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【模板】高精度运算

高精度加法

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 200 + 1;
int a[LEN], b[LEN], c[LEN];
char s1[LEN], s2[LEN];

int main() {
    scanf("%s%s", s1, s2);
    a[0] = strlen(s1), b[0] = strlen(s2);
    c[0] = max(a[0], b[0]) + 1;
    for(int i = 0; i < a[0]; i++) a[i + 1] = s1[a[0] - i - 1] - '0';
    for(int i = 0; i < b[0]; i++) b[i + 1] = s2[b[0] - i - 1] - '0';
    int x = 0;
    for(int i = 1; i <= c[0]; i++) {
        c[i] = a[i] + b[i] + x;
        x = c[i] / 10;
        c[i] %= 10;
    }
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    for(int i = c[0]; i >= 1; i--) putchar(c[i] + '0');
}

View Code

高精度减法

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 200 + 1;
int a[LEN], b[LEN], c[LEN];
char s1[LEN], s2[LEN];

int main() {
    scanf("%s%s", s1, s2);
    a[0] = strlen(s1), b[0] = strlen(s2);
    c[0] = max(a[0], b[0]) + 1;
    for(int i = 0; i < a[0]; i++) a[i + 1] = s1[a[0] - i - 1] - '0';
    for(int i = 0; i < b[0]; i++) b[i + 1] = s2[b[0] - i - 1] - '0';
    for(int i = 1; i <= c[0]; i++) {
        c[i] = a[i] - b[i];
        if(c[i] < 0) {
            c[i] += 10;
            a[i + 1]--;
        }
    }
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    for(int i = c[0]; i >= 1; i--) putchar(c[i] + '0');
}

View Code

高精度乘法

高精度乘单精度

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 200 + 1;

int b, lenb, a[LEN], c[LEN << 1];
char s[LEN];

int Digit_num(int x) {
    int ret = 0;
    while(x) {
        x /= 10;
        ret++;
    }
    return ret;
}
int main() {
    scanf("%s%d", s, &b);
    a[0] = strlen(s), lenb = Digit_num(b);
    c[0] = a[0] + lenb;
    for(int i = 0; i < a[0]; i++) a[i + 1] = s[a[0] - i - 1] - '0';
    int x = 0;
    for(int i = 1; i <= c[0]; i++) {
        c[i] = a[i] * b + x;
        x = c[i] / 10;
        c[i] %= 10;
    }
    while(x) {
        c[c[0]++] = x % 10;
        x /= 10;
    }
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    for(int i = c[0]; i >= 1; i--) putchar(c[i] + '0');
}

View Code

高精度乘高精度

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 200 + 1;
int a[LEN], b[LEN], c[LEN << 1];
char s1[LEN], s2[LEN];

int main() {
    scanf("%s%s", s1, s2);
    a[0] = strlen(s1), b[0] = strlen(s2);
    c[0] = a[0] + b[0];
    for(int i = 0; i < a[0]; i++) a[i + 1] = s1[a[0] - i - 1] - '0';
    for(int i = 0; i < b[0]; i++) b[i + 1] = s2[b[0] - i - 1] - '0';
    
    for(int i = 1; i <= a[0]; i++) {
        int x = 0;
        for(int j = 1; j <= b[0]; j++) {
            c[i + j - 1] += a[i] * b[j] + x;
            x = c[i + j - 1] / 10;
            c[i + j - 1] %= 10;
        }
        c[i + b[0]] = x;
    }
    while(c[c[0]] > 0) c[0]++;
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    for(int i = c[0]; i >= 1; i--) putchar(c[i] + '0');
}

View Code

高精度除法

高精度除以单精度

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 200 + 1;

int a[LEN], c[LEN], b;
char s[LEN];

int main() {
    scanf("%s%d", s, &b);
    a[0] = strlen(s);
    for(int i = 0; i < a[0]; i++) a[i + 1] = s[i] - '0';
    int x = 0;
    for(int i = 1; i <= a[0]; i++) {
        x = x * 10 + a[i];
        c[++c[0]] = x / b;
        x %= b;
    }
    int start = 1;
    while(c[start] == 0 && start < c[0]) start++;
    for(int i = start; i <= c[0]; i++) putchar(c[i] + '0');
    printf("
mod: %d", x);
}

