2017 07 30 得分：65
一句话：原来OI是个文科竞赛……
A、Password
吐槽：尼玛啊……我为什么要旷了HEOI2017 day1讲评……
题解：就是那个毕老师的“相逢是问候”思路啊……观察数列可以意识到这个数列的指数是$Fibonacci$数列，因此一个矩阵快速幂日翻；然而它的增长速度过快，需要减小幂次。这时我们请出完美错过的欧拉定理，降次之后再套一个快速幂即可。
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 #include<cmath> 6 using namespace std; 7 const int prime[]={0,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8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01,42131,42139,42157,42169,42179,42181,42187,42193,42197,42209,42221,42223,42227,42239,42257,42281,42283,42293,42299,42307,42323,42331,42337,42349,42359,42373,42379,42391,42397,42403,42407,42409,42433,42437,42443,42451,42457,42461,42463,42467,42473,42487,42491,42499,42509,42533,42557,42569,42571,42577,42589,42611,42641,42643,42649,42667,42677,42683,42689,42697,42701,42703,42709,42719,42727,42737,42743,42751,42767,42773,42787,42793,42797,42821,42829,42839,42841,42853,42859,42863,42899,42901,42923,42929,42937,42943,42953,42961,42967,42979,42989,43003,43013,43019,43037,43049,43051,43063,43067,43093,43103,43117,43133,43151,43159,43177,43189,43201,43207,43223,43237,43261,43271,43283,43291,43313,43319,43321,43331,43391,43397,43399,43403,43411,43427,43441,43451,43457,43481,43487,43499,43517,43541,43543,43573,43577,43579,43591,43597,43607,43609,43613,43627,43633,43649,43651,43661,43669,43691,43711,43717,43721,43753,43759,43777,43781,43783,43787,43789,43793,43801,43853,43867,43889,43891,43913,43933,43943,43951,43961,43963,43969,43973,43987,43991,43997,44017,44021,44027,44029,44041,44053,44059,44071,44087,44089,44101,44111,44119,44123,44129,44131,44159,44171,44179,44189,44201,44203,44207,44221,44249,44257,44263,44267,44269,44273,44279,44281,44293,44351,44357,44371,44381,44383,44389,44417,44449,44453,44483,44491,44497,44501,44507,44519,44531,44533,44537,44543,44549,44563,44579,44587,44617,44621,44623,44633,44641,44647,44651,44657,44683,44687,44699,44701,44711,44729,44741,44753,44771,44773,44777,44789,44797,44809,44819,44839,44843,44851,44867,44879,44887,44893,44909,44917,44927,44939,44953,44959,44963,44971,44983,44987,45007,45013,45053,45061,45077,45083,45119,45121,45127,45131,45137,45139,45161,45179,45181,45191,45197,45233,45247,45259,45263,45281,45289,45293,45307,45317,45319,45329,45337,45341,45343,45361,45377,45389,45403,45413,45427,45433,45439,45481,45491,45497,45503,45523,45533,45541,45553,45557,45569,45587,45589,45599,45613,45631,45641,45659,45667,45673,45677,45691,45697,45707,45737,45751,45757,45763,45767,45779,45817,45821,45823,45827,45833,45841,45853,45863,45869,45887,45893,45943,45949,45953,45959,45971,45979,45989,46021,46027,46049,46051,46061,46073,46091,46093,46099,46103,46133,46141,46147,46153,46171,46181,46183,46187,46199,46219,46229,46237,46261,46271,46273,46279,46301,46307,46309,46327,46337,46349}; 