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。
1 #pragma comment(linker, "/STACK:10240000,10240000") 2 3 #include <iostream> 4 #include <cstdio> 5 #include <algorithm> 6 #include <cstdlib> 7 #include <cstring> 8 #include <map> 9 #include <queue> 10 #include <deque> 11 #include <cmath> 12 #include <vector> 13 #include <ctime> 14 #include <cctype> 15 #include <set> 16 #include <bitset> 17 #include <functional> 18 #include <numeric> 19 #include <stdexcept> 20 #include <utility> 21 22 using namespace std; 23 24 #define mem0(a) memset(a, 0, sizeof(a)) 25 #define mem_1(a) memset(a, -1, sizeof(a)) 26 #define lson l, m, rt << 1 27 #define rson m + 1, r, rt << 1 | 1 28 #define rep_up0(a, b) for (int a = 0; a < (b); a++) 29 #define rep_up1(a, b) for (int a = 1; a <= (b); a++) 30 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--) 31 #define rep_down1(a, b) for (int a = b; a > 0; a--) 32 #define all(a) (a).begin(), (a).end() 33 #define lowbit(x) ((x) & (-(x))) 34 #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) {} 35 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {} 36 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {} 37 #define pchr(a) putchar(a) 38 #define pstr(a) printf("%s", a) 39 #define sstr(a) scanf("%s", a) 40 #define sint(a) scanf("%d", &a) 41 #define sint2(a, b) scanf("%d%d", &a, &b) 42 #define sint3(a, b, c) scanf("%d%d%d", &a, &b, &c) 43 #define pint(a) printf("%d ", a) 44 #define test_print1(a) cout << "var1 = " << a << endl 45 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl 46 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = " << b << ", var3 = " << c << endl 47 #define mp(a, b) make_pair(a, b) 48 #define pb(a) push_back(a) 49 50 typedef unsigned int uint; 51 typedef long long LL; 52 typedef pair<int, int> pii; 53 typedef vector<int> vi; 54 55 const int dx[8] = {0, 0, -1, 1, 1, 1, -1, -1}; 56 const int dy[8] = {-1, 1, 0, 0, 1, -1, 1, -1 }; 57 const int maxn = 1e5 + 7; 58 const int md = 998244353; 59 const int inf = 1e9 + 7; 60 const LL inf_L = 1e18 + 7; 61 const double pi = acos(-1.0); 62 const double eps = 1e-6; 63 64 template<class T>T gcd(T a, T b){return b==0?a:gcd(b,a%b);} 65 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;} 66 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;} 67 template<class T>T condition(bool f, T a, T b){return f?a:b;} 68 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];} 69 int make_id(int x, int y, int n) { return x * n + y; } 70 71 const int maxI = 1e8; 72 const int Len = 8; 73 74 struct BigInt { 75 76 vi num; 77 bool symbol; 78 79 BigInt() { num.clear(); symbol = 0; } 80 BigInt(int x) { symbol = 0; if (x < 0) { symbol = 1; x = -x; } num.push_back(x % maxI); if (x >= maxI) num.push_back(x / maxI); } 81 BigInt(bool s, vi x) { symbol = s; num = x; } 82 BigInt(char s[]) { 83 int len = strlen(s), x = 1, sum = 0, p = s[0] == '-'; 84 symbol = p; 85 for (int i = len - 1; i >= p; i--) { 86 sum += (s[i] - '0') * x; 87 x *= 10; 88 if (x == 1e8 || i == p) { 89 num.push_back(sum); 90 sum = 0; 91 x = 1; 92 } 93 } 94 while (num.back() == 0 && num.size() > 1) num.pop_back(); 95 } 96 97 void push(int x) { num.push_back(x); } 98 99 BigInt abs() const { return BigInt(false, num); } 100 101 bool smaller(const vi &a, const vi &b) const { 102 if (a.size() != b.size()) return a.size() < b.size(); 103 for (int i = a.size() - 1; i >= 0; i--) { 104 if (a[i] != b[i]) return a[i] < b[i]; 105 } 106 return 0; 107 } 108 109 bool operator < (const BigInt &p) const { 110 if (symbol && !p.symbol) return true; 111 if (!symbol && p.symbol) return false; 112 if (symbol && p.symbol) return smaller(p.num, num); 113 return smaller(num, p.num); 114 } 115 116 bool operator > (const BigInt &p) const { 117 return p < *this; 118 } 119 120 bool operator == (const BigInt &p) const { 121 return !