链接：http://acm.hdu.edu.cn/showproblem.php?pid=1502
思路：给定一个n，分别由n个a,b,c组成的字符串的所有前缀中a的个数大于等于b的个数大于等于c的个数，求满足这一条件的字符串的个数有多少，本题要用到dp及大数运算，转移方程：dp[i][j][k]=dp[i-1][j][k]+dp[i][j-1][k]+dp[i][j][k-1],其中i,j,k分别代表a,b,c的个数
老实说并不会写大数，不过发现了一段很神奇的代码
1 #include<iostream> 2 #include<iomanip> 3 #include<cstdio> 4 #include<cstring> 5 #include<sstream> 6 #include<stack> 7 #include<queue> 8 #include<fstream> 9 #include<algorithm> 10 #include<map> 11 #include<set> 12 #include<vector> 13 #include<cmath> 14 #define CLR(x) memset(x,0,sizeof(x)) 15 #define ll long long 16 #define eps 1e-6 17 #define pow2(x) ((x)*(x)) 18 #define forto(i,n) for(int i=0;i<n;i++) 19 #define for1to(i,n) for(int i=1;i<=n;i++) 20 #define VI vector<int> 21 using namespace std; 22 const double PI=acos(-1.0); 23 #define INF 0x3fffffff ///INT_MAX一半防止上溢 24 #define NINF 0xbfffffff 25 26 int dp[61][61][61][100]; 27 28 int add(int A[],int B[]) ///Add B to A 29 { 30 for (int i=0;i<100;i++) 31 { 32 A[i]+=B[i]; 33 A[i+1]+=A[i]/10000; 34 A[i]%=10000; 35 } 36 } 37 38 39 40 int main() 41 { 42 dp[0][0][0][0]=1; 43 for (int i=1;i<=60;i++) 44 for (int j=0;j<=i;j++) 45 for (int k=0;k<=j;k++) 46 { 47 add(dp[i][j][k],dp[i-1][j][k]); 48 add(dp[i][j][k],dp[i][j-1][k]); 49 add(dp[i][j][k],dp[i][j][k-1]); 50 } 51 52 int n; 53 while (cin>>n) 54 { 55 int k(99); 56 while (!dp[n][n][n][k]) 57 k--; 58 for (int i=k;i>=0;i--) 59 { 60 if (i!=k) 61 cout<<setw(4)<<setfill('0'); 62 cout<<dp[n][n][n][i]; 63 } 64 cout<<" "<<endl; 65 } 66 return 0; 67 }
还有打表的代码
1 #include<iostream> 2 #include<stdio.h> 3 #include<string.h> 4 using namespace std; 5 char s[150][1000]={ 6 "1", 7 "1", 8 "5", 9 "42", 10 "462", 11 "6006", 12 "87516", 13 "1385670", 14 "23371634", 15 "414315330", 16 "7646001090", 17 "145862174640", 18 "2861142656400", 19 "57468093927120", 20 "1178095925505960", 21 "24584089974896430", 22 "521086299271824330", 23 "11198784501894470250", 24 "243661974372798631650", 25 "5360563436201569896300", 26 "119115896614816702500900", 27 "2670926804331443293626900", 28 "60386171228363065768956000", 29 "1375596980582110638216817680", 30 "31554078431506568639711925552", 31 "728440733705121725605657358256", 32 "16916012593818937850175820875056", 33 "394984727560107218767652172156480", 34 "9269882950945137003216002357575872", 35 "218589820552932101591964442689934272", 36 "5177405669064206309480641678873685136", 37 "123139887106265725065261170839575261246", 38 "2940211742938376804365727956142799686970", 39 "70461309651358512358741033490151564263034", 40 "1694426732092192797198296281548882854896770", 41 "40879953049935966764838175153044218787509460", 42 "989318124094680800242093703952690318964293660", 43 "24011992526103689868224096174884123328708261100", 44 "584414956558400574946623386902564355477176447080", 45 "14261150342358043298392602404780869211095488665940", 46 "348876433985002864104580005170614922408018905657020", 47 "8555006509113973886896694412506009110609925390878620", 48 "210257823823361408953856390159370731312558948560177500", 49 "5178713915261459187808923452167773648813573133021584000", 50 "127816663734641521693312994768720558317819058630953008000", 51 "3160890723051037742300958639363743464856851891194511344000", 52 "78316111638147520232116305011469771592038383559489541704000", 53 "1943917771018304520047172570820410402016667020494472553010000", 54 "48334523581589010102952513742546024844918906756931542442556400", 55 "1203813957908516875152358489329058054078745007110871474716375280", 56 "30029983483935083858438698423851117882968874317657169412268673840", 57 "750270153399794678576435057573545926324276055884108148422050727840", 58 "18772482769028405636917719941593858764528793976890630506115671775200", 59 "470373947038907707302405010980987131831213397364392909428995307126880", 60 "11802109943885320655951253002795677125946808879324767545672973160638080", 61 "296516920131524804299707608337156053506400465189952712435084509896783040", 62 "7459203321130790040650176332416188852363369960068846727881499803410725440", 63 "187875141510304732204453155491218970539216498205240765481036372897711988800", 64 "4737637890492057297860769571861620074038072983555206964113320603342642320960", 65 "119605940186192921945993199027326146131452990076639651225155962772912609414400", 66 "3022912056752362939484322031260179006906680462576858197252183463144268821651200", 67 }; 68 int main() 69 { 70 int n; 71 while(scanf("%d",&n)>0) 72 { 73 printf("%s ",s[n]); 74 } 75 return 0; 76 }