标签：style class blog code http tar
550
结论：同一层的交点共线。
很容易猜到，也可以跑几组数据验证。
利用结论就可以按层算，再利用对称性简化计算。
1 using namespace std; 2 #define maxn 70100 3 class TriangleXor { 4 public: 5 int theArea(int); 6 }; 7 double l[maxn] , x[maxn] , y[maxn] , H; 8 int idx; 9 10 void addpoint(double k,double w) {// y = kx + 1 , y = x/w 11 double X = w/(1.0-k*w); 12 double Y = X/w; 13 x[++idx] = X; 14 y[idx] =Y; 15 } 16 17 double dist(double x0,double y0,double x1,double y1) { 18 return sqrt((x0-x1)*(x0-x1)+(y0-y1)*(y0-y1)); 19 } 20 21 int TriangleXor::theArea(int w) { 22 double ans = 0.0; 23 if (w%2==0) { 24 ans = 0.5 * w / 2.0; 25 } 26 x[0] = y[0] = 0; 27 for (int i=1 ; i<=w ; i++ ) { 28 addpoint(-1.0/(double)i,w); 29 } 30 // H = (double)w / sqrt(1.0+w*w); 31 for (int i=0 ; i<w ; i+=2 ) { 32 if (i+1<=w) { 33 // double tmp = dist(x[i],y[i],x[i+1],y[i+1]); 34 // ans += tmp*H; 35 H = x[i+1]-x[i]; 36 ans += H; 37 } 38 } 39 for (int i=0 ; i<w ; i+=2 ) if (i+2<=w) { 40 H = y[i+2] - y[i]; 41 double len = 2.0 * (0.5-y[i+1]) * (double)w; 42 // double len = w-2*x[i+1]; 43 ans += len * H / 2.0; 44 } 45 cout<<ans<<endl; 46 return (int)floor(ans); 47 }
900
结论：用01串表示"NZ",任意两行（两列）要么相等，要么取反。
利用结论，贪心地在每一位枚举并检验，枚举复杂度O(n^2) ,检验复杂度O(n^3),总复杂度O(n^5)。
检验方法： g[i][j]表示第i,j行是否相同,利用cells求出部分i,用类似传递闭包的办法递推所有能求出来的关系，同时检验是否会有矛盾。
1 class ThreeColorability { 2 public: 3 vector <string> lexSmallest(vector <string>); 4 }; 5 #define maxn 55 6 int g[maxn][maxn],n,m; 7 8 int check(vector<string> c) { 9 memset(g,-1,sizeof(g)); 10 for (int i=0; i<n; i++ ) { 11 g[i][i] = 0; 12 for (int j=i+1; j<n; j++ ) { 13 for (int k=0; k<m; k++ ) if (c[i][k]!=‘?‘ && c[j][k]!=‘?‘) { 14 if (g[i][j]==-1) { 15 g[i][j] = (c[i][k]!=c[j][k]); 16 g[j][i] = g[i][j]; 17 } else { 18 if (g[i][j] && c[i][k]==c[j][k]) return 0; 19 if (!g[i][j] && c[i][k]!=c[j][k]) return 0; 20 } 21 } 22 } 23 } 24 for (int i=0; i<n; i++ ) 25 for (int j=0; j<n; j++ ) 26 for (int k=0; k<n; k++ ) 27 if (g[j][i]!=-1 && g[i][k]!=-1) { 28 if (g[j][k]==-1) g[j][k] = g[j][i]^g[i][k]; 29 else if (g[j][k] != (g[j][i]^g[i][k])) return 0; 30 } 31 return 1; 32 } 33 34 vector <string> ThreeColorability::lexSmallest(vector <string> c) { 35 n = c.size(); 36 m = c[0].size(); 37 memset(g,-1,sizeof(g)); 38 39 if (!check(c)) return {}; 40 41 for (int i=0; i<n; i++ ) for (int j=0; j<m; j++ ) if (c[i][j]==‘?‘) { 42 c[i][j]=‘N‘; 43 if (!check(c)) c[i][j] = ‘Z‘; 44 } 45 return c; 46 }
标签：style class blog code http tar
原文地址：http://www.cnblogs.com/eggeek/p/3783659.html