8 long long euler_phi(int x) 9 { 10 long long m=(long long)sqrt(x+0.5); 11 long long ans=x; 12 for(int i=1;prime[i]<=m;i++) 13 if(x%prime[i]==0) 14 { 15 ans=ans/prime[i]*(prime[i]-1); 16 while(x%prime[i]==0)x/=prime[i]; 17 } 18 if(x>1)ans=ans/x*(x-1); 19 return ans; 20 } 21 int m,p,q,n,mod; 22 struct matrix 23 { 24 long long a[2][2]; 25 matrix operator *(const matrix &b) 26 { 27 matrix c; 28 for(int i=0;i<=1;i++) 29 for(int j=0;j<=1;j++)c.a[i][j]=0; 30 for(int i=0;i<=1;i++) 31 for(int j=0;j<=1;j++) 32 for(int k=0;k<=1;k++)c.a[i][j]=(c.a[i][j]+a[i][k]*b.a[k][j])%mod; 33 return c; 34 } 35 }ans,Fibonacci={1,1,1,0}; 36 int qpow(matrix x,int tim) 37 { 38 matrix tmp={1,0,0,1}; 39 for(;tim;tim>>=1,x=x*x) 40 if(tim&1)tmp=tmp*x; 41 return tmp.a[0][1]; 42 } 43 long long qpow(long long base,int tim) 44 { 45 long long tmp=1; 46 for(;tim;tim>>=1,base=base*base%q) 47 if(tim&1)tmp=tmp*base%q; 48 return tmp%q; 49 } 50 int haha() 51 { 52 scanf("%d%d",&m,&p); 53 while(m--) 54 { 55 scanf("%d%d",&n,&q); 56 Fibonacci=(matrix){1,1,1,0}; 57 mod=euler_phi(q); 58 int tim=qpow(Fibonacci,n); 59 printf("%d ",qpow(p,tim)); 60 } 61 } 62 int sb=haha(); 63 int main(){;}
（比较懒，直接贴了个素数表……）
B、斗地主
吐槽：早就听说这题是个偏题坑题防AK好题，今日一见名不虚传！辣鸡出题人！你斗没斗过地主懂不懂规则啊！怎么可以四个二带俩王啊！题面什么破玩意啊！根本看不出这是斗地主啊！还有那个花色，什么破玩意，****……（此处省略$2147483647$个*）
题解：经典大爆搜，注意顺序。
1 #include<iostream> 2 #include<cstdio> 3 #include<algorithm> 4 #include<cstring> 5 using namespace std; 6 int num[25],ans,nume[25]; 7 int convert(int x) 8 { 9 if(x==1)return 12; 10 if(x==2)return 13; 11 if(!x)return 14; 12 return x-2; 13 } 14 int doit() 15 { 16 int tmp=0; 17 while(nume[4]&&nume[2]>=2) 18 { 19 tmp++; 20 nume[4]--; 21 nume[2]-=2; 22 } 23 while(nume[4]&&nume[1]>=2) 24 { 25 tmp++; 26 nume[4]--; 27 nume[1]-=2; 28 } 29 while(nume[3]&&nume[2]) 30 { 31 tmp++; 32 nume[3]--; 33 nume[2]--; 34 } 35 while(nume[3]&&nume[1]) 36 { 37 tmp++; 38 nume[3]--; 39 nume[1]--; 40 } 41 tmp+=nume[1]+nume[2]+nume[3]+nume[4]; 42 return tmp; 43 } 44 void dfs(int cnt,int st) 45 { 46 if(cnt<0)return; 47 if(st>ans)return; 48 if(cnt==0) 49 { 50 ans=min(ans,st); 51 return; 52 } 53 for(int i=1;i<=4;i++)nume[i]=0; 54 for(int i=1;i<=14;i++) 55 nume[num[i]]++; 56 int k=doit(); 57 ans=min(ans,st+k); 58 for(int i=1;i<=12;i++) 59 { 60 int k=i; 61 for(k=i;k<=12&&num[k]>=3;k++); 62 k--; 63 if(k-i>=1) 64 { 65 for(int l=k;l>=i+1;l--) 66 { 67 for(int j=i;j<=l;j++) 68 { 69 num[j]-=3; 70 cnt-=3; 71 } 72 dfs(cnt,st+1); 73 for(int j=i;j<=l;j++) 74 { 75 num[j]+=3; 