View Code

高精度除以高精度

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int LEN = 100 + 1;
int a[LEN], b[LEN], c[LEN], tmp[LEN];
char s1[LEN], s2[LEN];

void Sub(int a[], int b[]) {
    for(int i = 1; i <= a[0]; i++) {
        a[i] = a[i] - b[i];
        if(a[i] < 0) {
            a[i] += 10;
            a[i + 1]--; 
        }
    }
    while(a[a[0]] == 0 && a[0] > 1) a[0]--;
}
int Comp(int a[], int b[]) {
    int up = max(a[0], b[0]);
    for(int i = a[0] + 1; i <= up; i++) a[i] = 0;
    for(int i = b[0] + 1; i <= up; i++) b[i] = 0;
    for(int i = 0; i < up; i++) {
        if(a[up - i] > b[up - i]) return 1;
        if(a[up - i] < b[up - i]) return -1;
    }
    return 0;
}
void Joint(int p[], int q[], int det) {
    for(int i = 1; i <= p[0]; i++) q[i + det - 1] = p[i];
    q[0] = p[0] + det - 1;
}
int main() {
    scanf("%s%s", s1, s2);
    a[0] = strlen(s1), b[0] = strlen(s2);
    c[0] = a[0] - b[0] + 1; 
    for(int i = 0; i < a[0]; i++) a[i + 1] = s1[a[0] - i - 1] - '0';
    for(int i = 0; i < b[0]; i++) b[i + 1] = s2[b[0] - i - 1] - '0';
    
    for(int i = c[0]; i >= 1; i--) {
        memset(tmp, 0, sizeof(tmp));
        Joint(b, tmp, i);
        while(Comp(a, tmp) >= 0) {
            Sub(a, tmp);
            c[i]++;
        }
    }
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    if(c[0] < 1) c[c[0] = 1] = 0;
    for(int i = c[0]; i >= 1; i--) printf("%d", c[i]);
}

