大数相乘

package recursion;
/**
 * 大数相乘思想：
 *  0 1 2 3 4  5   6  7 8 9 10 11
 *  个  十  百  千  万   十万  百万   ……
 *  0 = 0 * 0 ;
 *  1 = 1 * 0  + 0 * 1 + 0*0的进位
 *  2 = 1 * 1  + 0 * 2 + 2 * 0  +  1对应的进位
 *  ……= …… 
 * @author my
 *
 */
public class BigMultiply {
    public static void main(String[] args) {
        String str1 ="2342466546456";
        String str2 = "5364576545645464";

        int len1= str1.length();
        int len2= str2.length();

        char[] s1 = str1.toCharArray();
        char[] s2 = str2.toCharArray();

        //高低位对调
        coverdata(s1,len1);
        coverdata(s2,len2);
        System.out.println("乘数："+ str1);
        System.out.println("乘数："+ str2);
        multiply(s1,len1,s2,len2);
    }

    private static void multiply(char[] a, int alen, char[] b, int blen) {
        //两个数乘积位数不会超过乘数位数的和 +3位
        int csize = alen +blen +3;
        //开辟乘积的数组
        int [] c = new  int[csize];
        //对齐诸位相乘
        for(int j =0;j<blen;j++) {
            for(int i =0;i<alen;i++) {
                c[i+j] += Integer.parseInt(String.valueOf(a[i]))*Integer.parseInt(String.valueOf(b[j]));
            }
        }
        //进位处理
        int m = 0;
        for(m = 0; m<csize;m++) {
            int carray = c[m] /10;
            c[m] = c[m] %10;
            if(carray>0) {
                c[m+1] += carray; 
            }
        }
        //找到最高位
        for(m = csize-1;m>=0;m--) {
            if(c[m]>0)break;
        }

        System.out.println("乘积为：");
        for(int n = 0;n<=m;n++) {
            System.out.print(c[m-n]);
        }
        System.out.println("");

    }

    private static void coverdata(char[]data, int len) {
        //高低位对调
        for(int i=0;i<len/2;i++) {
            /**
             * a = a+b;
             * b = a - b;
             * a = a - b;
             */
            data[i] += data[len -1 -i];
            data[len -1 -i] = (char)(data[i]-data[len-1-i]);
            data[i] = (char)(data[i]-data[len-1-i]);
        }
    }
}