76 cnt+=3; 77 } 78 } 79 } 80 for(k=i;k<=12&&num[k]>=2;k++); 81 k--; 82 if(k-i>=2) 83 { 84 for(int l=k;l>=i+2;l--) 85 { 86 for(int j=i;j<=l;j++) 87 { 88 num[j]-=2; 89 cnt-=2; 90 } 91 dfs(cnt,st+1); 92 for(int j=i;j<=l;j++) 93 { 94 num[j]+=2; 95 cnt+=2; 96 } 97 } 98 } 99 for(k=i;k<=12&&num[k]>=1;k++); 100 k--; 101 if(k-i>=4) 102 { 103 for(int l=k;l>=i+4;l--) 104 { 105 for(int j=i;j<=l;j++) 106 { 107 num[j]--; 108 cnt--; 109 } 110 dfs(cnt,st+1); 111 for(int j=i;j<=l;j++) 112 { 113 num[j]++; 114 cnt++; 115 } 116 } 117 } 118 } 119 } 120 int haha() 121 { 122 //freopen("landlords.in","r",stdin); 123 //freopen("landlords.out","w",stdout); 124 int t,n;scanf("%d%d",&t,&n); 125 while(t--) 126 { 127 memset(num,0,sizeof(num)); 128 for(int i=1;i<=n;i++) 129 { 130 int x;scanf("%d%*d",&x); 131 num[convert(x)]++; 132 } 133 ans=0x7f7f7f7f; 134 dfs(n,0); 135 printf("%d ",ans); 136 } 137 } 138 int sb=haha(); 139 int main(){;}
C、抵制克苏恩
吐槽：出题人你不会玩炉石就不要来瞎吹好不好！你见过哪个克苏恩活过50回合的！再说了，你打个克苏恩至于弄一群奴隶主精神污染！弄个血厚的上去他不就滚粗了！退一步不说你技术不行，好歹你解释清题意啊！你可以把炉石可以加护盾这个东西放上去，不要只放个$30$滴血还用阿拉伯数字特殊标明，故意不让我们A是不是！*****……（此处省略$9223372036854775807LL$个*）
题解：很明显可以概率dp。设$f[i][j][k][l]$为第$i$回合，有$j$个一血奴隶主，$k$个二血奴隶主，$l$个三血奴隶主。那么克苏恩日到每个角色的概率就是[frac{1}{1+j+k+l}]。
如果日到自己，就会转移到$f[i+1][j][k][l]$，概率为[frac{1}{1+j+k+l}]。
如果日到一血奴隶主，就会转移到$f[i+1][j-1][k][l]$，概率为[frac{j}{1+j+k+l}]。
如果日到二血奴隶主，视场上情况会转移到$f[i+1][j+1][k-1][l+1]$或$f[i+1][j+1][k-1][l]$，概率为[frac{k}{1+j+k+l}]。
如果日到三血奴隶主，视场上情况会转移到$f[i+1][j][k+1][l]$或$f[i+1][j][k+1][l-1]$，概率为[frac{l}{1+j+k+l}]。
那么结果就是
[ sum_{j=0,k=0,l=0}^{j+k+l<=7} {frac{f[n][j][k][l]}{j+k+l+1}}]
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 double f[55][8][8][8]; 7 int a[5],K; 8 int haha() 9 { 10 int t;scanf("%d",&t); 11 while(t--) 12 { 13 scanf("%d%d%d%d",&K,&a[1],&a[2],&a[3]); 14 memset(f,0,sizeof(f)); 15 f[1][a[1]][a[2]][a[3]]=1.0; 16 double ans=0; 17 for(int i=1;i<K;i++) 18 for(int j=0;j<=7;j++) 19 for(int k=0;j+k<=7;k++) 20 for(int l=0;j+k+l<=7;l++) 21 { 22 double p=1.0/((j+k+l+1)*1.0); 23 f[i+1][j][k][l]+=f[i][j][k][l]*p; 24 ans+=f[i][j][k][l]*p; 25 if(j) 26 f[i+1][j-1][k][l]+=f[i][j][k][l]*j*p; 27 if(j+k+l<7) 28 { 29 if(k)f[i+1][j+1][k-1][l+1]+=f[i][j][k][l]*k*p; 30 if(l)f[i+1][j][k+1][l]+=f[i][j][k][l]*l*p; 31 } 32 else 33 { 34 if(k)f[i+1][j+1][k-1][l]+=f[i][j][k][l]*k*p; 35 if(l)f[i+1][j][k+1][l-1]+=f[i][j][k][l]*l*p; 36 } 37 } 38 for(int i=0;i<=7;i++) 39 for(int j=0;i+j<=7;j++) 40 for(int k=0;i+j+k<=7;k++) 41 ans+=(f[K][i][j][k]*1.0)/((i+j+k+1)*1.0); 42 printf("%0.2lf ",ans); 43 //while(1); 44 } 45 } 46 int sb=haha(); 47 int main(){;}
无限○|￣|_前五神犇！我明天要爆零了……明天一定全是AK的……世界再见我要AFO了……
（上方空白处滑动有惊喜）