zoj 1022 - Parallel Expectations
题目：有两个指令序列，在执行时，能够执行随意指令序列的下一条指令。每条指令要一直执行到结束。
求两组指令执行结束后，每一个变量里面存储值的期望。
分析：dp，模拟。这道题算不上难题，只是算得上的麻烦题了。
设状态 T[ i ][ j ] 为程序1运行i条指令，程序2运行j条指令后的变量平均值。P1为程序1指令i的概率，
P2为程序2指令j的概率。则easy推出，T[ i ][ j ] = （T[ i-1 ][ j ]*P1+T[ i ][ j-1 ]*P2）/（P1+P2）；
只是须要注意几点：
1.理解题意非常重要，这个题非常easy误解 。
假设觉得每种指令运行的情况是一样的话。就会求错方程：（设N[ i ][ j ]为状态T[ i ][ j ]数量）
P1 = N[ i-1 ][ j ]/N[ i ][ j ]。P2 = N[ i ][ j-1 ]/N[ i ][ j ]。
以下是POJ discuss 里得解释，看了这个就会明确了：
Exactly one execution of the sample input results in S=8。and the probability of that execution is
not 1/C(8,4)=1/70, but (1/2)^4=1/16，since the program automatically execute remaining operations.
It is true that there are 70 different executions, but not all of them have the same probability.
正确的概率计算为：（设N1为程序1指令总条数，N2为程序2指令总条数）
if（i == N1 && j == N2）P1 = P[ i-1 ][ j ] ,P2 = P[ i ][ j-1 ]；
if（i < N1 && j == N2）P1 = P[ i-1 ][ j ] ,P2 = P[ i ][ j-1 ]/2；
if（i == N1 && j < N2） P1 = P[ i-1 ][ j ]/2,P2 = P[ i ][ j-1 ]；
if（i < N1 && j < N2）P1 = P[ i-1 ][ j ]/2,P2 = P[ i ][ j-1 ]/2。
P[ i ][ j ] = P1 + P2。
2.实现起来有点麻烦，要是比赛，仅仅能无题可做时才会做吧，由于这类似个小型的编译器了。
说明：囧，把P[ i-1 ][ j ]当成P1。P[ i ][ j-1 ]当成P2，WA了N次。（2011-09-19 09:35）
/* zoj1022 2011-03-22 03:05:19 */ #include <stdio.h> #include <stdlib.h> #include <string.h> #define max(a,b) ((a)>(b)?(a):(b)) #define min(a,b) ((a)<(b)?(a):(b)) char Command[ 2 ][ 26 ][ 65 ]; struct asmmble { int Varible1; int Varible2; char Operator; }Asmmble[ 2 ][ 105 ]; int Read( char Command[][ 65 ] ) { int List = 0; char ch = 0; while ( 1 ) { int Count = 0; while ( ( ch = getchar() ) != '\n' ) { while ( ch == ' ' ) ch = getchar(); Command[ List ][ Count ++ ] = ch; } Command[ List ][ Count ] = '\0'; if ( !strcmp( Command[ List ], "END" ) ) break; if ( strcmp( Command[ List ], "" ) ) ++ List; } return List; } struct word { int Start; int End; }Word[ 3 ]; struct varible { char Name[ 21 ]; int Length; double Value; bool IsConst; }Varible[ 155 ]; int Search( int& Number, char* String, int number ) { for ( int i = 4 ; i < Number ; ++ i ) if ( Varible[ i ].Length == number && !strcmp( Varible[ i ].Name, String ) ) return i; strcpy( Varible[ Number ].Name, String ); Varible[ Number ].Length = number; Varible[ Number ].IsConst = false; Varible[ Number ].Value = 0.0; return Number ++; } char Change( char ch ) { if ( ch >= 'a' && ch <= 'z' ) return ch - 'a' + 'A'; return ch; } int searchVarible( char* Command, word Word, int& Number ) { int count = 0; char String[ 21 ]; if ( Command[ Word.Start ] >= '0' && Command[ Word.Start ] <= '9' ) { count = Command[ Word.Start ++ ]-'0'; while ( Word.Start <= Word.End ) { count *= 10; count += Command[ Word.Start ++ ]-'0'; } strcpy( Varible[ Number ].Name, "0"); Varible[ Number ].Length = 1; Varible[ Number ].IsConst = true; Varible[ Number ].Value = count; return Number ++; }else { int number = 0; String[ number ++ ] = Change( Command[ Word.Start ++ ] ); while ( Word.Start <= Word.End ) String[ number ++ ] = Change( Command[ Word.Start ++ ] ); String[ number ] = '\0'; return Search( Number, String, number ); } } void commbine( int m, int n, int v1, int v2 ,char o3 ) { Asmmble[ m ][ n ].Varible1 = v1; Asmmble[ m ][ n ].Varible2 = v2; Asmmble[ m ][ n ].Operator = o3; } void Operat( int n, int m, int XX, int YY, int ZZ, char O ) { int R1 = 2*m+0; int R2 = 2*m+1; commbine( m, 4*n+1, R1, YY, ':' ); commbine( m, 4*n+2, R2, ZZ, ':' ); commbine( m, 4*n+3, R1, R2, O ); commbine( m, 4*n+4, XX, R1, ':' ); } int FindChar( char* p, char O ) { int count = 0; while ( p[ count ] ) { if ( p[ count ] == O ) return count; ++ count; } return -1; } int command( int machine, char Command[][ 65 ], int List, int Number ) { for ( int i = 0 ; i < List ; ++ i ) { int space1 = FindChar( Command[ i ], ':' ); int space2 = max( FindChar( Command[ i ], '+' ), FindChar( Command[ i ], '-' ) ); int space3 = strlen( Command[ i ] ); Word[ 0 ].Start = 0; Word[ 0 ].End = space1-1; Word[ 1 ].Start = space1+2; Word[ 1 ].End = space2-1; Word[ 2 ].Start = space2+1; Word[ 2 ].End = space3-1; int X = searchVarible( Command[ i ], Word[ 0 ], Number ); int Y = searchVarible( Command[ i ], Word[ 1 ], Number ); int Z = searchVarible( Command[ i ], Word[ 2 ], Number ); Operat( i, machine, X, Y, Z, Command[ i ][ space2 ] ); } return Number; } void calculate( double* Var, asmmble Asm ) { switch( Asm.Operator ) { case ':': Var[ Asm.Varible1 ] = Var[ Asm.Varible2 ];break; case '+': Var[ Asm.Varible1 ] += Var[ Asm.Varible2 ];break; case '-': Var[ Asm.Varible1 ] -= Var[ Asm.Varible2 ];break; } } int cmpstr( char* a, char* b, int n ) { for ( int i = 0 ; i < n ; ++ i ) if ( a[ i ] != b[ i ] ) return a[ i ] - b[ i ]; return 0; } int cmp( const void* a, const void* b ) { struct varible* p = (struct varible*)a; struct varible* q = (struct varible*)b; if ( p->IsConst == q->IsConst ) { int value = cmpstr( p->Name, q->Name, min( p->Length, q->Length ) ); if ( !value ) return p->Length - q->Length; else return value; }else return q->IsConst - p->IsConst; } double M1[ 55 ],M2[ 55 ]; double P[ 105 ][ 105 ],P1,P2; double T[ 101 ][ 101 ][ 35 ]; void dp( int number1, int number2, int count ) { P[ 0 ][ 0 ] = 1.0; for ( int k = 0 ; k < count ; ++ k ) if ( Varible[ k ].IsConst ) T[ 0 ][ 0 ][ k ] = Varible[ k ].Value+0.0; else T[ 0 ][ 0 ][ k ] = 0.0; for ( int i = 1 ; i <= number1 ; ++ i ) { P[ i ][ 0 ] = 0.5*P[ i-1 ][ 0 ]; for ( int k = 0 ; k < count ; ++ k ) T[ i ][ 0 ][ k ] = T[ i-1 ][ 0 ][ k ]; calculate( T[ i ][ 0 ], Asmmble[ 0 ][ i ] ); } for ( int j = 1 ; j <= number2 ; ++ j ) { P[ 0 ][ j ] = 0.5*P[ 0 ][ j-1 ]; for ( int k = 0 ; k < count ; ++ k ) T[ 0 ][ j ][ k ] = T[ 0 ][ j-1 ][ k ]; calculate( T[ 0 ][ j ], Asmmble[ 1 ][ j ] ); } for ( int i = 1 ; i <= number1 ; ++ i ) for ( int j = 1 ; j <= number2 ; ++ j ) { for ( int k = 0 ; k < count ; ++ k ) { M1[ k ] = T[ i-1 ][ j ][ k ]; M2[ k ] = T[ i ][ j-1 ][ k ]; } calculate( M1, Asmmble[ 0 ][ i ] ); calculate( M2, Asmmble[ 1 ][ j ] ); if ( i < number1 && j < number2 ) { P1 = P[ i-1 ][ j ]/2;P2 = P[ i ][ j-1 ]/2; }else if ( i < number1 ) { P1 = P[ i-1 ][ j ]; P2 = P[ i ][ j-1 ]/2; }else if ( j < number2 ) { P1 = P[ i-1 ][ j ]/2;P2 = P[ i ][ j-1 ]; }else { P1 = P[ i-1 ][ j ] ;P2 = P[ i ][ j-1 ]; } P[ i ][ j ] = P1 + P2; //用 P[ i-1 ][ j ],P[ i ][ j-1 ] 取代 P1,P2的值了。
。。
for ( int k = 0 ; k < count ; ++ k ) T[ i ][ j ][ k ] = (P1*M1[ k ]+P2*M2[ k ])/(P[ i ][ j ]); } for ( int k = 0 ; k < count ; ++ k ) Varible[ k ].Value = T[ number1 ][ number2 ][ k ]; qsort( &Varible[ 4 ], count-4, sizeof( Varible[ 0 ] ), cmp ); int start = 4; while ( Varible[ start ].IsConst ) ++ start; for ( int i = start ; i < count ; ++ i ) printf("%.4lf\n",Varible[ i ].Value); } void Initial( void ) { for ( int k = 0 ; k < 4 ; ++ k ) { Varible[ k ].IsConst = false; Varible[ k ].Value = 0.0; } } int main() { int t,line1,line2,numb1,numb2; while ( scanf("%d",&t) != EOF ) while ( t -- ) { Initial(); line1 = Read( Command[ 0 ] ); line2 = Read( Command[ 1 ] ); numb1 = command( 0, Command[ 0 ], line1, 00004 ); numb2 = command( 1, Command[ 1 ], line2, numb1 ); dp( 4*line1, 4*line2, numb2 ); if ( t ) printf("\n"); } return 0; } /* 測试 ////////////////////////////////////////////// void test( int number1, int number2, int count ) { int save[ 2 ]; save[ 0 ] = number1; save[ 1 ] = number2; for ( int machine = 0 ; machine <= 1 ; ++ machine ) { printf("machine %d:\n__________________\n",machine+1); for ( int k = 1 ; k <= save[ machine ] ; ++ k ) printf("%3s %3s %3s\n",deal1(Asmmble[ machine ][ k ].Operator, A1), deal2(Asmmble[ machine ][ k ].Varible1, A2), deal2(Asmmble[ machine ][ k ].Varible2, A3)); printf("\n"); } } char* deal1( char Operator, char* Answer ) { switch( Operator ) { case ':': strcpy( Answer, "MOV" );break; case '+': strcpy( Answer, "ADD" );break; case '-': strcpy( Answer, "SUB" );break; } return Answer; } char* deal2( int Value, char* Answer ) { if ( Value < 4 ) { Answer[ 0 ] = 'R'; Answer[ 1 ] = Value/2+'1'; Answer[ 2 ] = Value%2+'1'; Answer[ 3 ] = '\0'; }else if ( Varible[ Value ].IsConst ) { Answer[ 0 ] = (int)Varible[ Value ].Value/100+'0'; Answer[ 1 ] = (int)Varible[ Value ].Value%100/10+'0'; Answer[ 2 ] = (int)Varible[ Value ].Value%10+'0'; Answer[ 3 ] = '\0'; }else strcpy( Answer, Varible[ Value ].Name ); return Answer; } char A1[ 20 ],A2[ 20 ],A3[ 20 ]; ///////////////////////////////////////////////////// */
