Luogu5285 [十二省联考2019] 骗分过样例
题目分析：
观察前3个点，$361=19*19$，所以可以发现实际上就是快速幂，然后模数猜测是$998244353$，因为功能编号里面有这个数字，用费马小定理处理一下。 $pts:12$
观察第4个点，读入很大而结果很小，说明模数不是很大，所以枚举法，配合欧拉定理可以求出来模数为$1145141$，很巧的是这个数是个质数，所以接下来同上。 $pts:7$
观察第5个点，读入很小而结果很大，那我们可以yy一下，读入里面有两个靠得很近的数，所以将读入排序之后求相邻的差值，会发现读入里面有：
$264708066$和$264708068$，输出是x=1996649514996338529和y=1589589654696467295，把$x*361-y$，这个数一定是模数的倍数。这个数等于$719200885258981741674$。
肉眼观察法发现这个数可以被$2$，被$3$整除，然后枚举发现可以被$23$整除，接着我们搞进linux的计算器里面发现剩下的$5211600617818708273$是个质数，所以模数就是它了。 $pts:9$
第6,7个点写了WA掉了，结合提示可以猜测是自然溢出了，而且是枚举乘法的时候溢出了，我们需要找出循环节。$pts:13$
观察第8,9,10个点，因为叫$2p$,所以猜测是prime的意思，也就是求$[l,r]$之间的prime，是质数为$"p"$，不是为$"."$。
最后一个点到了$10^18$的程度，但区间大小只有$10^6$。我想到了可以用区间的埃拉托斯特尼筛来做8,9号点，第十个点我就采用了压缩打表法。 $pts:18$
观察11,12,13个点，因为叫$2u$，所以猜测和$\mu$有关，也就是莫比乌斯函数，对于11,12号点，可以用8,9点的方法，对于13号点，我有一个绝妙的想法。
首先先判定质数，这一步可以用上面的表去判定。对于没判定到的数，用小于等于$10^6$的质数去筛它，这样是没筛干净的。
对于剩下的数，如果等于$1$，那么不用再判断了；如果大于$1e6$那么有三种情况，一种是它是个质数，一种是它是两个相同的质数的乘积，一种是它是两个不同的质数的乘积。所以对于第一种，miller-rabin，第二种，开方，第三种，除了上面两种。 $pts:20$
最后一个部分，14,15,16号点，因为叫$2g$，所以猜测和原根有关。14号点直接枚举，16号点可以先筛出质数，再判是否拟合，如果不拟合就直接break。
十五号点有点难。。我一开始想了一个线性筛的做法，是$O(8n)$的，但是超时了，看了KB的sol之后得到了启发。
对于一个原根g，只要g^d=x，且d与phi(p)互质，那么x就是一个原根
代码：
1 #include<bits/stdc++.h> 2 using namespace std; 3 4 string ss = 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6 7 char str[120]; 8 9 int fast_pow(int now,int pw,int mod){ 10 int ans = 1,dt = now,bit = 1; 11 while(bit <= pw){ 12 if(bit & pw) ans = 1ll*ans*dt%mod; 13 dt = 1ll*dt*dt%mod; bit <<= 1; 14 } 15 return ans; 16 } 17 18 namespace solve1{ 19 int n; const int mod = 998244353; 20 void work(){ 21 scanf("%d",&n); 22 for(int i=1;i<=n;i++){ 23 char ch = getchar(); 24 while(ch > '9' || ch < '0') ch = getchar(); 25 int zz = 0; 26 while(ch<='9'&&ch>='0')zz=(zz*10ll+ch-'0')%(mod-1),ch=getchar(); 27 printf("%d\n",fast_pow(19,zz,mod)); 28 } 29 } 30 } 31 32 namespace solve2{ 33 int n; int mod=1145141; 34 void work(){ 35 scanf("%d",&n); 36 for(int i=1;i<=n;i++){ 37 char ch = getchar(); 38 while(ch > '9' || ch < '0') ch = getchar(); 39 int zz = 0; 40 while(ch<='9'&&ch>='0')zz=(zz*10ll+ch-'0')%(mod-1),ch=getchar(); 41 printf("%d\n",fast_pow(19,zz,mod)); 42 } 43 } 44 } 45 46 namespace solve3{ 47 int n; unsigned long long mod=5211600617818708273ll; 48 unsigned long long fast_multi(unsigned long long now,unsigned long long pw){ 49 unsigned long long dt = now,bit = 1,ans = 0; 50 while(bit <= pw){ 51 if(bit & pw){ans = ans+dt; if(ans >= mod) ans-=mod;} 52 dt = (dt+dt); if(dt >= mod) dt -= mod; 53 bit<<=1; 54 } 55 return ans; 56 } 57 unsigned long long fast_pow(int now,int pw){ 58 unsigned long long dt = now,bit = 1,ans = 1; 59 while(bit <= pw){ 60 if(bit & pw){ans = fast_multi(dt,ans);} 61 bit <<=1; dt = fast_multi(dt,dt); 62 } 63 return ans; 64 } 65 void work(){ 66 scanf("%d",&n); 67 for(int i=1;i<=n;i++){ 68 int zz; scanf("%d",&zz);printf("%llu\n",fast_pow(19,zz)); 69 } 70 } 71 } 72 73 namespace solve4{ 74 int n; const int mod = 998244353; 75 int res[102000]; 76 void work(){ 77 res[0] = 