网上一搜一大把，搜出来的结果几乎都是我很崇敬的张孝祥老师写的这道题的思路，甚至有的直接把原文copy paste过来，没有一个用代码实现了的。于是自己琢磨了下，这里发布出来。虽然标题是一百亿，但实现结果可用于任意大整数。
直接上代码。这里只实现了大整数相加。有了这个，不难实现减、乘等其他操作。代码复制粘帖即可运行。
MyBigInteger.java
import java.util.ArrayList;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
/**
* Created by Rocky on 14-3-26.
*/
public class MyBigInteger {
private char sign = '0'; // 0 表示正数 - 表示负数
private byte[] data;
public MyBigInteger() {
this.data = "0".getBytes();
}
public MyBigInteger(String value) throws Exception {
//正则表达式，输入字符串要求以 零个或一个 - 开头，其余都是数字
Pattern pattern = Pattern.compile("^-?\\d+$");
if (value == null || value.length() <= 0) {
value = "0";
}
Matcher matcher = pattern.matcher(value);
if (!matcher.find()) {
throw new Exception("the value is not a number string :" + value);
}
//获取字符串的第一个字符
char firstChar = value.charAt(0);
//data应该保存的是第一个非0数字后的字符串
if (firstChar == '-') { //说明输入的是个负数
if (value.length() >=2) {
sign = firstChar;
value = value.substring(1);
value = getTemp(value); //得到value中第一个非0后的子字符串。
}
} else {
value = getTemp(value);
}
this.data = value.getBytes();
}
/**
* 得到一个字符串第一个非0后的字符串，如果没有找到，则返回 "0" 。如：00003435534，则返回3435534
* @return
*/
private String getTemp(String value){
Pattern pattern = Pattern.compile("[^0]{1}");
Matcher matcher = pattern.matcher(value);
if (matcher.find()) {
value = value.substring(matcher.start());
} else {
value = "0";
}
return value;
}
public MyBigInteger add(MyBigInteger other) {
MyBigInteger result = new MyBigInteger();
int thisLength = this.data.length;
int otherLength = other.data.length;
int shorterLength = thisLength > otherLength ? otherLength : thisLength;
ArrayList<Byte> resultData = new ArrayList<Byte>();
int flag = 0; //表示相加时的 进位，或相减时的 借位
int i = thisLength - 1;
int j = otherLength - 1;
int k = shorterLength;
//两个数的符号相同
if (other.sign == this.sign) {
//从两个整数的个位开始依次相加
while (k > 0) {
Integer temp = new Integer(new String(new byte[]{this.data[i]})) + new Integer(new String(new byte[]{other.data[j]})) + flag;
flag = temp / 10; //相加结果超过10时的进位。没有超过10，进位为 0
resultData.add(0, ((temp % 10) + "").getBytes()[0]); //把相加结果保存起来
k--;
i--;
j--;
}
//把多出的位加入到结果中
if (i == -1) {
while (j >= 0) {
Integer temp = new Integer(new String(new byte[]{other.data[j]})) + flag;
flag = temp / 10;
resultData.add(0, ((temp % 10) + "").getBytes()[0]);
j--;
}
} else if (j == -1) {
while (i >= 0) {
Integer temp = new Integer(new String(new byte[]{this.data[i]})) + flag;
flag = temp / 10;
resultData.add(0, ((temp % 10) + "").getBytes()[0]);
i--;
}
}
//最后把flag加进结果中
if (flag != 0) {
for (byte by : (flag + "").getBytes()) {
resultData.add(0, by);
}
}
result.sign = other.sign;
} else { //符号不同
if (thisLength > otherLength) { //说明this表示的整数绝对值大，所以最终结果的符号为this的符号
result.sign = this.sign;
resultData = subtract(this.data, other.data); //执行减法
} else if (thisLength < otherLength) { //other表示的整数绝对值大，所以最终结果的符号为other的符号
result.sign = other.sign;
resultData = subtract(other.data, this.data);
} else { //如果两个数据的位数相同
Integer thisInt = 0;
Integer otherInt = 0;
//从第一位开始比较，直到两者不相等
for (int n = 0; n < thisLength; n++) {
thisInt = new Integer(new String(new byte[]{this.data[n]}));
otherInt = new Integer(new String(new byte[]{other.data[n]}));
if (!thisInt.equals(otherInt)) { //注意这里要使用equals方法，因为这里需要比较的是两者的内容
break;
}
}
//如果this的绝对值大
if (thisInt > otherInt) {
result.sign = this.sign;
resultData = subtract(this.data, other.data);
} else {
result.sign = other.sign;
resultData = subtract(other.data, this.data);
}
}
}
result.data = new byte[resultData.size()];
for (int m = 0; m < resultData.size(); m++) {
result.data[m] = resultData.get(m);
}
return result;
}
private ArrayList<Byte> subtract(byte[] larger, byte[] smaller) {
ArrayList<Byte> resultData = new ArrayList<Byte>();
int flag = 0;
int i = smaller.length - 1;
int j = larger.length - 1;
int k = smaller.length;
while (k > 0) {
Integer temp = new Integer(new String(new byte[]{larger[j]})) + flag - new Integer(new String(new byte[]{smaller[i]}));
if (temp < 0) { //如果相减结果小于0，说明需要借位，则把flag置为 -1，以便下一位减去
flag = -1;
temp += 10;
} else { //如果大于零，需要把flag置为 0.不要忘记了
flag = 0;
}
resultData.add(0, (temp + "").getBytes()[0]);
j--;
i--;
k--;
}
//下面的代码就不写注释了
while (j >= 0) {
Integer temp = new Integer(new String(new byte[]{larger[j]})) + flag;
if (temp < 0) {
flag = -1;
temp += 10;
} else {
flag = 0;
}
resultData.add(0, (temp + "").getBytes()[0]);
j--;
}
return resultData;
}
@Override
public String toString() {
String str = new String(this.data);
str = getTemp(str);
if (sign == '-' && str !="0") {
str = sign + str;
}
return str;
}
}
MyBigIntegerTest.java
import junit.framework.TestCase;
import java.math.BigInteger;
/**
* Created by Rocky on 14-3-26.
*/
public class MyBigIntegerTest extends TestCase {
public void test1() throws Exception {
String a1 = "-5453450543044355356576980545345054545453453454344435353254545345054304435535657698087756454543454345454534534543444353532545453450543044355356454543454354353450136546534534545345345054353450136546534534545345345043044355356576980657698087756454543454354353450136546534534545345345054353450136546534534545345345043044355356576980877564545434543543534501877564545434543543534501";
String b1 = "4545453453454344435353254545345054304435535657698087756454543454354345454534534543444353532545453450543044355356576980877564545434545454534534564545434543543534501365465345345453453450543534501365465345345453453450430443553565769804344435353254545345054304435535657698087756454543454354353450136546534534545345345043543534501365465345345453453450534501365465345345453453450";
MyBigInteger a = new MyBigInteger(a1);
MyBigInteger b = new MyBigInteger(b1);
MyBigInteger c = a.add(b);
System.out.println(c);
BigInteger a2 = new BigInteger(a1);
BigInteger b2 = new BigInteger(b1);
BigInteger c2 = a2.add(b2);
System.out.println(c2);
System.out.println(c2.toString().equals(c.toString()));
}
}
