大整数乘法运算

// // Created by Administrator on 2026/3/28. // #include <stdio.h> #include <stdlib.h> #include <string.h> #define MAXSIZE 1000 // 大整数支持的最大位数 // 大整数结构体定义（与教材完全一致） typedef struct { int digits[MAXSIZE]; // 低位到高位依次存储，digits[0] 是个位 int length; // 有效数字位数 int sign; // 符号：1 为正，-1 为负 } BigInt; // ------------------- 1. 字符串转大整数 ------------------- BigInt StrToBigInt(const char *s) { BigInt num; num.length = 0; num.sign = 1; int len = strlen(s); int i = 0; if (s[0] == '-') { num.sign = -1; i = 1; } // 从后往前读，低位存到数组前面 for (int j = len - 1; j >= i; j--) { num.digits[num.length++] = s[j] - '0'; } return num; } // ------------------- 2. 打印大整数 ------------------- void PrintBigInt(BigInt num) { if (num.length == 0) { printf("0\n"); return; } if (num.sign == -1) { printf("-"); } // 从高位到低位打印 for (int i = num.length - 1; i >= 0; i--) { printf("%d", num.digits[i]); } printf("\n"); } // ------------------- 3. 大整数乘法（教材伪代码实现） ------------------- BigInt BigIntMultiply(BigInt a, BigInt b) { BigInt c; // 1. 处理结果为0的特殊情况 if (a.length == 0 || b.length == 0) { c.sign = 1; c.length = 0; return c; } // 2. 判断结果的符号位 if (a.sign == b.sign) { c.sign = 1; } else { c.sign = -1; } // 3. 确定结果的位数，并初始化 c.length = a.length + b.length - 1; for (int i = 0; i < c.length; i++) { c.digits[i] = 0; } // 4. 按位相乘并累加 for (int i = 0; i < a.length; i++) { for (int j = 0; j < b.length; j++) { c.digits[i + j] += a.digits[i] * b.digits[j]; } } // 5. 从低位到高位处理进位 int carry = 0; for (int i = 0; i < c.length; i++) { int temp = c.digits[i] + carry; c.digits[i] = temp % 10; carry = temp / 10; } // 6. 处理最高位进位 if (carry > 0) { c.digits[c.length++] = carry; } // 7. 消除高位前导0 while (c.length > 0 && c.digits[c.length - 1] == 0) { c.length--; } return c; } // ------------------- 测试主函数 ------------------- int main() { // 测试用例1：正数相乘 123 × 456 = 56088 BigInt a = StrToBigInt("123"); BigInt b = StrToBigInt("456"); printf("a = "); PrintBigInt(a); printf("b = "); PrintBigInt(b); BigInt product = BigIntMultiply(a, b); printf("a × b = "); PrintBigInt(product); // 测试用例2：带负数相乘 -123 × 456 = -56088 BigInt c = StrToBigInt("-123"); printf("\nc = "); PrintBigInt(c); printf("b = "); PrintBigInt(b); BigInt product2 = BigIntMultiply(c, b); printf("c × b = "); PrintBigInt(product2); // 测试用例3：乘以0 999 × 0 = 0 BigInt d = StrToBigInt("999"); BigInt zero = StrToBigInt("0"); printf("\nd = "); PrintBigInt(d); printf("zero = "); PrintBigInt(zero); BigInt product3 = BigIntMultiply(d, zero); printf("d × zero = "); PrintBigInt(product3); return 0; }

两数相乘，其结果的位数至少是两数位数之和-1.

乘法思想：个位乘个位算个位，个位累加。

个位乘百位算百位，百位乘个位算百位，十位乘十位算百位。百位累加。