高精度
constexpr int MAXN = 9999;
// MAXN 是一位中最大的数字
constexpr int MAXSIZE = 10024;
// MAXSIZE 是位数
constexpr int DLEN = 4;
// DLEN 记录压几位
struct Big {
int a[MAXSIZE], len;
bool flag; // 标记符号'-'
Big() {
len = 1;
memset(a, 0, sizeof a);
flag = false;
}
Big(const int);
Big(const char*);
Big(const Big&);
Big& operator=(const Big&);
Big operator+(const Big&) const;
Big operator-(const Big&) const;
Big operator*(const Big&) const;
Big operator/(const int&) const;
// TODO: Big / Big;
Big operator^(const int&) const;
// TODO: Big ^ Big;
// TODO: Big 位运算;
int operator%(const int&) const;
// TODO: Big ^ Big;
bool operator<(const Big&) const;
bool operator<(const int& t) const;
void print() const;
};
Big::Big(const int b) {
int c, d = b;
len = 0;
// memset(a,0,sizeof a);
CLR(a);
while (d > MAXN) {
c = d - (d / (MAXN + 1) * (MAXN + 1));
d = d / (MAXN + 1);
a[len++] = c;
}
a[len++] = d;
}
Big::Big(const char* s) {
int t, k, index, l;
CLR(a);
l = strlen(s);
len = l / DLEN;
if (l % DLEN) ++len;
index = 0;
for (int i = l - 1; i >= 0; i -= DLEN) {
t = 0;
k = i - DLEN + 1;
if (k < 0) k = 0;
g(j, k, i) t = t * 10 + s[j] - '0';
a[index++] = t;
}
}
Big::Big(const Big& T) : len(T.len) {
CLR(a);
f(i, 0, len) a[i] = T.a[i];
// TODO:重载此处？
}
Big& Big::operator=(const Big& T) {
CLR(a);
len = T.len;
f(i, 0, len) a[i] = T.a[i];
return *this;
}
Big Big::operator+(const Big& T) const {
Big t(*this);
int big = len;
if (T.len > len) big = T.len;
f(i, 0, big) {
t.a[i] += T.a[i];
if (t.a[i] > MAXN) {
++t.a[i + 1];
t.a[i] -= MAXN + 1;
}
}
if (t.a[big])
t.len = big + 1;
else
t.len = big;
return t;
}
Big Big::operator-(const Big& T) const {
int big;
bool ctf;
Big t1, t2;
if (*this < T) {
t1 = T;
t2 = *this;
ctf = true;
} else {
t1 = *this;
t2 = T;
ctf = false;
}
big = t1.len;
int j = 0;
f(i, 0, big) {
if (t1.a[i] < t2.a[i]) {
j = i + 1;
while (t1.a[j] == 0) ++j;
--t1.a[j--];
// WTF?
while (j > i) t1.a[j--] += MAXN;
t1.a[i] += MAXN + 1 - t2.a[i];
} else
t1.a[i] -= t2.a[i];
}
t1.len = big;
while (t1.len > 1 && t1.a[t1.len - 1] == 0) {
--t1.len;
--big;
}
if (ctf) t1.a[big - 1] = -t1.a[big - 1];
return t1;
}
Big Big::operator*(const Big& T) const {
Big res;
int up;
int te, tee;
f(i, 0, len) {
up = 0;
f(j, 0, T.len) {
te = a[i] * T.a[j] + res.a[i + j] + up;
if (te > MAXN) {
tee = te - te / (MAXN + 1) * (MAXN + 1);
up = te / (MAXN + 1);
res.a[i + j] = tee;
} else {
up = 0;
res.a[i + j] = te;
}
}
if (up) res.a[i + T.len] = up;
}
res.len = len + T.len;
while (res.len > 1 && res.a[res.len - 1] == 0) --res.len;
return res;
}
Big Big::operator/(const int& b) const {
Big res;
int down = 0;
gd(i, len - 1, 0) {
res.a[i] = (a[i] + down * (MAXN + 1)) / b;
down = a[i] + down * (MAXN + 1) - res.a[i] * b;
}
res.len = len;
while (res.len > 1 && res.a[res.len - 1] == 0) --res.len;
return res;
}
int Big::operator%(const int& b) const {
int d = 0;
