面试题1：实现大数加减乘除四则运算

通过c++字符串string实现大数的加、减、乘、除

string addTwoString(string s1, string s2) {
    char carry = '0';
    string res;
    int l1 = s1.length();
    int l2 = s2.length();

    int n = max(l1, l2);
    for (int i = 0; i <= n; i++) {
        char a = '0';
        char b = '0';
        if (l1 - i - 1 >= 0) {
            a = s1[l1 - i - 1];
        }
        if (l2 - i - 1 >= 0) {
            b = s2[l2 - i - 1];
        }
        int sum = a - '0' + b - '0' + carry - '0';
        carry = sum / 10 + '0';
        res.insert(res.begin(), sum % 10 + '0');
    }

    while (*res.begin() == '0') {
        res.erase(res.begin());
    }
    return res;
}

string multiplyTwoString(string s1,string s2){
    int l1 = s1.length();
    int l2 = s2.length();
    if(l1 > l2) return multiplyTwoString(s2,s1);

    string res = "0";
    for(int i=0;i<l1;i++){
        char carry = '0';
        string tmp;
        for(int j=0;j<l2;j++){
            int sum = (s1[l1-i-1]- '0') * (s2[l2-j-1] - '0') + carry - '0';
            carry = sum / 10 + '0';
            tmp.insert(tmp.begin(),sum%10+'0');
        }
        for(int j=0;j<i;j++){
            tmp.push_back('0');
        }
        res = addTwoString(res, tmp);
    }
    return res;
}

#include <iostream>
#include <cstdlib>
#include <vector>
#include <sstream>
#include <algorithm>
using namespace std;

class Solution {
public:
    string addTwoString(string nums1, string nums2) {
        int n1 = nums1.size();
        int n2 = nums2.size();
        //便于操作，统一转换为长数加短数
        if (n1 < n2)
            return addTwoString(nums2, nums1);

        int minlen = n2;
        int maxlen = n1;
        string result;
        int carry = 0;
        for (int i = 0; i < minlen; i++) {
            int sum = nums1[--n1] - '0' + nums2[--n2] - '0' + carry;
            carry = sum / 10;
            int a = sum % 10;
            result.push_back(a + '0');
        }
        for (int i = minlen; i < maxlen; i++) {
            int sum = nums1[--n1] - '0' + carry;
            carry = sum / 10;
            int a = sum % 10;
            result.push_back(a + '0');
        }

        if (carry != 0)
            result.push_back(carry + '0');

        reverse(result.begin(), result.end());
        return result;
    }

    string multiplyTwoString(string nums1, string nums2) {
        string result = "0";
        if (nums1 == "0" || nums2 == "0")
            return result;

        vector<string> tmpResult;
        int n1 = nums1.size();
        int n2 = nums2.size();

        int carry = 0;
        reverse(nums1.begin(), nums1.end());
        reverse(nums2.begin(), nums2.end());

        for (int i = 0; i < n1; i++) {
            string str;
            for (int j = 0; j < n2; j++) {
                int sum = (nums1[i] - '0') * (nums2[j] - '0') + carry;
                carry = sum / 10;
                int a = sum - carry * 10;
                str.push_back(a + '0');
            }
            if (carry != 0)
                str.push_back(carry + '0');
            carry = 0;
            reverse(str.begin(), str.end());
            for (int k = 0; k < i; k++) {
                str.push_back('0');
            }
            tmpResult.push_back(str);
        }

        int size = tmpResult.size();

        for (int i = 0; i < size; i++) {
            result = addTwoString(result, tmpResult[i]);
        }
        return result;
    }

    string substractTwoString(string nums1, string nums2) {
        string result;
        int n1 = nums1.size();
        int n2 = nums2.size();

        //判断符号为正负
        char sign = '+';
        if (n1 < n2) {
            sign = '-';
            nums1.swap(nums2);

        } else if (n1 == n2) {
            for (int i = 0; i < n1; i++) {
                if (nums1[i] > nums2[i]) {
                    break;
                } else if (nums1[i] < nums2[i]) {
                    sign = '-';
                    nums1.swap(nums2);
                    break;
                }
            }
        }
        int borrow = 0;
        reverse(nums1.begin(), nums1.end());
        reverse(nums2.begin(), nums2.end());

        n1 = nums1.size();
        n2 = nums2.size();

        for (int i = 0; i < n2; i++) {
            int r = nums1[i] - nums2[i] - borrow;
            borrow = 0;
            if (r < 0) {
                r = r + 10;
                borrow = 1;
            }
            result.push_back(r + '0');
        }

        for (int i = n2; i < n1; i++) {
            int r = nums1[i] - '0' - borrow;
            borrow = 0;
            if (r < 0) {
                r = r + 10;
                borrow = 1;
            }
            result.push_back(r + '0');
        }

        for (int i = n1 - 1; i >= 0; i--) {
            if (result[i] == '0')
                result.erase(result.begin() + i);
            else
                break;
        }
        reverse(result.begin(), result.end());
        if (sign == '-') {
            result.insert(result.begin(), '-');
        }
        return result;
    }


    string divideTwoString(string nums1, string nums2) {
        string result;
        result = substractTwoString(nums1, nums2);
        if (result[0] == '-') {
            result = "0";
            return result;
        }
        result = "";
        int n1 = nums1.size();

        stringstream stream;
        string dividend;

        for (int j = 0; j < n1; j++) {
            dividend.push_back(nums1[j]);   //被除数
            //从9到0，试探性的找商，当余数不为负数时，为当前位的值
            for (int i = 9; i >= 0; i--) {
                stream.str("");
                stream << i;
                string s = stream.str();
                string sj = multiplyTwoString(nums2, s);
                string remain = substractTwoString(dividend, sj);

                if(remain[0] != '-'){
                    result.push_back(i+'0');
                    dividend = remain;
                    break;
                }
            }
        }
        //去掉商前面的零位
        int size = result.size();
        for(int i=0;i<size;i++){
            if(result[0]=='0'){
                result.erase(result.begin());
            }else {
                break;
            }
        }
        //四舍五入
        string s = substractTwoString(multiplyTwoString(dividend,"2"),nums2);
        if(s[0] == '-')  addTwoString(result,"1");

        return result;
    }
};

int main() {
    string nums1 = "123456";
    string nums2 = "789";
    Solution s;
    cout << s.addTwoString(nums1, nums2) << endl;
    cout << s.multiplyTwoString(nums1, nums2) << endl;
    cout << s.substractTwoString(nums1, nums2) << endl;
    cout << s.divideTwoString(nums1, nums2) << endl;
    return 0;
}