View Code

高精度四则运算BIGNUM型

写了两节课QwQ

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 using namespace std;
  5 
  6 const int LEN = 10000 + 1;
  7 
  8 //支持任意两个非负整数的加、减、乘、除、取模运算
  9 struct BIGNUM {
 10     int s[LEN << 1];
 11     bool flag;
 12     BIGNUM() {
 13         memset(s, 0, sizeof(s));
 14         flag = s[0] = 1;
 15     }
 16     void init() {
 17         memset(s, 0, sizeof(s));
 18         s[0] = 1;
 19     }
 20     
 21     BIGNUM operator = (const char *num) {
 22         s[0] = strlen(num);
 23         for(int i = 0; i < s[0]; i++) s[i + 1] = num[s[0] - i - 1] - '0';
 24         return *this;
 25     }
 26     BIGNUM operator = (const int num) {
 27         char a[LEN];
 28         sprintf(a, "%d", num);
 29         *this = a;
 30         return *this;
 31     }
 32     BIGNUM(int num) { *this = num; }
 33     BIGNUM(const char *num) { *this = num; }
 34     BIGNUM operator = (const BIGNUM &num) {
 35         int l = max(s[0], num.s[0]);
 36         for(int i = 0; i <= l; i++) s[i] = num.s[i];
 37     }
 38     
 39     
 40     BIGNUM operator + (const BIGNUM &a) {
 41         BIGNUM c;
 42         int x = 0;
 43         c.s[0] = max(a.s[0], s[0]) + 1;
 44         for(int i = 1; i <= c.s[0]; i++) {
 45             c.s[i] = a.s[i] + s[i] + x;
 46             x = c.s[i] / 10;
 47             c.s[i] %= 10;
 48         }
 49         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
 50         return c;
 51     }
 52     BIGNUM operator += (const BIGNUM &a) {
 53         *this = *this + a;
 54         return *this;
 55     }
 56     
 57     bool operator == (const BIGNUM &a) {
 58         int up = max(s[0], a.s[0]);
 59         for(int i = 0; i < up; i++)
 60             if(s[up - i] != a.s[up - i]) return false;
 61         return true;
 62     }
 63     bool operator > (const BIGNUM &a) {
 64         if(s[0] != a.s[0]) return s[0] > a.s[0];
 65         int up = max(s[0], a.s[0]);
 66         for(int i = 0; i < up; i++)
 67             if(s[up - i] != a.s[up - i]) return s[up - i] > a.s[up - i];
 68         return false;
 69     }
 70     bool operator < (const BIGNUM &a) {
 71         if(s[0] != a.s[0]) return s[0] < a.s[0];
 72         int up = max(s[0], a.s[0]);
 73         for(int i = 0; i < up; i++)
 74             if(s[up - i] != a.s[up - i]) return s[up - i] < a.s[up - i];
 75         return false;
 76     }
 77     bool operator >= (const BIGNUM &a) {
 78         if(*this > a || *this == a) return true;
 79         return false;
 80     }
 81     bool operator <= (const BIGNUM &a) {
 82         if(*this < a || *this == a) return true;
 83         return false;
 84     }
 85     
 86     BIGNUM operator - (const BIGNUM &a) {
 87         BIGNUM c;
 88         c.s[0] = max(a.s[0], s[0]) + 1;
 89         if(*this < a) c.flag = false;
 90         for(int i = 1; i <= c.s[0]; i++) {
 91             if(c.flag) c.s[i] += s[i] - a.s[i];
 92             else c.s[i] += a.s[i] - s[i];
 93             if(c.s[i] < 0) {
 94                 c.s[i] += 10;
 95                 c.s[i + 1]--;
 96             }
 97         }
 98         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
 99         return c;
100     }
101     BIGNUM operator -= (const BIGNUM &a) {
102         *this = *this - a;
103         return *this;
104     }
105     BIGNUM operator * (const BIGNUM &a) {
106         BIGNUM c;
107         c.s[0] = s[0] + a.s[0];
108         for(int i = 1; i <= s[0]; i++) {
109             int x = 0;
110             for(int j = 1; j <= a.s[0]; j++) {
111                 c.s[i + j - 1] += s[i] * a.s[j] + x;
112                 x = c.s[i + j - 1] / 10;
113                 c.s[i + j - 1] %= 10;
114             }
115             c.s[i + a.s[0]] = x;
116         }
117         while(c.s[c.s[0]] > 0) c.s[0]++;
118         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
119         return c;
120     }
121     BIGNUM operator *= (const BIGNUM &a) {
122         *this = *this * a;
123         return *this;
124     }
125     
126     
127     
128     BIGNUM operator / (const BIGNUM &a) {
129         BIGNUM c, tmp;
130         c.s[0] = s[0] - a.s[0] + 1;
131         for(int i = c.s[0]; i >= 1; i--) {
132             tmp.init();
133             for(int j = 1; j <= a.s[0]; j++) tmp.s[i + j - 1] = a.s[j];
134             tmp.s[0] = a.s[0] + i - 1;
135             while(*this >= tmp) {
136                 *this = *this - tmp;
137                 c.s[i]++;
138             }
139         }
140         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
141         if(c.s[0] < 1) c.s[c.s[0] = 1] = 0;
142         return c;
143     }
144     BIGNUM operator /= (const BIGNUM &a) {
145         *this = *this / a;
146         return *this;
147     }
148     BIGNUM operator % (const BIGNUM &a) {
149         BIGNUM d = *this, c = *this / a;
150         c *= a;
151         return d - c;
152     }
153     BIGNUM operator %= (const BIGNUM &a) {
154         *this = *this % a;
155         return *this;
156     }
157 };
158 ostream& operator << (ostream &out, const BIGNUM &a) {
159     if(!a.flag) putchar('-');
160     for(int i = a.s[0]; i >= 1; i--)
161         cout << a.s[i];
162     return out;
163 }
164 istream& operator >> (istream &in, BIGNUM &a) {
165     char str[LEN];
166     in >> str;
167     a = str;
168     return in;
169 }
170 
171 BIGNUM a, b;
172 int main() {
173     cin >> a >> b;
174     cout << a + b << endl;
175     cout << a - b << endl;
176     cout << a * b << endl;
177     cout << a / b << endl;
178     cout << a % b << endl;
179 }