1; 78 for(int i=1;i<=100943;i++) res[i] = res[i-1]*19%mod; 79 scanf("%d",&n); 80 for(int i=1;i<=n;i++){ 81 long long zz; scanf("%lld",&zz); 82 if(zz > 100943) {zz -= 55245; zz %= 45699; zz += 55245;} 83 printf("%d\n",res[zz]); 84 } 85 } 86 } 87 88 namespace solve5{ 89 int n,prime[260000],flag[1000010],num; 90 void solveit(long long l,long long r){ 91 if(r <= 1e12+5){ 92 flag[1] = 1;int N = 1000000; 93 for(int i=2;i<=N;i++){ 94 if(!flag[i]) prime[++num] = i; 95 for(int j=1;j<=num&&i*prime[j]<=N;j++){ 96 flag[i*prime[j]] = 1; 97 if(i%prime[j] == 0) break; 98 } 99 } 100 memset(flag,0,sizeof(flag)); 101 for(int i=1;i<=num;i++){ 102 long long st = l/prime[i]+(l%prime[i]!=0); 103 if(st == 1) st++; 104 for(long long j=st;j*prime[i]<=r;j++){ 105 flag[j*prime[i]-l+1] = 1; 106 } 107 } 108 for(long long i=l;i<=r;i++) 109 if(flag[i-l+1] == 1) printf("."); 110 else printf("p"); 111 puts(""); 112 }else{ 113 for(int i=0;i<ss.length();i++){ 114 if(i!=0){printf("p");} 115 int dd = 0; 116 if(ss[i] == '!') dd = 92-'9'; 117 else if(ss[i]>'9') dd = ss[i]-'9'; 118 else{ 119 for(int j=i;j<ss.length()&&ss[j]!='.';j++,i++) 120 dd = dd*10+ss[j]-'0'; 121 } 122 for(int j=1;j<=dd;j++) printf("."); 123 } 124 puts(""); 125 } 126 } 127 void work(){ 128 scanf("%d",&n); 129 for(int i=1;i<=n;i++){ 130 long long l,r; scanf("%lld%lld",&l,&r); 131 if(i == 1){puts("pp.p.p...");} 132 else if(i == 2){puts("p.p...");} 133 else if(i == 3){puts("pp.p.p...p.p..");} 134 else solveit(l,r); 135 } 136 } 137 } 138 139 140 namespace solve6{ 141 int n,prime[3600000],flag[40000010],num; 142 long long oth[40000100]; 143 int res[203456]; 144 void solveit(long long l,long long r){ 145 flag[1] = 1;int N = 40000000; 146 for(int i=2;i<=N;i++){ 147 if(!flag[i]) prime[++num] = i; 148 for(int j=1;j<=num&&i*prime[j]<=N;j++){ 149 flag[i*prime[j]] = 1; 150 if(i%prime[j] == 0) break; 151 } 152 } 153 for(long long i=l;i<=r;i++) flag[i-l+1]=1,oth[i-l+1]=i; 154 if(r <= 1e12+5){ 155 for(int i=1;prime[i]<=1000000;i++){ 156 long long st = l/prime[i]+(l%prime[i]!=0); 157 if(st == 1) st++; 158 for(long long j=st;j*prime[i]<=r;j++){ 159 while(oth[j*prime[i]-l+1] % prime[i]==0) oth[j*prime[i]-l+1]/=prime[i]; 160 if(j%prime[i] == 0) flag[j*prime[i]-l+1] = 0; 161 else flag[j*prime[i]-l+1]*=-1; 162 } 163 } 164 for(long long i=l;i<=r;i++) if(oth[i-l+1]!=1) flag[i-l+1] *=-1; 165 for(long long i=l;i<=r;i++) 166 if(flag[i-l+1] == -1) printf("-"); 167 else if(flag[i-l+1] == 1) printf("+"); 168 else printf("0"); 169 puts(""); 170 }else{ 171 int nur = 0; 172 for(int i=0;i<sk.length();i++){ 173 int um = (int)sk[i]-'9'; 174 if(sk[i] == '!')um = 92-'9'; 175 for(int j=5;j>=0;j--) res[i*6+j] = (um&1),um>>=1; 176 } 177 for(int i=0;i<ss.length();i++){ 178 if(i!=0){flag[++nur] = -1; oth[nur] = 1;} 179 int dd = 0; 180 if(ss[i] == '!') dd = 92-'9'; 181 else if(ss[i]>'9') dd = ss[i]-'9'; 182 else{for(int j=i;j<ss.length()&&ss[j]!='.';j++,i++)dd = dd*10+ss[j]-'0';}nur += dd; 183 } 184 for(int i=1;i<=num;i++){ 185 long long st = l/prime[i]+(l%prime[i]!