程序中的数学 一，大数

#include <cstdio>
#include <cmath>
#include <cstring>
#include <iostream>
using namespace std;

#define MAXN 500
struct BigNum {
    int num[MAXN];
    int len;
};
//高精度比较 a > b return 1, a == b return 0; a < b return -1;
int Comp(BigNum &a, BigNum &b) {
    int i;
    if (a.len != b.len)
        return (a.len > b.len) ? 1 : -1;
    for (i = a.len - 1; i >= 0; i--)
        if (a.num[i] != b.num[i])
            return (a.num[i] > b.num[i]) ? 1 : -1;
    return 0;
}
//高精度加法
BigNum Add(BigNum &a, BigNum &b) {
    BigNum c;
    int i, len;
    len = (a.len > b.len) ? a.len : b.len;
    memset(c.num, 0, sizeof(c.num));
    for (i = 0; i < len; i++) {
        c.num[i] += (a.num[i] + b.num[i]);
        if (c.num[i] >= 10) {
            c.num[i + 1]++;
            c.num[i] -= 10;
        }
    }
    if (c.num[len])
        len++;
    c.len = len;
    return c;
}
//高精度减法,保证a >= b
BigNum Sub(BigNum &a, BigNum &b) {
    BigNum c;
    int i, len;
    len = (a.len > b.len) ? a.len : b.len;
    memset(c.num, 0, sizeof(c.num));
    for (i = 0; i < len; i++) {
        c.num[i] += (a.num[i] - b.num[i]);
        if (c.num[i] < 0) {
            c.num[i] += 10;
            c.num[i + 1]--;
        }
    }
    while (c.num[len - 1] == 0 && len > 1)
        len--;
    c.len = len;
    return c;
}
BigNum Mul(BigNum &a, BigNum &b) {
    int i, j, len = 0;
    BigNum c;
    memset(c.num, 0, sizeof(c.num));
    for (i = 0; i < a.len; i++) {
        for (j = 0; j < b.len; j++) {
            c.num[i + j] += (a.num[i] * b.num[j]);
            if (c.num[i + j] >= 10) {
                c.num[i + j + 1] += c.num[i + j] / 10;
                c.num[i + j] %= 10;
            }
        }
    }
    len = a.len + b.len - 1;
    while (c.num[len - 1] == 0 && len > 1)
        len--;
    if (c.num[len])
        len++;
    c.len = len;
    return c;
}
BigNum Pow(BigNum &a, int n) {
    BigNum ans;
    ans.num[0] = 1, ans.len = 1;
    while (n) {
        if (n & 1)
            ans = Mul(ans, a);
        a = Mul(a, a);
        n >>= 1;
    }
    return ans;
}
//高精度除以低精度,除的结果为c, 余数为f
void Div1(BigNum &a, int &b, BigNum &c, int &f) {
    int i, len = a.len;
    memset(c.num, 0, sizeof(c.num));
    f = 0;
    for (i = a.len - 1; i >= 0; i--) {
        f = f * 10 + a.num[i];
        c.num[i] = f / b;
        f %= b;
    }
    while (len > 1 && c.num[len - 1] == 0)
        len--;
    c.len = len;
}
//高精度*10
void Mul10(BigNum &a) {
    int i, len = a.len;
    for (i = len; i >= 1; i--)
        a.num[i] = a.num[i - 1];
    a.num[i] = 0;
    len++;
    while (a.num[len - 1] == 0 && len > 1)
        len--;
    a.len = len;
}

//高精度除以高精度，除的结果为c，余数为f
void Div2(BigNum &a, BigNum &b, BigNum &c, BigNum &f) {
    int i, len = a.len;
    memset(c.num, 0, sizeof(c.num));
    memset(f.num, 0, sizeof(f.num));
    f.len = 1;
    for (i = len - 1; i >= 0; i--) {
        Mul10(f);
        f.num[0] = a.num[i];
        while (Comp(f, b) >= 0) {
            f = Sub(f, b);
            c.num[i]++;
        }
    }
    while (len > 1 && c.num[len - 1] == 0)
        len--;
    c.len = len;
}
void print(BigNum &a) {  //输出大数
    int i;
    for (i = a.len - 1; i >= 0; i--)
        printf("%d", a.num[i]);
    puts("");
}

void Init(BigNum &a, char *s, int &tag) {  //字符串转化为大数
    memset(a.num, 0, sizeof(a.num));
    int i = 0, j = strlen(s);
    if (s[0] == '-') {
        j--;
        i++;
        tag *= -1;
    }
    a.len = j;
    for (; s[i] != '