf.add (lattice.getButtonPanel(), "South");
            lf.add (lattice, "Center");
            lf.setDefaultCloseOperation (JFrame.EXIT_ON_CLOSE);
            lf.pack();
            lf.setVisible (true);
        } catch (NumberFormatException nex) {
            JOptionPane.showMessageDialog (lf, "Invalid numbers to multiply",
                    "Lattice Multiplier Error", JOptionPane.ERROR_MESSAGE);
            System.exit (1);
    }} else {   System.exit (2);
}}}