1.问一个圆上的最多不交弧的个数。
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int maxn=1E6+5; 4 int n,m,tot; 5 int totT,tmp[maxn],jump[maxn][20]; 6 struct line 7 { 8 int l,r; 9 bool operator<(const line&A)const 10 { 11 return r<A.r; 12 } 13 }a[maxn]; 14 int t[maxn*4]; 15 void change(int l,int r,int pos,int x,int num) 16 { 17 if(t[num]==0||a[x].r<a[t[num]].r) 18 t[num]=x; 19 if(l==r) 20 return; 21 int mid=(l+r)>>1; 22 if(pos<=mid) 23 change(l,mid,pos,x,num<<1); 24 else 25 change(mid+1,r,pos,x,num<<1|1); 26 } 27 int ask(int L,int R,int l,int r,int num) 28 { 29 if(L<=l&&r<=R) 30 return t[num]; 31 int mid=(l+r)>>1; 32 if(R<=mid) 33 return ask(L,R,l,mid,num<<1); 34 else if(mid<L) 35 return ask(L,R,mid+1,r,num<<1|1); 36 int x=ask(L,R,l,mid,num<<1),y=ask(L,R,mid+1,r,num<<1|1); 37 if(x==0) 38 return y; 39 else if(y==0) 40 return x; 41 else if(a[x].r<a[y].r) 42 return x; 43 return y; 44 } 45 inline void solve() 46 { 47 for(int i=1;i<=tot;++i) 48 tmp[++totT]=a[i].l,tmp[++totT]=a[i].r; 49 sort(tmp+1,tmp+totT+1); 50 totT=unique(tmp+1,tmp+totT+1)-tmp-1; 51 sort(a+1,a+tot+1); 52 int ans=0; 53 for(int i=tot;i>=1;--i) 54 { 55 int pos=lower_bound(tmp+1,tmp+totT+1,a[i].r)-tmp; 56 int x=ask(pos,totT,1,totT,1); 57 jump[i][0]=x; 58 pos=lower_bound(tmp+1,tmp+totT+1,a[i].l)-tmp; 59 change(1,totT,pos,i,1); 60 } 61 for(int j=1;j<20;++j) 62 for(int i=1;i<=tot;++i) 63 jump[i][j]=jump[jump[i][j-1]][j-1]; 64 for(int i=1;i<=tot;++i) 65 { 66 int s=1; 67 int u=i; 68 for(int j=19;j>=0;--j) 69 if(jump[u][j]&&a[jump[u][j]].r-a[i].l<=m) 70 { 71 s+=1<<j; 72 u=jump[u][j]; 73 } 74 ans=max(ans,s); 75 } 76 cout<<ans<<endl; 77 } 78 int main() 79 { 80 freopen("circular.in","r",stdin); 81 freopen("circular.out","w",stdout); 82 ios::sync_with_stdio(false); 83 cin>>m>>n; 84 for(int i=1;i<=n;++i) 85 { 86 int l,r; 87 cin>>l>>r; 88 if(l<r) 89 { 90 a[++tot]=(line){l,r}; 91 a[++tot]=(line){l+m,r+m}; 92 } 93 else 94 a[++tot]=(line){l,r+m}; 95 } 96 solve(); 97 return 0; 98 }
2.用L字型的骨牌覆盖，棋盘上只有(x+y)%2==1的位置有数字，一个骨牌会有贡献当且仅当拐角处有数字。问最大贡献。
1 #include<bits/stdc++.h> 2 using namespace std; 3 typedef long long int ll; 4 const int maxn=1E6+5; 5 const ll inf=1E12; 6 int tot,n,m,k,a[505][505],id1[505][505],id2[505][505]; 7 int dx[4]={0,1,0,-1}; 8 int dy[4]={1,0,-1,0}; 9 bool ban[505][505]; 10 namespace FLOW 11 { 12 int S,T; 13 int size=1,head[maxn],from[maxn]; 14 ll dis[maxn],maxF[maxn]; 15 bool vis[maxn]; 16 struct edge 17 { 18 int to,next; 19 ll cost,flow; 20 }E[maxn*2]; 21 inline void addE(int u,int v,int c,int f) 22 { 23 E[++size].to=v; 24 E[size].next=head[u]; 25 E[size].cost=c; 26 E[size].flow=f; 27 head[u]=size; 28 } 29 inline void add(int u,int v,int c,int f) 30 { 31 // cout<<"ADD "<<u<<" "<<v<<" "<<c<<" "<<f<<endl; 32 addE(u,v,c,f); 33 addE(v,u,-c,0); 34 } 35 inline bool bfs() 36 { 37 for(int i=0;i<=T;++i) 38 maxF[i]=0,dis[i]=-inf; 39 queue<int>Q; 40 Q.push(S); 41 dis[S]=0; 42 maxF[S]=inf; 43 while(!Q.empty()) 44 { 45 int u=Q.front(); 46 Q.pop(); 47 vis[u]=0; 48 for(int i=head[u];i;i=E[i].next) 49 { 50 int v=E[i].to; 51 ll nw=E[i].cost+dis[u]; 52 if(E[i].flow==0||nw<=dis[v]) 53 continue; 54 dis[v]=nw; 55 from[v]=i; 56 maxF[v]=min(maxF[u],E[i].flow); 57 if(!vis[v]) 58 Q.push(v); 59 vis[v]=1; 60 } 61 } 62 return dis[T]>0; 63 } 64 inline void MCMF() 65 { 66 ll s=0; 67 for(int i=1;i<=n;++i) 68 for(int j=1;j<=n;++j) 69 s+=a[i][j]; 70 while(bfs()) 71 { 72 int pos=T,f=maxF[T]; 73 s-=f*dis[T]; 74 while(pos!