Implement Biginteger Multiply
I failed to implement this class and thought it for a few weeks, couldn't get the answer.
Anybody can help me implement it using C#/Java? Thanks a lot.
Do you know how to do multiplication on paper?
123
x 456
-----
738
615
492
-----
56088
I would just implement that algorithm in code.
C++ Implementation:
Source Code:
#include <iostream>
using namespace std;
int main()
{
int a[10] = {8,9,8,8,9,2};
int b[10] = {2,1,9,8,5,4,3,6,3};
// INPUT DISPLAY
for(int i=9;i>=0;i--) cout << a[i];
cout << " x ";
for(int i=9;i>=0;i--) cout << b[i];
cout << " = ";
int c[20] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
for(int i=0;i<10;i++)
{
int carry = 0;
for(int j=0;j<10;j++)
{
int t = (a[j] * b[i]) + c[i+j] + carry;
carry = t/10;
c[i+j] = t%10;
}
}
// RESULT DISPLAY
for(int i=19;i>=0;i--) cout << c[i];
cout << endl;
}
Output:
0000298898 x 0363458912 = 00000108637141878976
There is a superb algorithm called Karatsuba algorithm..Here
Which uses divide and conquer startegy..Where you can multiply large numbers..
I have implemented my it in java..
Using some manipulation..
package aoa;
import java.io.*;
public class LargeMult {
/**
* @param args the command line arguments
*/
public static void main(String[] args) throws IOException
{
// TODO code application logic here
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
System.out.println("Enter 1st number");
String a=br.readLine();
System.out.println("Enter 2nd number");
String b=br.readLine();
System.out.println("Result:"+multiply(a,b));
}
static String multiply(String t1,String t2)
{
if(t1.length()>1&&t2.length()>1)
{
int mid1=t1.length()/2;
int mid2=t2.length()/2;
String a=t1.substring(0, mid1);//Al
String b=t1.substring(mid1, t1.length());//Ar
String c=t2.substring(0, mid2);//Bl
String d=t2.substring(mid2, t2.length());//Br
String s1=multiply(a, c);
String s2=multiply(a, d);
String s3=multiply(b, c);
String s4=multiply(b, d);
long ans;
ans=Long.parseLong(s1)*(long)Math.pow(10,
b.length()+d.length())+Long.parseLong(s3)*(long)Math.pow(10,d.length())+
Long.parseLong(s2)*(long)Math.pow(10, b.length())+Long.parseLong(s4);
return ans+"";
}
else
{
return (Integer.parseInt(t1)*Integer.parseInt(t2))+"";
}
}
}
I hope this helps!!Enjoy..
Give the number you want to multiply in integer type array i.e. int[] one & int[] two.
public class VeryLongMultiplication {
public static void main(String args[]){
int[] one={9,9,9,9,9,9};
String[] temp=new String[100];
int c=0;
String[] temp1=new String[100];
int c1=0;
int[] two={9,9,9,9,9,9};
int car=0,mul=1; int rem=0; int sum=0;
String str="";
////////////////////////////////////////////
for(int i=one.length-1;i>=0;i--)
{
for(int j=two.length-1;j>=0;j--)
{
mul=one[i]*two[j]+car;
rem=mul%10;
car=mul/10;
if(j>0)
str=rem+str;
else
str=mul+str;
}
temp[c]=str;
c++;
str="";
car=0;
}
////////////////////////////////////////
for(int jk=0;jk<c;jk++)
{
for(int l=c-jk;l>0;l--)
str="0"+str;
str=str+temp[jk];
for(int l=0;l<=jk-1;l++)
str=str+"0";
System.out.println(str);
temp1[c1]=str;
c1++;
str="";
}
///////////////////////////////////
String ag="";int carry=0;
System.out.println("========================================================");
for(int jw=temp1[0].length()-1;jw>=0;jw--)
{
for(int iw=0;iw<c1;iw++)
{
int x=temp1[iw].charAt(jw)-'0';
sum+=x;
}
sum+=carry;
int n=sum;
sum=n%10;carry=n/10;
ag=sum+ag;
sum=0;
}
System.out.println(ag);
}
}
Output:
0000008999991 0000089999910 0000899999100 0008999991000 0089999910000 0899999100000 ______________ 0999998000001
If you do it the long-hand way, you'll have to implement an Add() method too to add up all the parts at the end. I started there just to get the ball rolling. Once you have the Add() down, the Multipy() method gets implemented along the same lines.
public static int[] Add(int[] a, int[] b) {
var maxLen = (a.Length > b.Length ? a.Length : b.Length);
var carryOver = 0;
var result = new List<int>();
for (int i = 0; i < maxLen; i++) {
var idx1 = a.Length - i - 1;
var idx2 = b.Length - i - 1;
var val1 = (idx1 < 0 ? 0 : a[idx1]);
var val2 = (idx2 < 0 ? 0 : b[idx2]);
var addResult = (val1 + val2) + carryOver;
var strAddResult = String.Format("{0:00}", addResult);
carryOver = Convert.ToInt32(strAddResult.Substring(0, 1));
var partialAddResult = Convert.ToInt32(strAddResult.Substring(1));
result.Insert(0, partialAddResult);
}
if (carryOver > 0) result.Insert(0, carryOver);
return result.ToArray();
}
Hint: use divide-and-conquer to split the int into halves, this can effectively reduce the time complexity from O(n^2) to O(n^(log3)). The gist is the reduction of multiplication operations.
I'm posting java code that I wrote. Hope, this will help
import org.junit.Test;
import static org.junit.Assert.*;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
/**
* Created by ${YogenRai} on 11/27/2015.
*
* method multiply BigInteger stored as digits in integer array and returns results
*/
public class BigIntegerMultiply {
public static List<Integer> multiply(int[] num1,int[] num2){
BigInteger first=new BigInteger(toString(num1));
BigInteger result=new BigInteger("0");
for (int i = num2.length-1,k=1; i >=0; i--,k=k*10) {
result = (first.multiply(BigInteger.valueOf(num2[i]))).multiply(BigInteger.valueOf(k)).add(result);
}
return convertToArray(result);
}
private static List<Integer> convertToArray(BigInteger result) {
List<Integer> rs=new ArrayList<>();
while (result.intValue()!=0){
int digit=result.mod(BigInteger.TEN).intValue();
rs.add(digit);
result = result.divide(BigInteger.TEN);
}
Collections.reverse(rs);
return rs;
}
public static String toString(int[] array){
StringBuilder sb=new StringBuilder();
for (int element:array){
sb.append(element);
}
return sb.toString();
}
@Test
public void testArray(){
int[] num1={2, 9, 8, 8, 9, 8};
int[] num2 = {3,6,3,4,5,8,9,1,2};
System.out.println(multiply(num1, num2));
}
}