gd(i, len - 1, 0) d = (d * (MAXN + 1) % b + a[i]) % b;
return d;
}
Big Big::operator^(const int& n) const {
Big t(n), res(1);
int y = n;
while (y) {
if (y & 1) res = res * t;
t = t * t;
y >>= 1;
}
return res;
}
bool Big::operator<(const Big& T) const {
int ln;
if (len < T.len) return true;
if (len == T.len) {
ln = len - 1;
while (ln >= 0 && a[ln] == T.a[ln]) --ln;
if (ln >= 0 && a[ln] < T.a[ln]) return true;
return false;
}
return false;
}
bool Big::operator<(const int& t) const {
Big tee(t);
return *this < tee;
}
void Big::print() const {
printf("%d", a[len - 1]);
gd(i, len - 2, 0) { printf("%04d", a[i]); }
}
void print(const Big& s) {
int len = s.len;
printf("%d", s.a[len - 1]);
gd(i, len - 2, 0) { printf("%04d", s.a[i]); }
}
char s[100024];
使用示例：
基本用法
1. 头文件包含和宏定义
#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
#define CLR(a) memset(a, 0, sizeof a)
#define f(i, a, b) for (int i = a; i < b; i++)
#define g(i, a, b) for (int i = a; i <= b; i++)
#define gd(i, a, b) for (int i = a; i >= b; i--)
2. 基本使用示例
int main() {
// 从整数创建大数
Big a(123456789);
Big b(987654321);
// 从字符串创建大数
Big c("12345678901234567890");
// 基本运算
Big sum = a + b;
Big diff = a - b;
Big product = a * b;
Big quotient = a / 123; // 除以普通整数
int remainder = a % 123; // 取模
// 幂运算
Big power = a ^ 3; // a的3次方
// 比较运算
if (a < b) {
cout << "a is smaller than b" << endl;
}
// 输出结果
cout << "a = "; a.print(); cout << endl;
cout << "b = "; b.print(); cout << endl;
cout << "a + b = "; sum.print(); cout << endl;
cout << "a - b = "; diff.print(); cout << endl;
cout << "a * b = "; product.print(); cout << endl;
return 0;
}
3. 更复杂的示例
// 计算阶乘
Big factorial(int n) {
Big result(1);
for (int i = 2; i <= n; i++) {
result = result * Big(i);
}
return result;
}
// 计算斐波那契数列
Big fibonacci(int n) {
if (n <= 1) return Big(n);
Big a(0), b(1), c;
for (int i = 2; i <= n; i++) {
c = a + b;
a = b;
b = c;
}
return b;
}
int main() {
// 计算大数阶乘
Big fact = factorial(100);
cout << "100! = "; fact.print(); cout << endl;
// 计算大斐波那契数
Big fib = fibonacci(100);
cout << "fib(100) = "; fib.print(); cout << endl;
// 从字符串读取大数
char numStr[] = "123456789012345678901234567890";
Big bigNum(numStr);
cout << "Big number: "; bigNum.print(); cout << endl;
return 0;
}
4. 处理用户输入
int main() {
char s1[100024], s2[100024];
cout << "Enter first big number: ";
cin >> s1;
cout << "Enter second big number: ";
cin >> s2;
Big a(s1), b(s2);
cout << "a + b = "; (a + b).print(); cout << endl;
cout << "a - b = "; (a - b).print(); cout << endl;
cout << "a * b = "; (a * b).print(); cout << endl;
return 0;
}
注意事项
- 压位存储：这个实现使用4位十进制数作为一个存储单元（DLEN=4）
- 内存分配：最大支持10024位数字，即约10000位十进制数
- 运算限制：
- 目前支持：加减乘、除以整数、幂运算（整数指数）
- 不支持：大数除大数、大数的大数次方
- 性能：压位存储提高了运算效率
编译运行
确保使用C++11或更高版本编译：
g++ -std=c++11 -o bigint bigint.cpp
./bigint
这个类适合需要处理超出普通整数范围的大数运算场景，如密码学、大数计算、组合数学等应用。
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