POJ-3185 The Water Bowls 高斯消元

　　题目连接：http://poj.org/problem?id=3185

　　异或高斯消元简单题。

  1 //STATUS:C++_AC_16MS_488KB

  2 #include <functional>

  3 #include <algorithm>

  4 #include <iostream>

  5 //#include <ext/rope>

  6 #include <fstream>

  7 #include <sstream>

  8 #include <iomanip>

  9 #include <numeric>

 10 #include <cstring>

 11 #include <cassert>

 12 #include <cstdio>

 13 #include <string>

 14 #include <vector>

 15 #include <bitset>

 16 #include <queue>

 17 #include <stack>

 18 #include <cmath>

 19 #include <ctime>

 20 #include <list>

 21 #include <set>

 22 #include <map>

 23 using namespace std;

 24 //using namespace __gnu_cxx;

 25 //define

 26 #define pii pair<int,int>

 27 #define mem(a,b) memset(a,b,sizeof(a))

 28 #define lson l,mid,rt<<1

 29 #define rson mid+1,r,rt<<1|1

 30 #define PI acos(-1.0)

 31 //typedef

 32 typedef long long LL;

 33 typedef unsigned long long ULL;

 34 //const

 35 const int N=300;

 36 const int INF=0x3f3f3f3f;

 37 const int MOD=100000,STA=8000010;

 38 const LL LNF=1LL<<60;

 39 const double EPS=1e-8;

 40 const double OO=1e15;

 41 const int dx[4]={-1,0,1,0};

 42 const int dy[4]={0,1,0,-1};

 43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};

 44 //Daily Use ...

 45 inline int sign(double x){return (x>EPS)-(x<-EPS);}

 46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}

 47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}

 48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}

 49 template<class T> inline T Min(T a,T b){return a<b?a:b;}

 50 template<class T> inline T Max(T a,T b){return a>b?a:b;}

 51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}

 52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}

 53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}

 54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}

 55 //End

 56 

 57 int ma[N],A[N][N],B[N],vis[N],num[N];

 58 

 59 void getA(int n)

 60 {

 61     int i,j,k;

 62     mem(A,0);

 63     for(i=0;i<n;i++){

 64         A[i][i]=1;A[i][n]=ma[i];

 65         if(i-1>=0)A[i][i-1]=1;

 66         if(i+1<n)A[i][i+1]=1;

 67     }

 68 }

 69 

 70 int gauss(int n)

 71 {

 72     int i,j,k,cnt,row,ok,ret,up,free;

 73     for(i=row=0;i<n;i++){

 74         if(!A[row][i]){

 75             for(j=row+1;j<n;j++){

 76                 if(A[j][i]){

 77                     for(k=i;k<=n;k++)swap(A[row][k],A[j][k]);

 78                     break;

 79                 }

 80             }

 81         }

 82         if(A[row][i]!=1)continue;

 83         for(j=0;j<n;j++){

 84             if(j!=row && A[j][i]){

 85                 for(k=i;k<=n;k++)

 86                     A[j][k]^=A[row][k];

 87             }

 88         }

 89         row++;

 90     }

 91     for(i=n-1;i>=row;i--)

 92         if(A[i][n])return -1;

 93     if(row==n){

 94         for(i=ret=0;i<n;i++)if(A[i][n])ret++;

 95         return ret;

 96     }

 97     mem(vis,0);

 98     for(i=k=j=0;i<n;i++,j++){

 99         while(!A[i][j] && j<n){

100             vis[j]=1;

101             num[k++]=j++;

102         }

103     }

104     ret=INF;free=n-row;

105     up=1<<free;

106     for(k=0;k<up;k++){

107         for(i=0;i<free;i++)B[num[i]]=(k&(1<<i))?1:0;

108         for(i=n-1;i>=0;i--){

109             if(vis[i])continue;

110             B[i]=0;

111             for(j=row;j<n;j++)B[i]^=B[j]*A[i][j];

112             B[i]^=A[i][n];

113         }

114         for(i=cnt=0;i<n;i++)if(B[i])cnt++;

115         ret=Min(ret,cnt);

116     }

117     return ret;

118 }

119 

120 int main()

121 {

122  //   freopen("in.txt","r",stdin);

123     int i,j,ans;

124     while(~scanf("%d",&ma[0]))

125     {

126         for(i=1;i<20;i++)

127             scanf("%d",&ma[i]);

128 

129         getA(20);

130 

131         ans=gauss(20);

132         if(ans>=0)printf("%d\n",ans);

133     }

134     return 0;

135 }