BIGNUM大整数型

压位高精度：

加法

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int LEN = 200 + 1;
const int BIT = 8;
const int MOD = 100000000;//1eBIT 

int a[LEN/BIT], b[LEN/BIT], c[LEN/BIT];
char s1[LEN], s2[LEN];

int main() {
    scanf("%s%s", s1, s2);
    int la = strlen(s1), lb = strlen(s2);
    for(int i = la - 1; i >= 0; i -= BIT) {
        ++a[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            a[a[0]] += (s1[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    for(int i = lb - 1; i >= 0; i -= BIT) {
        ++b[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            b[b[0]] += (s2[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    int x = 0;
    c[0] = max(a[0], b[0]);
    for(int i = 1; i <= c[0]; i++) {
        c[i] = a[i] + b[i] + x;
        x = c[i] / MOD;
        c[i] %= MOD;
    }
    c[++c[0]] = x;
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    printf("%d", c[c[0]]);
    for(int i = c[0] - 1; i >= 1; i--) printf("%08d", c[i]);
}

View Code

减法

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 200 + 1;
const int BIT = 8;
const int MOD = 100000000;//1eBIT 

int a[LEN/BIT], b[LEN/BIT], c[LEN/BIT];
char s1[LEN], s2[LEN];

int main() {
    scanf("%s%s", s1, s2);
    int la = strlen(s1), lb = strlen(s2);
    for(int i = la - 1; i >= 0; i -= BIT) {
        ++a[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            a[a[0]] += (s1[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    for(int i = lb - 1; i >= 0; i -= BIT) {
        ++b[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            b[b[0]] += (s2[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    c[0] = max(a[0], b[0]);
    for(int i = 1; i <= c[0]; i++) {
        c[i] += a[i] - b[i];
        if(c[i] < 0) {
            c[i] += MOD;
            c[i + 1]--;
        }
    }
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    printf("%d", c[c[0]]);
    for(int i = c[0] - 1; i >= 1; i--) printf("%08d", c[i]);
}

View Code

乘法

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int LEN = 2000 + 1;
const int BIT = 8;
const int MOD = 100000000;//1eBIT 

long long a[LEN/BIT], b[LEN/BIT], c[(LEN<<1)/BIT];
char s1[LEN], s2[LEN];

int main() {
    scanf("%s%s", s1, s2);
    int la = strlen(s1), lb = strlen(s2);
    for(int i = la - 1; i >= 0; i -= BIT) {
        ++a[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            a[a[0]] += (s1[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    for(int i = lb - 1; i >= 0; i -= BIT) {
        ++b[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            b[b[0]] += (s2[j]^48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    
    c[0] = a[0] + b[0];
    for(int i = 1; i <= a[0]; i++) {
        long long x = 0;
        for(int j = 1; j <= b[0]; j++) {
            c[i + j - 1] += a[i] * b[j] + x;
            x = c[i + j - 1] / MOD;
            c[i + j - 1] %= MOD;
        }
        c[i + b[0]] = x;
    }
    while(c[c[0] + 1] > 0) c[0]++;
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    printf("%d", c[c[0]]);
    for(int i = c[0] - 1; i >= 1; i--) printf("%08d", c[i]);
}

View Code

除法（模拟减法，倍增优化）

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int LEN = 5000 + 10;
const int BIT = 8;
const int MOD = 100000000;//1eBIT 


int a[LEN/BIT], b[LEN/BIT], c[LEN/BIT], tmp[LEN/BIT], lt[LEN/BIT];
char s1[LEN], s2[LEN];