=S) 75 { 76 E[from[pos]].flow-=f; 77 E[from[pos]^1].flow+=f; 78 pos=E[from[pos]^1].to; 79 } 80 } 81 cout<<s<<endl; 82 } 83 } 84 int main() 85 { 86 freopen("marshland.in","r",stdin); 87 freopen("marshland.out","w",stdout); 88 ios::sync_with_stdio(false); 89 cin>>n>>m>>k; 90 ++tot; 91 for(int i=1;i<=n;++i) 92 for(int j=1;j<=n;++j) 93 { 94 cin>>a[i][j]; 95 id1[i][j]=++tot; 96 } 97 for(int i=1;i<=n;++i) 98 for(int j=1;j<=n;++j) 99 if((i+j)&1) 100 id2[i][j]=++tot; 101 for(int i=1;i<=k;++i) 102 { 103 int x,y; 104 cin>>x>>y; 105 ban[x][y]=1; 106 } 107 FLOW::S=0,FLOW::T=tot+1; 108 FLOW::add(0,1,0,m); 109 for(int x=1;x<=n;++x) 110 for(int y=1;y<=n;++y) 111 { 112 if(ban[x][y]) 113 continue; 114 if((x+y)&1) 115 { 116 if(x&1) 117 { 118 if(id1[x-1][y]&&!ban[x-1][y]) 119 FLOW::add(id1[x][y],id1[x-1][y],0,1); 120 if(id1[x+1][y]&&!ban[x+1][y]) 121 FLOW::add(id1[x][y],id1[x+1][y],0,1); 122 } 123 else 124 { 125 if(id1[x][y-1]&&!ban[x][y-1]) 126 FLOW::add(id1[x][y],id1[x][y-1],0,1); 127 if(id1[x][y+1]&&!ban[x][y+1]) 128 FLOW::add(id1[x][y],id1[x][y+1],0,1); 129 } 130 FLOW::add(id2[x][y],id1[x][y],a[x][y],1); 131 } 132 else 133 { 134 if(x&1) 135 { 136 FLOW::add(1,id1[x][y],0,1); 137 for(int i=0;i<4;++i) 138 { 139 int nx=x+dx[i],ny=y+dy[i]; 140 if(ban[nx][ny]||id2[nx][ny]==0) 141 continue; 142 FLOW::add(id1[x][y],id2[nx][ny],0,1); 143 } 144 } 145 else 146 FLOW::add(id1[x][y],tot+1,0,1); 147 } 148 } 149 FLOW::MCMF(); 150 return 0; 151 }
3.CF321D
1 #include<bits/stdc++.h> 2 using namespace std; 3 typedef long long int ll; 4 const ll inf=1E15; 5 int tot,n,len,a[55][55],r[55][55]; 6 ll ans,tmp[(1<<18)+1]; 7 inline ll what(int x,int y) 8 { 9 if(r[x][y]==1) 10 return -a[x][y]; 11 return a[x][y]; 12 } 13 inline ll get(int col) 14 { 15 ll s=0; 16 for(int i=0;i<len-1;++i) 17 { 18 r[i][col]=0; 19 r[i][col+len]=r[i][col]^r[i][len-1]; 20 r[i+len][col]=r[i][col]^r[len-1][col]; 21 r[i+len][col+len]=r[i+len][col]^r[i+len][len-1]; 22 ll g=what(i,col)+what(i,col+len)+what(i+len,col)+what(i+len,col+len); 23 24 r[i][col]=1; 25 r[i][col+len]=r[i][col]^r[i][len-1]; 26 r[i+len][col]=r[i][col]^r[len-1][col]; 27 r[i+len][col+len]=r[i+len][col]^r[i+len][len-1]; 28 g=max(g,what(i,col)+what(i,col+len)+what(i+len,col)+what(i+len,col+len)); 29 30 s+=g; 31 } 32 return s; 33 } 34 inline void solve(int S) 35 { 36 ll s=0; 37 for(int i=0;i<len;++i) 38 if(S&(1<<i)) 39 r[i][len-1]=1; 40 else 41 r[i][len-1]=0; 42 for(int i=len;i<n;++i) 43 r[i][len-1]=r[i-len][len-1]^r[len-1][len-1]; 44 for(int i=0;i<n;++i) 45 s+=what(i,len-1); 46 for(int i=0;i<len-1;++i) 47 { 48 r[len-1][i]=0; 49 r[len-1][i+len]=r[len-1][i]^r[len-1][len-1]; 50 ll g=get(i)+what(len-1,i)+what(len-1,i+len); 51 52 r[len-1][i]=1; 53 r[len-1][i+len]=r[len-1][i]^r[len-1][len-1]; 54 g=max(g,get(i)+what(len-1,i)+what(len-1,i+len)); 55 56 s+=g; 57 } 58 ans=max(ans,s); 59 } 60 int main() 61 { 62 freopen("s.in","r",stdin); 63 freopen("s.out","w",stdout); 64 ios::sync_with_stdio(false); 65 cin>>n; 66 len=(n+1)/2; 67 for(int i=0;i<n;++i) 68 for(int j=0;j<n;++j) 69 cin>>a[i][j]; 70 for(int S=0;S<(1<<len);++S) 71 solve(S); 72 cout<<ans<<endl; 73 return 0; 74 }