=0); 186 if(st == 1) st++; 187 for(long long j=st;j*prime[i]<=r;j++){ 188 while(oth[j*prime[i]-l+1] % prime[i]==0) oth[j*prime[i]-l+1]/=prime[i]; 189 if(j%prime[i] == 0) flag[j*prime[i]-l+1] = 0; 190 else flag[j*prime[i]-l+1]*=-1; 191 } 192 } 193 nur = 0; 194 for(long long i=l;i<=r;i++){ 195 if(flag[i-l+1] == 0 || oth[i-l+1] == 1) { 196 ; 197 }else{ 198 if(oth[i-l+1] > 1e15){ 199 if(res[nur++] == 1) flag[i-l+1]*=-1; 200 //printf("%lld %d\n",i,flag[i-l+1]); 201 }else{flag[i-l+1] *= -1;} 202 } 203 if(flag[i-l+1] == 1) printf("+"); 204 else if(flag[i-l+1] == 0) printf("0"); 205 else printf("-"); 206 } 207 puts(""); 208 } 209 } 210 void work(){ 211 scanf("%d",&n); 212 for(int i=1;i<=n;i++){ 213 long long l,r; scanf("%lld%lld",&l,&r); 214 if(i == 1){puts("--0-+-00+");} 215 else if(i == 2){puts("-+-00+");} 216 else if(i == 3){puts("--0-+-00+-0-++");} 217 else solveit(l,r); 218 } 219 } 220 } 221 222 namespace solve8{ 223 void s99(int l,int r){ 224 int mod =998244353; 225 for(int i=l;i<=r;i++){ 226 int flag = 0; 227 if(fast_pow(i,(mod-1)/2,mod) == 1) flag = 1; 228 if(fast_pow(i,(mod-1)/7,mod) == 1) flag = 1; 229 if(fast_pow(i,(mod-1)/17,mod) == 1) flag = 1; 230 if(flag) printf("."); 231 else printf("g"); 232 } 233 puts(""); 234 } 235 int tab[23] = {0,2,3,5,7,11,13,19,23}; 236 int gg = 6; 237 int res[13500000]; 238 void s13(int l,int r,int p){ 239 for(int i=1;i<=p-1;i++,gg=1ll*gg*6%p){ 240 for(int j=1;j<=8;j++) if(i%tab[j] == 0) res[gg] = 1; 241 } 242 for(int i=1;i<p;i++) if(res[i]) printf("."); else printf("g"); 243 puts(""); 244 } 245 void work(){ 246 int n; scanf("%d",&n); 247 for(int i=1;i<=n;i++){ 248 int a,b,c; scanf("%d%d%d",&a,&b,&c); 249 if(i == 1){puts(".g");} 250 else if(i == 2){puts(".g.gg...g");} 251 else if(n == 4) s99(a,b); 252 else s13(a,b,c); 253 } 254 } 255 } 256 257 namespace solve7{ 258 const int mod = 1515343657; 259 void work(){ 260 int n; scanf("%d",&n); 261 for(int i=1;i<=n;i++){ 262 int l,r,c; 263 if(i != 3) scanf("%d%d%d",&l,&r,&c); 264 else scanf("%d%d",&l,&r); 265 if(i == 1){puts(".g");} 266 else if(i == 2){puts(".g.gg...g");} 267 else { 268 for(int i=l;i<=r;i++){ 269 int flag = 0; 270 if(fast_pow(i,(mod-1)/2,mod) == 1) flag = 1; 271 if(fast_pow(i,(mod-1)/3,mod) == 1) flag = 1; 272 if(fast_pow(i,(mod-1)/4003,mod) == 1) flag = 1; 273 if(fast_pow(i,(mod-1)/15773,mod) == 1) flag = 1; 274 if(flag) printf("."); 275 else printf("g"); 276 } 277 puts(""); 278 } 279 } 280 } 281 } 282 283 int main(){ 284 scanf("%s",str); 285 if(str[0] == '1' && str[1] == '_') solve1::work(); 286 else if(str[0] == '1' && str[1] == '?' && str[2] == '+') solve3::work(); 287 else if(str[0] == '1' && str[1] == '?') solve2::work(); 288 else if(str[0] == '1' && str[1] == 'w') solve4::work(); 289 else if(str[0] == '2' && str[1] == 'p') solve5::work(); 290 else if(str[0] == '2' && str[1] == 'u') solve6::work(); 291 else if(str[2] == '?') solve7::work(); 292 else if(str[1] == 'g') solve8::work(); 293 return 0; 294 }
