c++实现大数加减乘除四则运算

Posted 2020-06-16

通过c++字符串string实现大数的加、减、乘、除

  1 #include <iostream>
  3 #include <cstdlib>
  4 #include <vector>
  6 #include <sstream>
  7 #include <algorithm>
  9 using namespace std;
 10 
 11 class Solution {
 12 public:
 13     string addTwoString(string nums1, string nums2) {
 14         int n1 = nums1.size();
 15         int n2 = nums2.size();
 16         //便于操作，统一转换为长数加短数
 17         if (n1 < n2)
 18             return addTwoString(nums2, nums1);
 19 
 20         int minlen = n2;
 21         int maxlen = n1;
 22         string result;
 23         int carry = 0;
 24         for (int i = 0; i < minlen; i++) {
 25             int sum = nums1[--n1] - ‘0‘ + nums2[--n2] - ‘0‘ + carry;
 26             carry = sum / 10;
 27             int a = sum % 10;
 28             result.push_back(a + ‘0‘);
 29         }
 30         for (int i = minlen; i < maxlen; i++) {
 31             int sum = nums1[--n1] - ‘0‘ + carry;
 32             carry = sum / 10;
 33             int a = sum % 10;
 34             result.push_back(a + ‘0‘);
 35         }
 36 
 37         if (carry != 0)
 38             result.push_back(carry + ‘0‘);
 39 
 40         reverse(result.begin(), result.end());
 41         return result;
 42     }
 43 
 45     string multiplyTwoString(string nums1, string nums2) {
 46         string result = "0";
 47         if (nums1 == "0" || nums2 == "0")
 48             return result;
 49 
 50         vector<string> tmpResult;
 51         int n1 = nums1.size();
 52         int n2 = nums2.size();
 53 
 54         int carry = 0;
 55         reverse(nums1.begin(), nums1.end());
 56         reverse(nums2.begin(), nums2.end());
 57 
 58         for (int i = 0; i < n1; i++) {
 59             string str;
 60             for (int j = 0; j < n2; j++) {
 61                 int sum = (nums1[i] - ‘0‘) * (nums2[j] - ‘0‘) + carry;
 62                 carry = sum / 10;
 63                 int a = sum - carry * 10;
 64                 str.push_back(a + ‘0‘);
 65             }
 66             if (carry != 0)
 67                 str.push_back(carry + ‘0‘);
 68             carry = 0;
 69             reverse(str.begin(), str.end());
 70             for (int k = 0; k < i; k++) {
 71                 str.push_back(‘0‘);
 72             }
 73             tmpResult.push_back(str);
 74         }
 75 
 76         int size = tmpResult.size();
 77 
 78         for (int i = 0; i < size; i++) {
 79             result = addTwoString(result, tmpResult[i]);
 80         }
 81         return result;
 82     }
 83 
 84     string substractTwoString(string nums1, string nums2) {
 85         string result;
 86         int n1 = nums1.size();
 87         int n2 = nums2.size();
 88 
 89         //判断符号为正负
 90         char sign = ‘+‘;
 91         if (n1 < n2) {
 92             sign = ‘-‘;
 93             nums1.swap(nums2);
 94 
 95         } else if (n1 == n2) {
 96             for (int i = 0; i < n1; i++) {
 97                 if (nums1[i] > nums2[i]) {
 98                     break;
 99                 } else if (nums1[i] < nums2[i]) {
100                     sign = ‘-‘;
101                     nums1.swap(nums2);
102                     break;
103                 }
104             }
105         }
106         int borrow = 0;
107         reverse(nums1.begin(), nums1.end());
108         reverse(nums2.begin(), nums2.end());
109 
110         n1 = nums1.size();
111         n2 = nums2.size();
112 
113         for (int i = 0; i < n2; i++) {
114             int r = nums1[i] - nums2[i] - borrow;
115             borrow = 0;
116             if (r < 0) {
117                 r = r + 10;
118                 borrow = 1;
119             }
120             result.push_back(r + ‘0‘);
121         }
122 
123         for (int i = n2; i < n1; i++) {
124             int r = nums1[i] - ‘0‘ - borrow;
125             borrow = 0;
126             if (r < 0) {
127                 r = r + 10;
128                 borrow = 1;
129             }
130             result.push_back(r + ‘0‘);
131         }
132 
133         for (int i = n1 - 1; i >= 0; i--) {
134             if (result[i] == ‘0‘)
135                 result.erase(result.begin() + i);
136             else
137                 break;
138         }
139         reverse(result.begin(), result.end());
140         if (sign == ‘-‘) {
141             result.insert(result.begin(), ‘-‘);
142         }
143         return result;
144     }
145 
146 
147     string divideTwoString(string nums1, string nums2) {
148         string result;
149         result = substractTwoString(nums1, nums2);
150         if (result[0] == ‘-‘) {
151             result = "0";
152             return result;
153         }
154         result = "";
155         int n1 = nums1.size();
156 
157         stringstream stream;
158         string dividend;
159 
160         for (int j = 0; j < n1; j++) {
161             dividend.push_back(nums1[j]);   //被除数
162             //从9到0，试探性的找商，当余数不为负数时，为当前位的值
163             for (int i = 9; i >= 0; i--) {
164                 stream.str("");
165                 stream << i;
166                 string s = stream.str();
167                 string sj = multiplyTwoString(nums2, s);
168                 string remain = substractTwoString(dividend, sj);
169 
170                 if(remain[0] != ‘-‘){
171                     result.push_back(i+‘0‘);
172                     dividend = remain;
173                     break;
174                 }
175             }
176         }
177         //去掉商前面的零位
178         int size = result.size();
179         for(int i=0;i<size;i++){
180             if(result[0]==‘0‘){
181                 result.erase(result.begin());
182             }else {
183                 break;
184             }
185         }
186         //四舍五入
187         string s = substractTwoString(multiplyTwoString(dividend,"2"),nums2);
188         if(s[0] == ‘-‘)  addTwoString(result,"1");
189 
190         return result;
191     }
192 };
193 
194 int main() {
196     string nums1 = "123456";
197     string nums2 = "789";
199     Solution s;
201     cout << s.addTwoString(nums1, nums2) << endl;
202     cout << s.multiplyTwoString(nums1, nums2) << endl;
203     cout << s.substractTwoString(nums1, nums2) << endl;
204     cout << s.divideTwoString(nums1, nums2) << endl;
206     return 0;
207 }