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 }
