java-腾讯暑期实习生-输入一个数组A[1,2,...n]，求输入B，使得数组B中的第i个数字B[i]=A[0]*A[1]*...*A[i-1]*A[i+1]

这道题的具体思路请参看 何海涛的微博：http://weibo.com/zhedahht

import java.math.BigInteger;
import java.util.Arrays;

public class CreateBFromATencent {

	/**
	 * 题目：输入一个数组A[1,2,...n]，求输入B，使得数组B中的第i个数字B[i]=A[0]*A[1]*...*A[i-1]*A[i+1]*...*A[N-1].
	 * 要求
	 * 1.不得使用除法
	 * 2.不得新建变量--how?
	 * see http://weibo.com/zhedahht
	 */
	public static void main(String[] args) {
		int[] a=new int[20];
		for(int i=0;i<20;i++){
			a[i]=i+1;
		}
		
		System.out.println(Arrays.toString(a));
		BigInteger[] b1=create(a);//I don't like 'BigInteger',but program will overflow without using it.
		System.out.println(Arrays.toString(b1));
		
		BigInteger[] b2=createWithoutDivision(a);
		System.out.println(Arrays.toString(b2));
	}

	//general solution.Use division
	public static BigInteger[] create(int[] a){
		if(a==null||a.length==0){
			return new BigInteger[0];
		}
		int len=a.length;
		BigInteger[] b=new BigInteger[len];
		//BigInteger product=new BigInteger("1");
		BigInteger product=BigInteger.valueOf(1);//<Effective Java>.Use "static factory method" instead of constructor sometimes. 
		BigInteger[] aa=new BigInteger[len];
		for(int i=0;i<len;i++){
			aa[i]=BigInteger.valueOf(a[i]);
			product=product.multiply(aa[i]);
		}
		for(int i=0;i<len;i++){
			b[i]=product.divide(aa[i]);
		}
		return b;
	}
	
	//not use division.
	public static BigInteger[] createWithoutDivision(int[] a){
		if(a==null||a.length==0){
			return new BigInteger[0];
		}
		int len=a.length;
		BigInteger[] b=new BigInteger[len];
		BigInteger[] aa=new BigInteger[len];
		b[0]=BigInteger.valueOf(1);
		for(int i=0;i<len;i++){
			aa[i]=BigInteger.valueOf(a[i]);
			if(i+1<len){
				b[i+1]=b[i].multiply(aa[i]);
			}
		}
		BigInteger tmp=BigInteger.valueOf(1);
		for(int i=len-2;i>=0;i--){
			tmp=tmp.multiply(aa[i+1]);
			b[i]=b[i].multiply(tmp);
		}
		return b;
	}
}