在C语言中实现bigint的最简单方法是使用数组来存储大整数的每一位,并使用基本的数学运算来实现加、减、乘、除等操作。以下是一个简单的示例:
#include<stdio.h>
#include <stdlib.h>
#include<string.h>
#include <stdbool.h>
#define MAX_DIGITS 1000
typedef struct {
int digits[MAX_DIGITS];
int len;
} BigInt;
void init_bigint(BigInt *a) {
memset(a->digits, 0, sizeof(a->digits));
a->len = 0;
}
void print_bigint(BigInt a) {
for (int i = a.len - 1; i >= 0; i--) {
printf("%d", a.digits[i]);
}
printf("\n");
}
void add_bigint(BigInt a, BigInt b, BigInt *result) {
int carry = 0;
int max_len = a.len > b.len ? a.len : b.len;
for (int i = 0; i < max_len; i++) {
int sum = a.digits[i] + b.digits[i] + carry;
carry = sum / 10;
result->digits[i] = sum % 10;
}
if (carry > 0) {
result->digits[max_len++] = carry;
}
result->len = max_len;
}
void subtract_bigint(BigInt a, BigInt b, BigInt *result) {
int borrow = 0;
int max_len = a.len > b.len ? a.len : b.len;
for (int i = 0; i < max_len; i++) {
int diff = a.digits[i] - b.digits[i] - borrow;
if (diff < 0) {
diff += 10;
borrow = 1;
} else {
borrow = 0;
}
result->digits[i] = diff;
}
int i = max_len;
while (i < a.len && a.digits[i] != 0) {
result->digits[i] = a.digits[i];
i++;
}
result->len = i;
}
void multiply_bigint(BigInt a, BigInt b, BigInt *result) {
memset(result->digits, 0, sizeof(result->digits));
int max_len = a.len > b.len ? a.len : b.len;
for (int i = 0; i < max_len; i++) {
int carry = 0;
for (int j = 0; j < max_len; j++) {
int product = a.digits[i] * b.digits[j] + result->digits[i + j] + carry;
carry = product / 10;
result->digits[i + j] = product % 10;
}
if (carry > 0) {
result->digits[max_len++] = carry;
}
}
result->len = max_len;
}
bool is_zero(BigInt a) {
for (int i = 0; i < a.len; i++) {
if (a.digits[i] != 0) {
return false;
}
}
return true;
}
void divide_bigint(BigInt a, BigInt b, BigInt *quotient, BigInt *remainder) {
memset(quotient->digits, 0, sizeof(quotient->digits));
memset(remainder->digits, 0, sizeof(remainder->digits));
for (int i = a.len - 1; i >= 0; i--) {
remainder->digits[0] = a.digits[i];
int divisor = remainder->digits[0];
int quotient_digit = 0;
while (divisor >= b.digits[b.len - 1]) {
divisor -= b.digits[b.len - 1];
quotient_digit++;
}
remainder->len = 1;
BigInt temp;
init_bigint(&temp);
for (int j = b.len - 2; j >= 0; j--) {
multiply_bigint(*remainder, 10, &temp);
add_bigint(temp, *remainder, remainder);
multiply_bigint(*remainder, 10, &temp);
add_bigint(temp, *remainder, remainder);
if (divisor == 0) {
break;
}
if (remainder->len > b.len || remainder->digits[remainder->len - 1] >= b.digits[j]) {
divisor -= b.digits[j];
quotient_digit += b.digits[j];
subtract_bigint(*remainder, b, remainder);
}
}
quotient->digits[i] = quotient_digit;
}
quotient->len = a.len;
while (quotient->len > 1 && quotient->digits[quotient->len - 1] == 0) {
quotient->len--;
}
remainder->len = 1;
while (remainder->len > 1 && remainder->digits[remainder->len - 1] == 0) {
remainder->len--;
}
}
int main() {
BigInt a, b, result;
init_bigint(&a);
init_bigint(&b);
init_bigint(&result);
// 示例:123456789 * 987654321
a.len = 9;
for (int i = 0; i < 9; i++) {
a.digits[i] = i + 1;
}
b.len = 9;
for (int i = 0; i < 9; i++) {
b.digits[i] = 9 - i;
}
multiply_bigint(a, b, &result);
printf("Product of ");
print_bigint(a);
printf(" and ");
print_bigint(b);
printf(" is:\n");
print_bigint(result);
return 0;
}
这个示例中,我们使用了一个结构体BigInt
来存储大整数,其中digits
数组用于存储每一位,len
表示大整数的长度。我们实现了加、减、乘、除等基本的数学运算,并在main
函数中演示了如何使用这些函数。
这个实现方法虽然简单,但在处理大整数时可能会遇到性能问题。在实际应用中,可以考虑使用更高效的算法和数据结构,例如Karatsuba算法、Toom-Cook算法等。
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