(p < *this) && !(*this < p); 122 } 123 124 bool operator >= (const BigInt &p) const { 125 return !(*this < p); 126 } 127 128 bool operator <= (const BigInt &p) const { 129 return !(p < *this); 130 } 131 132 vi add(const vi &a, const vi &b) const { 133 vi c; 134 c.clear(); 135 int x = 0; 136 for (int i = 0; i < a.size(); i++) { 137 x += a[i]; 138 if (i < b.size()) x += b[i]; 139 c.push_back(x % maxI); 140 x /= maxI; 141 } 142 for (int i = a.size(); i < b.size(); i++) { 143 x += b[i]; 144 c.push_back(x % maxI); 145 x /= maxI; 146 } 147 if (x) c.push_back(x); 148 while (c.back() == 0 && c.size() > 1) c.pop_back(); 149 return c; 150 } 151 152 vi sub(const vi &a, const vi &b) const { 153 vi c; 154 c.clear(); 155 int x = 1; 156 for (int i = 0; i < b.size(); i++) { 157 x += maxI + a[i] - b[i] - 1; 158 c.push_back(x % maxI); 159 x /= maxI; 160 } 161 for (int i = b.size(); i < a.size(); i++) { 162 x += maxI + a[i] - 1; 163 c.push_back(x % maxI); 164 x /= maxI; 165 } 166 while (c.back() == 0 && c.size() > 1) c.pop_back(); 167 return c; 168 } 169 170 vi mul(const vi &a, const vi &b) const { 171 vi c; 172 c.resize(a.size() + b.size()); 173 for (int i = 0; i < a.size(); i++) { 174 for (int j = 0; j < b.size(); j++) { 175 LL tmp = (LL)a[i] * b[j] + c[i + j]; 176 c[i + j + 1] += tmp / maxI; 177 c[i + j] = tmp % maxI; 178 } 179 } 180 while (c.back() == 0 && c.size() > 1) c.pop_back(); 181 return c; 182 } 183 184 vi div(const vi &a, const vi &b) const { 185 vi c(a.size()), x(1, 0), y(1, 0), z(1, 0), t(1, 0); 186 y.push_back(1); 187 for (int i = a.size() - 1; i >= 0; i--) { 188 z[0] = a[i]; 189 x = add(mul(x, y), z); 190 if (smaller(x, b)) continue; 191 int l = 1, r = maxI - 1; 192 while (l < r) { 193 int m = (l + r + 1) >> 1; 194 t[0] = m; 195 if (smaller(x, mul(b, t))) r = m - 1; 196 else l = m; 197 } 198 c[i] = l; 199 t[0] = l; 200 x = sub(x, mul(b, t)); 201 } 202 while (c.back() == 0 && c.size() > 1) c.pop_back(); 203 return c; 204 } 205 206 BigInt operator + (const BigInt &p) const{ 207 if (!symbol && !p.symbol) return BigInt(false, add(num, p.num)); 208 if (!symbol && p.symbol) return *this >= p.abs()? BigInt(false, sub(num, p.num)) : BigInt(true, sub(p.num, num)); 209 if (symbol && !p.symbol) return (*this).abs() > p? BigInt(true, sub(num, p.num)) : BigInt(false, sub(p.num, num)); 210 return BigInt(true, add(num, p.num)); 211 } 212 213 BigInt operator - (const BigInt &p) const { 214 return *this + BigInt(!p.symbol, p.num); 215 } 216 217 BigInt operator * (const BigInt &p) const { 218 BigInt res(symbol ^ p.symbol, mul(num, p.num)); 219 if (res.symbol && res.num.size() == 1 && res.num[0] == 0) res.symbol = false; 220 return res; 221 } 222 223 BigInt operator / (const BigInt &p) const { 224 if (p == BigInt(0)) return p; 225 BigInt res(symbol ^ p.symbol, div(num, p.num)); 226 if (res.symbol && res.num.size() == 1 && res.num[0] == 0) res.symbol = false; 227 return res; 228 } 229 230 BigInt