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
  2 using namespace std;
  3 
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  5 string sk = 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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){
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'.';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){
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){
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'.';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;iif(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 }

 

转载于:https://www.cnblogs.com/Menhera/p/10959648.html