void Plus(int a[], int b[]) {
    int x = 0;
    a[0] = max(a[0], b[0]);
    for(int i = 1; i <= a[0]; i++) {
        a[i] = a[i] + b[i] + x;
        x = a[i] / MOD;
        a[i] %= MOD;
    }
    a[++a[0]] = x;
    while(a[a[0]] == 0 && a[0] > 1) a[0]--;
}
void Sub(int a[], int b[]) {
    for(int i = 1; i <= a[0]; i++) {
        a[i] = a[i] - b[i];
        if(a[i] < 0) {
            a[i] += MOD;
            a[i + 1]--; 
        }
    }
    while(a[a[0]] == 0 && a[0] > 1) a[0]--;
}
int Comp(int a[], int b[]) {
    int up = max(a[0], b[0]);
    for(int i = a[0] + 1; i <= up; i++) a[i] = 0;
    for(int i = b[0] + 1; i <= up; i++) b[i] = 0;
    for(int i = 0; i < up; i++) {
        if(a[up - i] > b[up - i]) return 1;
        if(a[up - i] < b[up - i]) return -1;
    }
    return 0;
}
void Joint(int p[], int q[]) {
    for(int i = p[0]; i > q[0]; i--) p[i] = 0;
    for(int i = 0; i <= q[0]; i++) p[i] = q[i];
}
void Left_move(int num[]) {
    ++num[0];
    for(int i = 1; i <= num[0]; i++) {
        num[i] <<= 1;
        if(num[i - 1] >= MOD)
            num[i - 1] -= MOD, ++num[i];
    }
    while(num[num[0]] == 0 && num[0] > 1) num[0]--;
}
void Right_move(int num[]) {
    for(int i = num[0]; i >= 1; i--) {
        if((num[i] & 1) && i > 1) num[i - 1] += MOD;
        num[i] >>= 1;
    }
    while(num[num[0]] == 0  && num[0] > 1) num[0]--;
}
int main() {
    scanf("%s%s", s1, s2);
    int la = strlen(s1), lb = strlen(s2);
    for(int i = la - 1; i >= 0; i -= BIT) {
        ++a[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            a[a[0]] += (s1[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    for(int i = lb - 1; i >= 0; i -= BIT) {
        ++b[0];
        long long w = 1;
        for(int j = i; j > i - BIT && j >= 0; j--) {
            b[b[0]] += (s2[j] ^ 48) * w;
            w = (w << 1) + (w << 3);
        }
    }
    
    tmp[1] = 1;
    while(Comp(a, b) >= 0) {
        Left_move(b), Left_move(tmp);
    }
    while(tmp[0] > 1 || tmp[1]) {
        if(Comp(a, b) >= 0) {
            Sub(a, b);
            Plus(lt, tmp);
        }
        Right_move(b), Right_move(tmp);
    }
    Joint(c, lt); Joint(lt, a);
    while(c[c[0]] == 0 && c[0] > 1) c[0]--;
    if(c[0] < 1) c[c[0] = 1] = 0;
    printf("%d", c[c[0]]);
    for(int i = c[0] - 1; i >= 1; i--) printf("%08d", c[i]);
}

