学步园

题意：奶牛有20只碗摆成一排，用鼻子顶某只碗的话，包括左右两只在内的一共三只碗会反向，现在给出碗的初始状态，问至少要用鼻子顶多少次才能使所有碗都朝上。

#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
using namespace std;

int a[30][30], x[30];
int fre[30], index[30], fnum;
int equ, var, order, ans;

void Debug ()
{
    for ( int i = 0; i < equ; i++ )
    {
        for ( int j = 0; j <= var; j++ )
            printf("%d ",a[i][j]);
        printf("\n");
    }
    printf("\n");
}

int cal ()
{
    int i, j, k, sum;
    k = var - 1; sum = 0;
    for ( i = order - 1; i >= 0 && k >= 0; i-- )
    {
        while ( k >= 0 && fre[k] )
            sum += x[k--];

        if ( k >= 0 )
        {
            x[k] = a[i][var];
            for ( j = k + 1; j < var; j++ )
                x[k] ^= ( a[i][j] && x[j] );
            sum += x[k--];
        }
    }
    return sum;
}

void dfs ( int k, int cnt )
{
    if ( cnt >= ans ) //剪枝
        return;
    if ( k >= fnum )
    {
        int tmp = cal();
        if ( ans > tmp ) ans = tmp;
        return;

    }
    x[index[k]] = 0;
    dfs ( k + 1, cnt );
    x[index[k]] = 1;
    dfs ( k + 1, cnt + 1 );
}

int Gauss ()
{
    int i, j, row, col, mr;
    row = col = fnum = 0;
    while ( row < equ && col < var )
    {
        mr = row;
        for ( i = row + 1; i < equ; i++ )
            if ( abs(a[i][col]) > abs(a[mr][col]) ) mr = i;

        if ( mr != row )
            for ( j = col; j <= var; j++ )
                swap ( a[mr][j], a[row][j] );

        if ( a[row][col] == 0 )
        {
            fre[col] = 1;
            index[fnum++] = col;
            col++; continue;
        }
        for ( i = row + 1; i < equ; i++ )
        {
            if ( a[i][col] == 0 ) continue;
            for ( j = col + 1; j <= var; j++ )
                a[i][j] ^= a[row][j];
        }
        row++; col++;
    }
    order = row;
    ans = 30;
    dfs ( 0, 0 );
    return ans;
}


int main()
{
    equ = var = 20;
    memset(a,0,sizeof(a));

    for ( int i = 0; i < equ; i++ )
    {
        a[i][i] = 1;
        if ( i != 0 ) a[i][i-1] = 1;
        if ( i != equ - 1 ) a[i][i+1] = 1;
    }
    for ( int i = 0; i < equ; i++ )
        scanf("%d",&a[i][var]);
    Gauss();
    printf("%d\n",ans);
    return 0;
}