本文主要整理了几个常用的大整数的算法:
大整数加法
大整数乘法
大整数阶乘
大整数幂
其实大体的思路都差不多，都是用数组来存储大整数。以下的代码仅仅实现功能，并没有充分详细的参数判断，在实际运用中，肯定是需要考虑的。
大整数相加
1 #include <stdio.h> 2 #include <string.h> 3 #define N 1000 4 void get_num(int *array) 5 { 6 char str[N] = {' '}; 7 int loop = 0; 8 int length = 0; 9 10 scanf("%s", str); 11 length = strlen(str); 12 for (loop = 0; loop < length; ++loop) { 13 array[loop] = str[length - loop - 1] - '0'; 14 } 15 array[loop] = -1; 16 } 17 18 void big_plus(int *num1, int *num2, int *result) 19 { 20 int num1_index = 0; 21 int num2_index = 0; 22 int result_index = 0; 23 int tmp_carry = 0; 24 int tmp_result = 0; 25 while (num1[num1_index] != -1 && num2[num2_index] != -1) { 26 tmp_result = num1[num1_index++] + num2[num2_index++] + tmp_carry; 27 result[result_index++] = tmp_result % 10; 28 tmp_carry = tmp_result / 10; 29 } 30 while (num1[num1_index] != -1) { 31 tmp_result = num1[num1_index++] + tmp_carry; 32 result[result_index++] = tmp_result % 10; 33 tmp_carry = tmp_result / 10; 34 } 35 while (num2[num2_index] != -1) { 36 tmp_result = num2[num2_index++] + tmp_carry; 37 result[result_index++] = tmp_result % 10; 38 tmp_carry = tmp_result / 10; 39 } 40 if (tmp_carry) { 41 result[result_index++] = tmp_carry; 42 } 43 result_index[result_index] = -1; 44 } 45 void print_result(int *array) 46 { 47 int i = 0; 48 int len = 0; 49 for (i = 0; array[i] != -1; ++i); 50 51 len = i; 52 for (i = len - 1; i >= 0; --i) { 53 printf("%d", array[i]); 54 } 55 if (len == 0) { 56 printf("0"); 57 } 58 printf(" "); 59 } 60 int main(int argc, char **argv) 61 { 62 int num1[N] = {0}; 63 int num2[N] = {0}; 64 int result[N] = {0}; 65 //将数用数组来存，并从低位向高位存. 66 get_num(num1); 67 get_num(num2); 68 //执行相加操作 69 big_plus(num1, num2, result); 70 print_result(result); 71 return 0; 72 }
大整数相乘
1 #include <stdio.h> 2 #include <string.h> 3 #define N 1000 4 5 void get_num(int *array) 6 { 7 char str[N] = {' '}; 8 int loop = 0; 9 int length = 0; 10 11 scanf("%s", str); 12 length = strlen(str); 13 for (loop = 0; loop < length; ++loop) { 14 array[loop] = str[length - loop - 1] - '0'; 15 } 16 array[length] = -1; 17 } 18 void big_multi(int *num1, int *num2, int *result) 19 { 20 int num1_index = 0; 21 int num2_index = 0; 22 int result_index = 0; 23 int tmp_carry = 0; 24 int tmp_result = 0; 25 for (num1_index = 0; num1[num1_index] != -1; ++num1_index) { 26 for (num2_index = 0; num2[num2_index] != -1; ++num2_index) { 27 tmp_result = num1[num1_index] * num2[num2_index] + result[num1_index + num2_index] + tmp_carry; 28 result[num1_index + num2_index] = tmp_result % 10; 29 tmp_carry = tmp_result / 10; 30 } 31 result_index = num1_index + num2_index - 1; 32 if (tmp_carry) { 33 result[++result_index] = tmp_carry; 34 } 35 } 36 result[++result_index] = -1; 37 } 38 void print_result(int *array) 39 { 40 int i = 0; 41 int len = 0; 42 for (i = 0; array[i] != -1; ++i); 43 44 len = i; 45 for (i = len - 1; i >= 0; --i) { 46 printf("%d", array[i]); 47 } 48 if (len == 0) { 49 printf("0"); 50 } 51 printf(" "); 52 } 53 int main(int argc, char **argv) 54 { 55 int num1[N] = {0}; 56 int num2[N] = {0}; 57 int result[2 * N] = {0}; 58 //将数用数组来存，并从低位向高位存. 59 get_num(num1); 60 get_num(num2); 61 //执行相乘操作 62 big_multi(num1, num2, result); 63 print_result(result); 64 return 0; 65 }
大整数阶乘
1 #include <stdio.h> 2 #include <string.h> 3 #define N 10000 4 5 void print_result(int *array) 6 { 7 int i = 0; 8 int len = 0; 9 for (i = 0; array[i] != -1; ++i); 10 11 len = i; 12 for (i = len - 1; i >= 0; --i) { 13 printf("%d", array[i]); 14 } 15 if (len == 0) { 16 printf("0"); 17 } 18 printf(" "); 19 } 20 21 void big_factor(int n, int *result) 22 { 23 int result_index = 0; 24 int carry = 0; 25 int tmp_result = 0; 26 int i = 0; 27 int j = 0; 28 result[0] = 1; 29 if (n <= 1) { 30 result[1] = -1; 31 return; 32 } 33 for (i = 1; i <= n; ++i) { 34 for (j = 0; j <= result_index; ++j) { 35 tmp_result = result[j] * i + carry; 36 result[j] = tmp_result % 10; 37 carry = tmp_result / 10; 38 } 39 while (carry) { 40 result[++result_index] = carry % 10; 41 carry = carry / 10; 42 } 43 } 44 result[++result_index] = -1; 45 } 46 47 int main(int argc, char **argv) 48 { 49 int n = 0; 50 int result[N] = {0}; 51 scanf("%d", &n); 52 //将数用数组来存，并从低位向高位存. 53 big_factor(n, result); 54 print_result(result); 55 return 0; 56 }
大整数幂
1 #include <stdio.h> 2 #include <string.h> 3 #define N 10000 4 5 void print_result(int *array) 6 { 7 int i = 0; 8 int len = 0; 9 for (i = 0; array[i] != -1; ++i); 10 11 len = i; 12 for (i = len - 1; i >= 0; --i) { 13 printf("%d", array[i]); 14 } 15 if (len == 0) { 16 printf("0"); 17 } 18 printf(" "); 19 } 20 21 int big_pow(int base, int power, int *result) 22 { 23 int result_index = 0; 24 int carry = 0; 25 int tmp_result = 0; 26 int i = 0; 27 int j = 0; 28 result[0] = 1; 29 if (base == 1 || power == 0) { 30 result[1] = -1; 31 } 32 for (i = 0; i < power; ++i) { 33 for (j = 0; j <= result_index; ++j) { 34 tmp_result = result[j] * base + carry; 35 result[j] = tmp_result % 10; 36 carry = tmp_result / 10; 37 } 38 while (carry) { 39 result[++result_index] = carry % 10; 40 carry = carry / 10; 41 } 42 } 43 result[++result_index] = -1; 44 } 45 46 int main(int argc, char **argv) 47 { 48 int base = 0; 49 int power = 0; 50 int result[N]; 51 //输入底数和指数 52 scanf("%d%d", &base, &power); 53 big_pow(base, power, result); 54 print_result(result); 55 return 0; 56 }