View Code

大整数型压位高精度：

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 using namespace std;
  5 
  6 const int LEN = 10000 + 1;
  7 
  8 //支持加、减、乘、除、取模等非负整数之间的运算
  9 //可调整压位位数，除法使用倍增优化
 10 struct BIGNUM {
 11     static const int BIT = 8;
 12     static const int MOD = 100000000;//1eBIT 
 13     
 14     long long s[LEN];
 15     bool flag;
 16     BIGNUM() {
 17         memset(s, 0, sizeof(s));
 18         flag = s[0] = 1;
 19     }
 20     void init() {
 21         memset(s, 0, sizeof(s));
 22         s[0] = 1;
 23     }
 24     
 25     BIGNUM operator = (const char *num) {
 26         int l = strlen(num);
 27         s[0] = 0;
 28         for(int i = l - 1; i >= 0; i -= BIT) {
 29             ++s[0];
 30             long long w = 1;
 31             for(int j = i; j > i - BIT && j >= 0; j--) {
 32                 s[s[0]] += (num[j] ^ 48) * w;
 33                 w = (w << 1) + (w << 3); 
 34             }
 35         }
 36         return *this;
 37     }
 38     BIGNUM operator = (const int num) {
 39         char a[LEN];
 40         sprintf(a, "%d", num);
 41         *this = a;
 42         return *this;
 43     }
 44     BIGNUM(int num) { *this = num; }
 45     BIGNUM(const char *num) { *this = num; }
 46     
 47     BIGNUM operator + (const BIGNUM &a) {
 48         BIGNUM c;
 49         int x = 0;
 50         c.s[0] = max(a.s[0], s[0]) + 1;
 51         for(int i = 1; i <= c.s[0]; i++) {
 52             c.s[i] = a.s[i] + s[i] + x;
 53             x = c.s[i] / MOD;
 54             c.s[i] %= MOD;
 55         }
 56         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
 57         return c;
 58     }
 59     BIGNUM operator += (const BIGNUM &a) {
 60         *this = *this + a;
 61         return *this;
 62     }
 63     
 64     bool operator == (const BIGNUM &a) {
 65         int up = max(s[0], a.s[0]);
 66         for(int i = 0; i < up; i++)
 67             if(s[up - i] != a.s[up - i]) return false;
 68         return true;
 69     }
 70     bool operator > (const BIGNUM &a) {
 71         if(s[0] != a.s[0]) return s[0] > a.s[0];
 72         int up = max(s[0], a.s[0]);
 73         for(int i = 0; i < up; i++)
 74             if(s[up - i] != a.s[up - i]) return s[up - i] > a.s[up - i];
 75         return false;
 76     }
 77     bool operator < (const BIGNUM &a) {
 78         if(s[0] != a.s[0]) return s[0] < a.s[0];
 79         int up = max(s[0], a.s[0]);
 80         for(int i = 0; i < up; i++)
 81             if(s[up - i] != a.s[up - i]) return s[up - i] < a.s[up - i];
 82         return false;
 83     }
 84     bool operator >= (const BIGNUM &a) {
 85         if(*this > a || *this == a) return true;
 86         return false;
 87     }
 88     bool operator <= (const BIGNUM &a) {
 89         if(*this < a || *this == a) return true;
 90         return false;
 91     }
 92     
 93     BIGNUM operator - (const BIGNUM &a) {
 94         BIGNUM c;
 95         c.s[0] = max(a.s[0], s[0]) + 1;
 96         if(*this < a) c.flag = false;
 97         for(int i = 1; i <= c.s[0]; i++) {
 98             if(c.flag) c.s[i] += s[i] - a.s[i];
 99             else c.s[i] += a.s[i] - s[i];
100             if(c.s[i] < 0) {
101                 c.s[i] += MOD;
102                 c.s[i + 1]--;
103             }
104         }
105         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
106         return c;
107     }
108     BIGNUM operator -= (const BIGNUM &a) {
109         *this = *this - a;
110         return *this;
111     }
112     BIGNUM operator * (const BIGNUM &a) {
113         BIGNUM c;
114         c.s[0] = s[0] + a.s[0];
115         for(int i = 1; i <= s[0]; i++) {
116             int x = 0;
117             for(int j = 1; j <= a.s[0]; j++) {
118                 c.s[i + j - 1] += s[i] * a.s[j] + x;
119                 x = c.s[i + j - 1] / MOD;
120                 c.s[i + j - 1] %= MOD;
121             }
122             c.s[i + a.s[0]] = x;
123         }
124         while(c.s[c.s[0]] > 0) c.s[0]++;
125         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
126         return c;
127     }
128     BIGNUM operator *= (const BIGNUM &a) {
129         *this = *this * a;
130         return *this;
131     }
132     
133     BIGNUM operator << (const int &num) {
134         s[0]++;
135         for(int i = 1; i <= s[0]; i++) {
136             s[i] <<= num;
137             if(s[i - 1] >= MOD)
138                 s[i - 1] -= MOD, ++s[i];
139         }
140         while(s[s[0]] == 0 && s[0] > 1) s[0]--;
141         return *this;
142     }
143     BIGNUM operator >> (const int &num) {
144         for(int i = s[0]; i >= 1; i--) {
145             if((s[i] & 1) && i > 1) s[i - 1] += MOD;
146             s[i] >>= num;
147         }
148         while(s[s[0]] == 0 && s[0] > 1) s[0]--;
149         return *this;
150     }
151     
152     BIGNUM operator / (const BIGNUM &k) {
153         BIGNUM c = *this, tmp, lt, a;
154         a = k;
155         tmp.s[1] = 1;
156         while(c >= a) {
157             a = a << 1;
158             tmp = tmp << 1;
159         }
160         while(tmp.s[0] > 1 || tmp.s[1]) {
161             if(c >= a) {
162                 c -= a;
163                 lt += tmp;
164             }
165             a = a >> 1;
166             tmp = tmp >> 1;
167         }
168         c = lt;
169         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
170         if(c.s[0] < 1) c.s[c.s[0] = 1] = 0;
171         return c;
172     }
173     BIGNUM operator /= (const BIGNUM &a) {
174         *this = *this / a;
175         return *this;
176     }
177     BIGNUM operator % (const BIGNUM &a) {
178         BIGNUM d = *this, c = *this / a;
179         c *= a;
180         return d - c;
181     }
182     BIGNUM operator %= (const BIGNUM &a) {
183         *this = *this % a;
184         return *this;
185     }
186 };
187 ostream& operator << (ostream &out, const BIGNUM &a) {
188     if(!a.flag) putchar('-');
189     printf("%d", a.s[a.s[0]]);
190     for(int i = a.s[0] - 1; i >= 1; i--)
191         printf("%08d", a.s[i]);
192     return out;
193 }
194 istream& operator >> (istream &in, BIGNUM &a) {
195     char str[LEN];
196     in >> str;
197     a = str;
198     return in;
199 }
200 
201 BIGNUM a, b;
202 int main() {
203     cin >> a >> b;
204     cout << a + b << endl;
205     cout << a - b << endl;
206     cout << a * b << endl;
207     cout << a / b << endl;
208     cout << a % b << endl;
209 }

