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 ];
/////////////////////////////////////////////////////
*/