[csu/coj 1619] 递归

题意：http://acm.csu.edu.cn/OnlineJudge/problem.php?id=1619

思路：由于式子具有递归的性质，考虑递归解，中间结果会超64位int，需用大数。另外自己写了个分数类，见代码。

 #pragma comment(linker, "/STACK:10240000,10240000")

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstdlib>
 #include <cstring>
 #include <map>
 #include <queue>
 #include <deque>
 #include <cmath>
 #include <vector>
 #include <ctime>
 #include <cctype>
 #include <set>
 #include <bitset>
 #include <functional>
 #include <numeric>
 #include <stdexcept>
 #include <utility>

 using namespace std;

 #define mem0(a) memset(a, 0, sizeof(a))
 #define mem_1(a) memset(a, -1, sizeof(a))
 #define lson l, m, rt << 1
 #define rson m + 1, r, rt << 1 | 1
 #define rep_up0(a, b) for (int a = 0; a < (b); a++)
 #define rep_up1(a, b) for (int a = 1; a <= (b); a++)
 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--)
 #define rep_down1(a, b) for (int a = b; a > 0; a--)
 #define all(a) (a).begin(), (a).end()
 #define lowbit(x) ((x) & (-(x)))
 #define constructInt4(name, a, b, c, d) name(int a = 0, int b = 0, int c = 0, int d = 0): a(a), b(b), c(c), d(d) {}
 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {}
 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {}
 #define pchr(a) putchar(a)
 #define pstr(a) printf("%s", a)
 #define sstr(a) scanf("%s", a)
 #define sint(a) scanf("%d", &a)
 #define sint2(a, b) scanf("%d%d", &a, &b)
 #define sint3(a, b, c) scanf("%d%d%d", &a, &b, &c)
 #define pint(a) printf("%d\n", a)
 #define test_print1(a) cout << "var1 = " << a << endl
 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl
 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = " << b << ", var3 = " << c << endl
 #define mp(a, b) make_pair(a, b)
 #define pb(a) push_back(a)

 typedef unsigned int uint;
 typedef long long LL;
 typedef pair<int, int> pii;
 typedef vector<int> vi;

 const int dx[] = {, , -, , , , -, -};
 const int dy[] = {-, , , , , -, , - };
 const int maxn = 1e5 + ;
 const int md = ;
 const int inf = 1e9 + ;
 const LL inf_L = 1e18 + ;
 const double pi = acos(-1.0);
 const double eps = 1e-;

 template<class T>T gcd(T a, T b){return b==?a:gcd(b,a%b);}
 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;}
 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;}
 template<class T>T condition(bool f, T a, T b){return f?a:b;}
 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];}
 int make_id(int x, int y, int n) { return x * n + y; }

 const int maxI = 1e8;
 const int Len = ;

 struct BigInt {

     vi num;
     bool symbol;

     BigInt() { num.clear(); symbol = ; }
     BigInt(int x) { symbol = ; if (x < ) { symbol = ; x = -x; } num.push_back(x % maxI); if (x >= maxI) num.push_back(x / maxI); }
     BigInt(bool s, vi x) { symbol = s;  num = x; }
     BigInt(char s[]) {
         int len = strlen(s), x = , sum = , p = s[] == '-';
         symbol = p;
         for (int i = len - ; i >= p; i--) {
             sum += (s[i] - '') * x;
             x *= ;
             if (x == 1e8 || i == p) {
                 num.push_back(sum);
                 sum = ;
                 x = ;
             }
         }
         while (num.back() ==  && num.size() > ) num.pop_back();
     }

     void push(int x) { num.push_back(x); }

     BigInt abs() const { return BigInt(false, num); }

     bool smaller(const vi &a, const vi &b) const {
         if (a.size() != b.size()) return a.size() < b.size();
         for (int i = a.size() - ; i >= ; i--) {
             if (a[i] != b[i]) return a[i] < b[i];
         }
         return ;
     }

     bool operator < (const BigInt &p) const {
         if (symbol && !p.symbol) return true;
         if (!symbol && p.symbol) return false;
         if (symbol && p.symbol) return smaller(p.num, num);
         return smaller(num, p.num);
     }

     bool operator > (const BigInt &p) const {
         return p < *this;
     }

     bool operator == (const BigInt &p) const {
         return !(p < *this) && !(*this < p);
     }

     bool operator >= (const BigInt &p) const {
         return !(*this < p);
     }

     bool operator <= (const BigInt &p) const {
         return !(p < *this);
     }

     vi add(const vi &a, const vi &b) const {
         vi c;
         c.clear();
         int x = ;
         for (int i = ; i < a.size(); i++) {
             x += a[i];
             if (i < b.size()) x += b[i];
             c.push_back(x % maxI);
             x /= maxI;
         }
         for (int i = a.size(); i < b.size(); i++) {
             x += b[i];
             c.push_back(x % maxI);
             x /= maxI;
         }
         if (x) c.push_back(x);
         while (c.back() ==  && c.size() > ) c.pop_back();
         return c;
     }

     vi sub(const vi &a, const vi &b) const {
         vi c;
         c.clear();
         int x = ;
         for (int i = ; i < b.size(); i++) {
             x += maxI + a[i] - b[i] - ;
             c.push_back(x % maxI);
             x /= maxI;
         }
         for (int i = b.size(); i < a.size(); i++) {
             x += maxI + a[i] - ;
             c.push_back(x % maxI);
             x /= maxI;
         }
         while (c.back() ==  && c.size() > ) c.pop_back();
         return c;
     }

     vi mul(const vi &a, const vi &b) const {
         vi c;
         c.resize(a.size() + b.size());
         for (int i = ; i < a.size(); i++) {
             for (int j = ; j < b.size(); j++) {
                 LL tmp = (LL)a[i] * b[j] + c[i + j];
                 c[i + j + ] += tmp / maxI;
                 c[i + j] = tmp % maxI;
             }
         }
         while (c.back() ==  && c.size() > ) c.pop_back();
         return c;
     }