BIGNUM压位高精度

也可以把压位压到9位..

时空复杂度都更优

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 using namespace std;
  5 
  6 const int LEN = 10000 + 1;
  7 
  8 struct BIGNUM {
  9     static const int BIT = 9;
 10     static const int MOD = 1000000000;//1eBIT 
 11     
 12     long long s[LEN];
 13     bool flag;
 14     BIGNUM() {
 15         memset(s, 0, sizeof(s));
 16         flag = s[0] = 1;
 17     }
 18     void init() {
 19         memset(s, 0, sizeof(s));
 20         s[0] = 1;
 21     }
 22     
 23     BIGNUM operator = (const char *num) {
 24         int l = strlen(num);
 25         s[0] = 0;
 26         for(int i = l - 1; i >= 0; i -= BIT) {
 27             ++s[0];
 28             long long w = 1;
 29             for(int j = i; j > i - BIT && j >= 0; j--) {
 30                 s[s[0]] += (num[j] ^ 48) * w;
 31                 w = (w << 1) + (w << 3); 
 32             }
 33         }
 34         return *this;
 35     }
 36     BIGNUM operator = (const int num) {
 37         char a[LEN];
 38         sprintf(a, "%d", num);
 39         *this = a;
 40         return *this;
 41     }
 42     BIGNUM(int num) { *this = num; }
 43     BIGNUM(const char *num) { *this = num; }
 44     
 45     BIGNUM operator + (const BIGNUM &a) {
 46         BIGNUM c;
 47         int x = 0;
 48         c.s[0] = max(a.s[0], s[0]) + 1;
 49         for(int i = 1; i <= c.s[0]; i++) {
 50             c.s[i] = a.s[i] + s[i] + x;
 51             x = c.s[i] / MOD;
 52             c.s[i] %= MOD;
 53         }
 54         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
 55         return c;
 56     }
 57     BIGNUM operator += (const BIGNUM &a) {
 58         *this = *this + a;
 59         return *this;
 60     }
 61     
 62     bool operator == (const BIGNUM &a) {
 63         int up = max(s[0], a.s[0]);
 64         for(int i = 0; i < up; i++)
 65             if(s[up - i] != a.s[up - i]) return false;
 66         return true;
 67     }
 68     bool operator > (const BIGNUM &a) {
 69         if(s[0] != a.s[0]) return s[0] > a.s[0];
 70         int up = max(s[0], a.s[0]);
 71         for(int i = 0; i < up; i++)
 72             if(s[up - i] != a.s[up - i]) return s[up - i] > a.s[up - i];
 73         return false;
 74     }
 75     bool operator < (const BIGNUM &a) {
 76         if(s[0] != a.s[0]) return s[0] < a.s[0];
 77         int up = max(s[0], a.s[0]);
 78         for(int i = 0; i < up; i++)
 79             if(s[up - i] != a.s[up - i]) return s[up - i] < a.s[up - i];
 80         return false;
 81     }
 82     bool operator >= (const BIGNUM &a) {
 83         if(*this > a || *this == a) return true;
 84         return false;
 85     }
 86     bool operator <= (const BIGNUM &a) {
 87         if(*this < a || *this == a) return true;
 88         return false;
 89     }
 90     
 91     BIGNUM operator - (const BIGNUM &a) {
 92         BIGNUM c;
 93         c.s[0] = max(a.s[0], s[0]) + 1;
 94         if(*this < a) c.flag = false;
 95         for(int i = 1; i <= c.s[0]; i++) {
 96             if(c.flag) c.s[i] += s[i] - a.s[i];
 97             else c.s[i] += a.s[i] - s[i];
 98             if(c.s[i] < 0) {
 99                 c.s[i] += MOD;
100                 c.s[i + 1]--;
101             }
102         }
