1 /* 2 POJ3318 Matrix Multiplication 3 http://poj.org/problem?id=3318 4 随机化算法 矩阵 5 随机一个1×n的矩阵h 6 在ab=c左右两边左乘h 7 验证是否相等 8 然而不知道为什么g++交就会RE， 9 c++交AC 10 * 11 */ 12 #include <cstdio> 13 #include <algorithm> 14 #include <cstring> 15 #include <cmath> 16 #include <vector> 17 #include <queue> 18 #include <iostream> 19 #include <map> 20 #include <set> 21 #include <ctime> 22 #include <cstdlib> 23 //#define test 24 using namespace std; 25 const int Nmax=505; 26 const int mod=500; 27 int n; 28 struct Matrix 29 { 30 int n,m; 31 int num[Nmax][Nmax]; 32 Matrix() 33 { 34 n=0; 35 m=0; 36 } 37 Matrix &operator = (const Matrix b) 38 { 39 n=b.n; 40 m=b.m; 41 for(int i=1;i<=n;i++) 42 for(int j=1;j<=m;j++) 43 num[i][j]=b.num[i][j]; 44 //show(); 45 return *this; 46 } 47 //Matrix(Matrix &a) 48 //{ 49 //*this=a; 50 //} 51 Matrix(int _n,int _m,int **_num) 52 { 53 n=_n; 54 m=_m; 55 for(int i=1;i<=n;i++) 56 for(int j=1;j<=m;j++) 57 num[i][j]=_num[i][j]; 58 } 59 friend Matrix operator + (Matrix a,Matrix b) 60 { 61 Matrix ans; 62 ans.n=a.n; 63 ans.m=a.m; 64 for(int i=1;i<=ans.n;i++) 65 for(int j=1;j<=ans.m;j++) 66 ans.num[i][j]=a.num[i][j]+b.num[i][j]; 67 return ans; 68 } 69 friend Matrix operator * (Matrix a,Matrix b) 70 { 71 Matrix ans; 72 if(a.m!=b.n) 73 { 74 printf("error! "); 75 return ans; 76 } 77 ans.n=a.n,ans.m=b.m; 78 int tmp=a.m; 79 for(int i=1;i<=ans.n;i++) 80 for(int j=1;j<=ans.m;j++) 81 ans.num[i][j]=0; 82 for(int i=1;i<=ans.n;i++) 83 for(int j=1;j<=ans.m;j++ ) 84 for(int k=1;k<=tmp;k++) 85 ans.num[i][j]+=a.num[i][k]*b.num[k][j]; 86 //ans.show(); 87 return ans; 88 } 89 friend bool operator != (Matrix a,Matrix b) 90 { 91 if(a.n!=b.n || a.m!=b.m) 92 return 1; 93 for(int i=1;i<=a.n;i++) 94 for(int j=1;j<=a.m;j++) 95 if(a.num[i][j]!=b.num[i][j]) 96 return 1; 97 return 0; 98 } 99 void show() 100 { 101 printf("n:%d m:%d ",n,m); 102 for(int i=1;i<=n;i++) 103 for(int j=1;j<=m;j++) 104 printf("%d%c",num[i][j],j==m? ' ':' '); 105 } 106 }; 107 Matrix a,b,c,h; 108 //Matrix tmpa,tmpb,tmpc; 109 int work() 110 { 111 srand(unsigned(time(0))); 112 h.n=1,h.m=n; 113 for(int t=1;t<=5;t++) 114 { 115 for(int i=1;i<=n;i++) 116 { 117 h.num[1][i]=rand()%mod; 118 119 } 120 //h.show(); 121 //tmpa=h*a; 122 //tmpb=tmpa*b; 123 //tmpc=h*c; 124 //tmpa.show(); 125 //tmpb.show(); 126 //tmpc.show(); 127 if( ( (h*a)*b )!=(h*c) ) 128 return 0; 129 } 130 131 return 1; 132 } 133 int main() 134 { 135 #ifdef test 136 #endif 137 //freopen("poj3318.in","r",stdin); 138 scanf("%d",&n); 139 a.n=a.m=b.n=b.m=c.n=c.m=n; 140 for(int i=1;i<=n;i++) 141 for(int j=1;j<=n;j++) 142 scanf("%d",&a.num[i][j]); 143 for(int i=1;i<=n;i++) 144 for(int j=1;j<=n;j++) 145 scanf("%d",&b.num[i][j]); 146 for(int i=1;i<=n;i++) 147 for(int j=1;j<=n;j++) 148 scanf("%d",&c.num[i][j]); 149 if(work()) 150 printf("YES "); 151 else 152 printf("NO "); 153 return 0; 154 }