     vi div(const vi &a, const vi &b) const {
         vi c(a.size()), x(, ), y(, ), z(, ), t(, );
         y.push_back();
         for (int i = a.size() - ; i >= ; i--) {
             z[] = a[i];
             x = add(mul(x, y), z);
             if (smaller(x, b)) continue;
             int l = , r = maxI - ;
             while (l < r) {
                 int m = (l + r + ) >> ;
                 t[] = m;
                 if (smaller(x, mul(b, t))) r = m - ;
                 else l = m;
             }
             c[i] = l;
             t[] = l;
             x = sub(x, mul(b, t));
         }
         while (c.back() ==  && c.size() > ) c.pop_back();
         return c;
     }

     BigInt operator + (const BigInt &p) const{
         if (!symbol && !p.symbol) return BigInt(false, add(num, p.num));
         if (!symbol && p.symbol) return *this >= p.abs()? BigInt(false, sub(num, p.num)) : BigInt(true, sub(p.num, num));
         if (symbol && !p.symbol) return (*this).abs() > p? BigInt(true, sub(num, p.num)) : BigInt(false, sub(p.num, num));
         return BigInt(true, add(num, p.num));
     }

     BigInt operator - (const BigInt &p) const {
         return *this + BigInt(!p.symbol, p.num);
     }

     BigInt operator * (const BigInt &p) const {
         BigInt res(symbol ^ p.symbol, mul(num, p.num));
         if (res.symbol && res.num.size() ==  && res.num[] == ) res.symbol = false;
         return res;
     }

     BigInt operator / (const BigInt &p) const {
         if (p == BigInt()) return p;
         BigInt res(symbol ^ p.symbol, div(num, p.num));
         if (res.symbol && res.num.size() ==  && res.num[] == ) res.symbol = false;
         return res;
     }

     BigInt operator % (const BigInt &p) const {
         return *this - *this / p * p;
     }

     BigInt operator += (const BigInt &that)  {
         return *this = *this + that;
     }
     BigInt operator -= (const BigInt &that)  {
         return *this = *this - that;
     }
     BigInt operator *= (const BigInt &that)  {
         return *this = *this * that;
     }
     BigInt operator /= (const BigInt &that)  {
         return *this = *this / that;
     }
     BigInt operator %= (const BigInt &that)  {
         return *this = *this % that;
     }

     void show() const {
         if (symbol) putchar('-');
         printf("%d", num[num.size() - ]);
         for (int i = num.size() - ; i >= ; i--) {
             printf("%08d", num[i]);
         }
         //putchar('\n');
     }

     int TotalDigit() const {
         int x = num[num.size() - ] / , t = ;
         while (x) {
             x /= ;
             t++;
         }
         return t + (num.size() - ) * Len;
     }

     friend inline ostream & operator << (ostream & os, BigInt t1){
         t1.show();
         return os;
     }

     friend inline istream & operator >> (istream & is, BigInt &t1){
         char s[];
         scanf("%s", s);
         t1 = BigInt(s);
         return is;
     }
 };

 template<class T>
 struct  Fraction {
     T a, b;
     Fraction(T a, T b): a(a), b(b) {}
     Fraction() {}
     Fraction operator + (const Fraction &that) const {
         T x = a * that.b + b * that.a, y = b * that.b;
         return Fraction(x, y);
     }
     Fraction operator - (const Fraction &that) const {
         T x = a * that.b - b * that.a, y = b * that.b;
         return Fraction(x, y);
     }
     Fraction operator * (const Fraction &that) const {
         T x = a * that.a, y = b * that.b;
         return Fraction(x, y);
     }
     Fraction operator / (const Fraction &that) const {
         T x = a * that.b, y = b * that.a;
         return Fraction(x, y);
     }
     Fraction operator += (const Fraction &that)  {
         return *this = *this + that;
     }
     Fraction operator -= (const Fraction &that)  {
         return *this = *this - that;
     }
     Fraction operator *= (const Fraction &that)  {
         return *this = *this * that;
     }
     Fraction operator /= (const Fraction &that)  {
         return *this = *this / that;
     }
     Fraction operator ! () const {
         return Fraction(b, a);
     }
 };

 typedef BigInt bi;
 typedef Fraction<BigInt> fb;

 fb get(int id, int n) {
     int x;
     cin >> x;
     fb ans(x, );
     if (id +  < n) ans += !get(id + , n);
     return ans;
 }

 void print(fb num) {
     cout << num.a / num.b;
     if (num.a % num.b > ) {
         cout << " ";
         num.a %= num.b;
         print(!num);
     }
     else cout << endl;
 }

 void solve(fb num) {
     if (num.a % num.b == ) {
         cout << num.a / num.b << endl;
         return ;
     }
     if (num.a * num.b < ) {
         if (num.a > ) {
             num.a *= -;
             num.b *= -;
         }
         cout << num.a / num.b -  << " ";
         num.a += (num.a / num.b - ) * - * num.b;
     }
     else {
         cout << num.a / num.b << " ";
         num.a %= num.b;
     }
     if (num.a < ) {
         num.a *= -;
         num.b *= -;
     }
     print(!num);
 }

 int main() {
     //freopen("in.txt", "r", stdin);
     int n, m, cas = ;
     while (cin >> n >> m, n || m) {
         cout << "Case " << ++ cas << ":" << endl;
         fb num1 = get(, n);
         fb num2 = get(, m);
         solve(num1 + num2);
         solve(num1 - num2);
         solve(num1 * num2);
         solve(num1 / num2);
     }
     return ;
 }