103         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
104         return c;
105     }
106     BIGNUM operator -= (const BIGNUM &a) {
107         *this = *this - a;
108         return *this;
109     }
110     BIGNUM operator * (const BIGNUM &a) {
111         BIGNUM c;
112         c.s[0] = s[0] + a.s[0];
113         for(int i = 1; i <= s[0]; i++) {
114             int x = 0;
115             for(int j = 1; j <= a.s[0]; j++) {
116                 c.s[i + j - 1] += s[i] * a.s[j] + x;
117                 x = c.s[i + j - 1] / MOD;
118                 c.s[i + j - 1] %= MOD;
119             }
120             c.s[i + a.s[0]] = x;
121         }
122         while(c.s[c.s[0]] > 0) c.s[0]++;
123         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
124         return c;
125     }
126     BIGNUM operator *= (const BIGNUM &a) {
127         *this = *this * a;
128         return *this;
129     }
130     
131     BIGNUM operator << (const int &num) {
132         s[0]++;
133         for(int i = 1; i <= s[0]; i++) {
134             s[i] <<= num;
135             if(s[i - 1] >= MOD)
136                 s[i - 1] -= MOD, ++s[i];
137         }
138         while(s[s[0]] == 0 && s[0] > 1) s[0]--;
139         return *this;
140     }
141     BIGNUM operator >> (const int &num) {
142         for(int i = s[0]; i >= 1; i--) {
143             if((s[i] & 1) && i > 1) s[i - 1] += MOD;
144             s[i] >>= num;
145         }
146         while(s[s[0]] == 0 && s[0] > 1) s[0]--;
147         return *this;
148     }
149     
150     BIGNUM operator / (const BIGNUM &k) {
151         BIGNUM c = *this, tmp, lt, a;
152         a = k;
153         tmp.s[1] = 1;
154         while(c >= a) {
155             a = a << 1;
156             tmp = tmp << 1;
157         }
158         while(tmp.s[0] > 1 || tmp.s[1]) {
159             if(c >= a) {
160                 c -= a;
161                 lt += tmp;
162             }
163             a = a >> 1;
164             tmp = tmp >> 1;
165         }
166         c = lt;
167         while(c.s[c.s[0]] == 0 && c.s[0] > 1) c.s[0]--;
168         if(c.s[0] < 1) c.s[c.s[0] = 1] = 0;
169         return c;
170     }
171     BIGNUM operator /= (const BIGNUM &a) {
172         *this = *this / a;
173         return *this;
174     }
175     BIGNUM operator % (const BIGNUM &a) {
176         BIGNUM d = *this, c = *this / a;
177         c *= a;
178         return d - c;
179     }
180     BIGNUM operator %= (const BIGNUM &a) {
181         *this = *this % a;
182         return *this;
183     }
184 };
185 ostream& operator << (ostream &out, const BIGNUM &a) {
186     if(!a.flag) putchar('-');
187     printf("%d", a.s[a.s[0]]);
188     for(int i = a.s[0] - 1; i >= 1; i--)
189         printf("%09d", a.s[i]);
190     return out;
191 }
192 istream& operator >> (istream &in, BIGNUM &a) {
193     char str[LEN];
194     in >> str;
195     a = str;
196     return in;
197 }
198 
199 BIGNUM a, b;
200 int main() {
201     cin >> a >> b;
202     cout << a + b << endl;
203     cout << a - b << endl;
204     cout << a * b << endl;
205     cout << a / b << endl;
206     cout << a % b << endl;
207 }

压9位BIGNUM

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原文地址：https://www.cnblogs.com/devilk-sjj/p/8992281.html