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  1. #include<bits/stdc++.h>
  2. #define f first
  3. #define int long long
  4. #define s second
  5. using namespace std;
  6. const int N=45,mod=1e9+7;
  7. int t,x[N],y[N],n,dp[N][N][N][N],fact[N],
  8. ans,ifact[N],A[N][N];
  9. string s;
  10. vector<int>inside[N][N][N];
  11. vector<pair<int,pair<int,pair<int,int> > > > triangles;
  12. int find_area(int X1,int Y1,int X2,int Y2){
  13. 	return abs(X1*Y2-Y1*X2);
  14. }
  15. bool is_inside(int i,int j,int k,int p){
  16. 	int X1=x[i],Y1=y[i],X2=x[j],Y2=y[j],X3=x[k],Y3=y[k],X4=x[p],Y4=y[p];
  17. 	 if(find_area(X2-X1,Y2-Y1,X3-X1,Y3-Y1) == find_area(X2-X1,Y2-Y1,X4-X1,Y4-Y1) 
  18. 	 										+ find_area(X3-X1,Y3-Y1,X4-X1,Y4-Y1)
  19. 											+  find_area(X3-X2,Y3-Y2,X4-X2,Y4-Y2) ) return 1;
  20. 	return 0;
  21. }
  22. void update(int a1,int a2,int a3,int c) {
  23. 	int all=inside[a1][a2][a3].size();
  24. 	int A1=min(a1,min(a2,a3)),A3=max(a1,max(a2,a3)),A2=a1+a2+a3-A1-A3;
  25. 	int B1=min(a1,min(a2,c)),B3=max(a1,max(a2,c)),B2=a1+a2+c-B1-B3;
  26. 	for(int i=0;i<=inside[B1][B2][B3].size();i++){
  27. 		dp[A1][A2][A3][i+1]+=dp[B1][B2][B3][i];
  28. 		dp[A1][A2][A3][i+1]%=mod;
  29. 	}
  30. } 
  31. int pwr(int u,int v){
  32. 	if(v==0) return 1;
  33. 	if(v==1) return u;
  34. 	if(v%2) return u*pwr(u,v-1)%mod;
  35. 	int p=pwr(u,v/2);
  36. 	return p*p%mod;
  37. }
  38.  main(){
  39. 	cin>>n;
  40. 	for(int i=1;i<=n;i++){
  41. 		cin>>x[i]>>y[i];
  42. 	}
  43. 	fact[0]=ifact[0]=1;
  44. 	for(int i=1;i<=n;i++){
  45. 		fact[i] = fact[i-1] * i%mod;
  46. 		ifact[i] = ifact[i-1]*pwr(i,mod-2)%mod;
  47. 	}
  48. 	for(int i=1;i<=n;i++){
  49. 		for(int j=i;j<=n;j++){
  50. 			A[i][j] = fact[j]*ifact[j-i]%mod;
  51. 		}
  52. 	}
  53. 	for(int i=1;i<=n;i++){
  54. 		for(int j=1;j<=n;j++){
  55. 			for(int k=1;k<=n;k++){
  56. 				for(int p=1;p<=n;p++){
  57. 					if(is_inside(i,j,k,p)) inside[i][j][k].push_back(p);
  58. 				}
  59. 				if(i<j && j<k)triangles.push_back({inside[i][j][k].size(),{i,{j,k}}});
  60. 			}
  61. 		}
  62. 	}
  63. 	sort(triangles.begin(),triangles.end());
  64. 	for(int k=0;k<triangles.size();k++) { 
  65. 		int a1=triangles[k].s.f,a2=triangles[k].s.s.f,a3=triangles[k].s.s.s;
  66. 		dp[a1][a2][a3][3]=1;
  67. 		for(int j=0;j<inside[a1][a2][a3].size();j++){
  68. 			int p = inside[a1][a2][a3][j]; 
  69. 			if(a1==p || a2==p || a3==p) continue; 
  70. 			update(a1,a2,a3,p);
  71. 			update(a1,a3,a2,p);
  72. 			update(a2,a3,a1,p);
  73. 		}
  74. 		int all=inside[a1][a2][a3].size();
  75. 		vector<int> new_dp(n+5);	
  76. 		for(int i=3;i<=all;i++){
  77. 			new_dp[i]+=dp[a1][a2][a3][i];	new_dp[i]%=mod;
  78. 			for(int j=i+1;j<=all;j++){
  79. 				// # of ways of choosing j-i from all-i A(j-i,all-i)
  80. 				new_dp[j]+=dp[a1][a2][a3][i]*A[j-i][all-i]%mod;
  81. 				new_dp[j]%=mod;
  82. 			} 
  83. 		}
  84. 		for(int i=0;i<=all;i++){
  85. 			dp[a1][a2][a3][i] = new_dp[i];
  86. 		}
  87. 		ans+=dp[a1][a2][a3][n]*6%mod;
  88. 		ans%=mod;
  89. 	} 
  90. 	cout<<ans;
  91. }
  92.  
Success #stdin #stdout 0.01s 6176KB
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https://ideone.com/AKPwVV
language:
C++14 (gcc 8.3)
created:
3 years ago
visibility:
public

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