大数相乘

所谓大数相乘（Multiplication algorithm），就是指数字比较大，相乘的结果超出了基本类型的表示范围，所以这样的数不能够直接做乘法运算。

import java.util.Arrays;
import java.util.Stack;
/**
 * 大数相乘
 */
public class BigNumberMutiply {

    // 反转字符串
    private String reverse(String s) {
        Stack stack = new Stack();
        StringBuffer buffer = new StringBuffer();
        for (int i = 0; i < s.length(); i++) {
            stack.push(s.charAt(i));
        }
        while (!stack.isEmpty()) {
            buffer.append(String.valueOf(stack.pop()));
        }

        return buffer.toString();
    }

    // 计算乘积
    private void mutiply(String factor1, String factor2) {

        factor1 = reverse(factor1);
        factor2 = reverse(factor2);
        int len1 = factor1.length();
        int len2 = factor2.length();

        // 保存结果的数组长度
        int size = len1 + len2 + 3;
        int[] res = new int[size];
        // 结果
        String result = "";

        // 逐位相乘
        for (int i = 0; i < len1; i++) {
            for (int j = 0; j < len2; j++) {
                res[i + j] += (Integer.parseInt(String.valueOf(factor1.charAt(i))))
                        * (Integer.parseInt(String.valueOf(factor2.charAt(j))));
            }
        }

        // 进位处理
        int m = 0;
        while (m < size) {
            int tmp = res[m] / 10;
            res[m] = res[m] % 10;
            if (tmp > 0) {
                res[m + 1] += tmp;
            }
            m++;
        }

        // 找到最高位
        m = size - 1;
        while (res[m] <= 0) {
            m--;
        }

        // 打印结果
        while (m >= 0) {
            result += res[m];
            m--;
        }
        System.out.println("结果：" + result);
    }

    public static void main(String[] args) {
        BigNumberMutiply mutiply = new BigNumberMutiply();
        String factor1 = "12723169871651635965371";
        String factor2 = "9867354656235626523526235665373";

        System.out.println("乘数:" + factor1 + "\n" + "乘数:" + factor2);
        mutiply.mutiply(factor1, factor2);

    }
}