#include <stdio.h>
#include <stdlib.h>
/*
A minimal big‑integer type using base‑10 digits.
Digits are stored in reverse order (least significant first)
to make multiplication straightforward.
*/
typedef struct {
int *digits; // dynamic array of digits
size_t size; // number of digits currently used
size_t capacity; // allocated capacity
} BigInt;
/*
Initialize a BigInt with a small integer value.
*/
BigInt bigint_init(int value) {
BigInt b;
b.capacity = 32; // initial capacity
b.size = 0;
b.digits = malloc(b.capacity * sizeof(int));
if (value == 0) {
b.digits[b.size++] = 0;
} else {
while (value > 0) {
b.digits[b.size++] = value % 10;
value /= 10;
}
}
return b;
}
/*
Ensure the BigInt has enough capacity for new digits.
*/
void bigint_reserve(BigInt *b, size_t new_cap) {
if (new_cap > b->capacity) {
b->capacity = new_cap * 2;
b->digits = realloc(b->digits, b->capacity * sizeof(int));
}
}
/*
Multiply BigInt by an integer n.
Uses classic grade‑school multiplication.
*/
void bigint_multiply(BigInt *b, int n) {
int carry = 0;
for (size_t i = 0; i < b->size; ++i) {
int product = b->digits[i] * n + carry;
b->digits[i] = product % 10;
carry = product / 10;
}
// Append remaining carry digits
while (carry > 0) {
bigint_reserve(b, b->size + 1);
b->digits[b->size++] = carry % 10;
carry /= 10;
}
}
/*
Convert BigInt to a printable string.
*/
char *bigint_to_string(const BigInt *b) {
char *str = malloc(b->size + 1);
for (size_t i = 0; i < b->size; ++i) {
str[b->size - 1 - i] = '0' + b->digits[i];
}
str[b->size] = '\0';
return str;
}
/*
Compute factorial using BigInt.
*/
BigInt factorial_big(size_t n) {
BigInt result = bigint_init(1);
for (size_t i = 2; i <= n; ++i) {
bigint_multiply(&result, (int)i);
}
return result;
}
/*
Entry point: reads a number, computes factorial,
and prints the result using big‑integer arithmetic.
*/
int main() {
size_t n;
printf("Enter a number greater than 20: ");
scanf("%zu", &n);
BigInt result = factorial_big(n);
char *str = bigint_to_string(&result);
printf("\nFactorial of %zu is:\n\n%s\n", n, str);
free(result.digits);
free(str);
return 0;
}
/*
run:
Enter a number greater than 20: 25
Factorial of 25 is:
15511210043330985984000000
*/
