大整数加法减法与乘法

模拟运算

用数组逆向保存大数每一位加法直接从尾向前相加（尾部已对齐）注意进位

减法类似确保大数减小数不够减了向前减一需要注意符号的有无问题

  1 #include <iostream>
  2 #include <cstring>
  3 #include <string>
  4 using namespace std;
  5 
  6 int a[11000], b[11000];
  7 string s1, s2;
  8 
  9 void Add()
 10 {
 11     int len1 = s1.length();
 12     int len2 = s2.length();
 13     int Max = max(len1, len2);
 14     int k;
 15     for (int i = len1-1, k = 0; i >= 0; i--)
 16         a[k++] = s1[i] - '0';
 17     for (int i = len2-1, k = 0; i >= 0; i--)
 18         b[k++] = s2[i] - '0';
 19 
 20     int up = 0;
 21     for (int i = 0; i < Max+1; i++) {
 22         a[i] = a[i] + b[i] + up;
 23         up = a[i] / 10;
 24         a[i] %= 10;
 25     }
 26     int first;
 27     for (first = Max+1; first >= 0; first--)
 28         if (a[first])
 29             break;
 30 
 31     if (first == -1)
 32         cout << "0";
 33     for (int i = first; i >= 0; i--)
 34         cout << a[i];
 35 
 36 }
 37 
 38 void Sub(string Max, string Min)  //a - b
 39 {
 40     int len1 = Max.length();
 41     int len2 = Min.length();
 42     int MaxLen = max(len1, len2);
 43 
 44     int k;
 45     for (int i = len1-1, k = 0; i >= 0; i--)
 46         a[k++] = Max[i] - '0';
 47     for (int i = len2 - 1, k = 0; i >= 0; i--)
 48         b[k++] = Min[i] - '0';
 49 
 50     int up = 0;
 51     for (int i = 0; i < MaxLen+1; i++) {
 52         a[i] = a[i] - b[i] - up;
 53         if (a[i] < 0) {
 54             up = 1;
 55             a[i] += 10;
 56         }
 57         else
 58             up = 0;
 59     }
 60 
 61     int first;
 62     for (first = MaxLen+1; first >= 0; first--)
 63         if (a[first])
 64             break;
 65 
 66     if (first == -1)
 67         cout << "0";
 68     else {
 69         for (int i = first; i >= 0; i--)
 70             cout << a[i];
 71     }
 72 }
 73 
 74 int main()
 75 {
 76     cin >> s1 >> s2;
 77 
 78     memset(a, 0, sizeof(a));
 79     memset(b, 0, sizeof(b));
 80 
 81     if (s1[0] == '-' && s2[0] == '-')
 82     {
 83         cout << '-';
 84         s1.erase(0, 1);
 85         s2.erase(0, 1);
 86         Add();
 87     }
 88     else if (s1[0] == '-' || s2[0] == '-')
 89     {
 90         string Max, Min;
 91         if (s1[0] == '-') {
 92             if (s1.length()-1 > s2.length())
 93                 cout << "-";
 94             if (s1.length()-1 == s2.length())
 95             {
 96                 if (s1[1] > s2[0])
 97                     cout << "-";
 98             }
 99             s1.erase(0, 1);
100         }
101 
102        if (s2[0] == '-') {
103 
104             if (s2.length()-1 > s1.length())
105                 cout << "-";
106             if (s1.length() == s2.length()-1)
107             {
108                 if (s2[1] > s1[0])
109                     cout << "-";
110             }
111             s2.erase(0, 1);
112         }
113 
114         if(s1.length() > s2.length())
115         {
116             Max = s1;
117             Min = s2;
118         }
119         else if (s1.length() == s2.length() && s1[0] > s2[0])
120         {
121             Max = s1;
122             Min = s2;
123         }
124         else {
125             Min = s1;
126             Max = s2;
127         }
128       Sub(Max, Min);
129     }
130     else
131         Add();
132 
133     return 0;
134 }

乘法

先乘再进位

 1 #include <iostream>
 2 #include <string>
 3 #include <cstring>
 4 using namespace std;
 5 int a[1100], b[1100], c[2300];
 6 
 7 void big_number_multipy(string s1, string s2)
 8 {
 9     int lenth1 = s1.length();
10     int lenth2 = s2.length();
11     int MaxLen = lenth1 + lenth2;
12 
13     int i, j, k;
14     for (i = lenth1-1, k = 0; i >= 0; i--)
15         a[k++] = s1[i] - '0';
16     for (i = lenth2-1, k = 0; i >= 0; i--)
17         b[k++] = s2[i] - '0';
18 
19     for (i = 0; i < lenth1; i++)
20         for (j = 0; j <lenth2; j++)
21             c[i+j] += a[i] * b[j];
22 
23     for (i = 0; i < MaxLen; i++) {
24         c[i+1] += c[i] / 10;
25         c[i] %= 10;
26     }
27 
28     int first;
29     for (first = MaxLen; first >= 0; first--)
30         if (c[first])
31             break;
32     if (first == -1)
33         cout << "0";
34     for (int i = first; i >= 0; i--)
35         cout << c[i];
36 }
37 
38 int main()
39 {
40     string s1, s2;
41 
42     cin >> s1 >> s2;
43     memset(a, 0, sizeof(a));
44     memset(b, 0, sizeof(b));
45     memset(c, 0, sizeof(c));
46     big_number_multipy(s1, s2);
47 
48 
49     return 0;
50 }