operator % (const BigInt &p) const { 231 return *this - *this / p * p; 232 } 233 234 BigInt operator += (const BigInt &that) { 235 return *this = *this + that; 236 } 237 BigInt operator -= (const BigInt &that) { 238 return *this = *this - that; 239 } 240 BigInt operator *= (const BigInt &that) { 241 return *this = *this * that; 242 } 243 BigInt operator /= (const BigInt &that) { 244 return *this = *this / that; 245 } 246 BigInt operator %= (const BigInt &that) { 247 return *this = *this % that; 248 } 249 250 void show() const { 251 if (symbol) putchar('-'); 252 printf("%d", num[num.size() - 1]); 253 for (int i = num.size() - 2; i >= 0; i--) { 254 printf("%08d", num[i]); 255 } 256 //putchar(' '); 257 } 258 259 int TotalDigit() const { 260 int x = num[num.size() - 1] / 10, t = 1; 261 while (x) { 262 x /= 10; 263 t++; 264 } 265 return t + (num.size() - 1) * Len; 266 } 267 268 friend inline ostream & operator << (ostream & os, BigInt t1){ 269 t1.show(); 270 return os; 271 } 272 273 friend inline istream & operator >> (istream & is, BigInt &t1){ 274 char s[22]; 275 scanf("%s", s); 276 t1 = BigInt(s); 277 return is; 278 } 279 }; 280 281 template<class T> 282 struct Fraction { 283 T a, b; 284 Fraction(T a, T b): a(a), b(b) {} 285 Fraction() {} 286 Fraction operator + (const Fraction &that) const { 287 T x = a * that.b + b * that.a, y = b * that.b; 288 return Fraction(x, y); 289 } 290 Fraction operator - (const Fraction &that) const { 291 T x = a * that.b - b * that.a, y = b * that.b; 292 return Fraction(x, y); 293 } 294 Fraction operator * (const Fraction &that) const { 295 T x = a * that.a, y = b * that.b; 296 return Fraction(x, y); 297 } 298 Fraction operator / (const Fraction &that) const { 299 T x = a * that.b, y = b * that.a; 300 return Fraction(x, y); 301 } 302 Fraction operator += (const Fraction &that) { 303 return *this = *this + that; 304 } 305 Fraction operator -= (const Fraction &that) { 306 return *this = *this - that; 307 } 308 Fraction operator *= (const Fraction &that) { 309 return *this = *this * that; 310 } 311 Fraction operator /= (const Fraction &that) { 312 return *this = *this / that; 313 } 314 Fraction operator ! () const { 315 return Fraction(b, a); 316 } 317 }; 318 319 typedef BigInt bi; 320 typedef Fraction<BigInt> fb; 321 322 fb get(int id, int n) { 323 int x; 324 cin >> x; 325 fb ans(x, 1); 326 if (id + 1 < n) ans += !get(id + 1, n); 327 return ans; 328 } 329 330 void print(fb num) { 331 cout << num.a / num.b; 332 if (num.a % num.b > 0) { 333 cout << " "; 334 num.a %= num.b; 335 print(!num); 336 } 337 else cout << endl; 338 } 339 340 void solve(fb num) { 341 if (num.a % num.b == 0) { 342 cout << num.a / num.b << endl; 343 return ; 344 } 345 if (num.a * num.b < 0) { 346 if (num.a > 0) { 347 num.a *= -1; 348 num.b *= -1; 349 } 350 cout << num.a / num.b - 1 << " "; 351 num.a += (num.a / num.b - 1) * -1 * num.b; 352 } 353 else { 354 cout << num.a / num.b << " "; 355 num.a %= num.b; 356 } 357 if (num.a < 0) { 358 num.a *= -1; 359 num.b *= -1; 360 } 361 print(!num); 362 } 363 364 int main() { 365 //freopen("in.txt", "r", stdin); 366 int n, m, cas = 0; 367 while (cin >> n >> m, n || m) { 368 cout << "Case " << ++ cas << ":" << endl; 369 fb num1 = get(0, n); 370 fb num2 = get(0, m); 371 solve(num1 + num2); 372 solve(num1 - num2); 373 solve(num1 * num2); 374 solve(num1 / num2); 375 } 376 return 0; 377 }