NOI2006 最大获利
在网上的题解都说的那么轻松，可我打了3个小时，算法换了无数。最终也是加inline优化才过的，唉
最大权闭合子图，模型很简单但是后两个数据大了点，
第一个算法：指针链表+dinic 最大点80s++
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1 program profit(input,output); 2 const 3 oo = 199500714; 4 type 5 node = ^link; 6 link = record 7 goal : longint; 8 flow : longint; 9 next : node; 10 end; 11 var 12 l : array[0..60000] of node; 13 q : array[0..60000] of longint; 14 d : array[0..60000] of longint; 15 s,t : longint; 16 n,m : longint; 17 answer : int64; 18 procedure add(xx,yy,cc: longint ); 19 var 20 tt : node; 21 begin 22 new(tt); 23 tt^.flow:=cc; 24 tt^.goal:=yy; 25 tt^.next:=l[xx]; 26 l[xx]:=tt; 27 end; { add } 28 procedure init; 29 var 30 i,xx,yy,cc : longint; 31 begin 32 readln(n,m); 33 s:=0; 34 t:=m+n+1; 35 for i:=s to t do 36 l[i]:=nil; 37 for i:=1 to n do 38 begin 39 read(cc); 40 add(s,i,cc); 41 add(i,s,0); 42 end; 43 readln; 44 answer:=0; 45 for i:=1 to m do 46 begin 47 readln(xx,yy,cc); 48 add(xx,i+n,oo); 49 add(i+n,xx,0); 50 add(yy,i+n,oo); 51 add(i+n,yy,0); 52 add(i+n,t,cc); 53 add(t,i+n,0); 54 inc(answer,cc); 55 end; 56 end; { init } 57 function bfs(now :longint ):boolean; 58 var 59 i,head,tail : longint; 60 tt : node; 61 begin 62 for i:=s to t do 63 d[i]:=-1; 64 head:=0; 65 tail:=1; 66 q[1]:=now; 67 d[now]:=0; 68 while head<tail do 69 begin 70 inc(head); 71 tt:=l[q[head]]; 72 while tt<>nil do 73 begin 74 if tt^.flow>0 then 75 if d[tt^.goal]=-1 then 76 begin 77 d[tt^.goal]:=d[q[head]]+1; 78 inc(tail); 79 q[tail]:=tt^.goal; 80 end; 81 tt:=tt^.next; 82 end; 83 end; 84 if d[t]=-1 then 85 exit(false); 86 exit(true); 87 end; { bfs } 88 function min(aa,bb :longint ):longint; 89 begin 90 if aa>bb then 91 exit(bb); 92 exit(aa); 93 end; { min } 94 function dfs(now,minf: longint ):longint; 95 var 96 tt : node; 97 ttt : node; 98 tmp : longint; 99 begin 100 if now=t then 101 exit(minf); 102 tt:=l[now]; 103 while tt<>nil do 104 begin 105 if d[tt^.goal]=d[now]+1 then 106 if tt^.flow>0 then 107 begin 108 tmp:=dfs(tt^.goal,min(minf,tt^.flow)); 109 if tmp<>0 then 110 begin 111 dec(tt^.flow,tmp); 112 ttt:=l[tt^.goal]; 113 while ttt<>nil do 114 begin 115 if ttt^.goal=now then 116 begin 117 inc(ttt^.flow,tmp); 118 break; 119 end; 120 ttt:=ttt^.next; 121 end; 122 exit(tmp); 123 end; 124 end; 125 tt:=tt^.next; 126 end; 127 exit(0); 128 end; { dfs } 129 procedure dinic(); 130 var 131 tmp : longint; 132 begin 133 while bfs(s) do 134 begin 135 tmp:=dfs(s,oo); 136 while tmp<>0 do 137 begin 138 dec(answer,tmp); 139 tmp:=dfs(s,oo); 140 end; 141 end; 142 end; { dinic } 143 procedure print; 144 begin 145 writeln(answer); 146 end; { print } 147 begin 148 assign(input,'profit.in');reset(input); 149 assign(output,'profit.out');rewrite(output); 150 init(); 151 dinic(); 152 print(); 153 close(input); 154 close(output); 155 end.
第二个算法：前向星存储+dinic 最大点55s++
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1 program profit(input,output); 2 const 3 oo = 199500714; 4 var 5 f,x,y,c : array[0..500000] of longint; 6 q : array[0..100000] of longint; 7 d : array[0..100000] of longint; 8 s,t : longint; 9 n,m : longint; 10 answer : int64; 11 tot : longint; 12 procedure add(xx,yy,cc: longint ); 13 begin 14 inc(tot); 15 x[tot]:=xx; 16 y[tot]:=yy; 17 c[tot]:=cc; 18 end; { add } 19 procedure init; 20 var 21 i,xx,yy,cc : longint; 22 begin 23 readln(n,m); 24 s:=0; 25 t:=m+n+1; 26 for i:=1 to n do 27 begin 28 read(cc); 29 add(s,i,cc); 30 add(i,s,0); 31 end; 32 readln; 33 answer:=0; 34 for i:=1 to m do 35 begin 36 readln(xx,yy,cc); 37 add(xx,i+n,oo); 38 add(i+n,xx,0); 39 add(yy,i+n,oo); 40 add(i+n,yy,0); 41 add(i+n,t,cc); 42 add(t,i+n,0); 43 inc(answer,cc); 44 end; 45 end; { init } 46 procedure swap(var aa,bb :longint ); 47 var 48 tt : longint; 49 begin 50 tt:=aa; 51 aa:=bb; 52 bb:=tt; 53 end; { swap } 54 procedure sort(p,q :longint ); 55 var 56 i,j,mid : longint; 57 begin 58 i:=p; 59 j:=q; 60 mid:=x[(i+j)>>1]; 61 repeat 62 while x[i]<mid do 63 inc(i); 64 while x[j]>mid do 65 dec(j); 66 if i<=j then 67 begin 68 swap(x[i],x[j]); 69 swap(y[i],y[j]); 70 swap(c[i],c[j]); 71 inc(i); 72 dec(j); 73 end; 74 until i>j; 75 if i<q then sort(i,q); 76 if j>p then sort(p,j); 77 end; { sort } 78 procedure make; 79 var 80 i : longint; 81 begin 82 fillchar(f,sizeof(f),0); 83 for i:=1 to tot do 84 if f[x[i]]=0 then 85 f[x[i]]:=i; 86 f[t+1]:=tot+1; 87 for i:=t downto s do 88 if f[i]=0 then 89 f[i]:=f[i+1]; 90 end; { make } 91 function bfs(now: longint ):boolean; 92 var 93 i,head,tail : longint; 94 begin 95 for i:=s to t do 96 d[i]:=-1; 97 head:=0; 98 tail:=1; 99 q[1]:=now; 100 d[now]:=0; 101 while head<tail do 102 begin 103 inc(head); 104 for i:=f[q[head]] to f[q[head]+1]-1 do 105 begin 106 if c[i]>0 then 107 if d[y[i]]=-1 then 108 begin 109 d[y[i]]:=d[q[head]]+1; 110 inc(tail); 111 q[tail]:=y[i]; 112 end; 113 end; 114 end; 115 if d[t]=-1 then 116 exit(false); 117 exit(true); 118 end; { bfs } 119 function min(aa,bb :longint ):longint; 120 begin 121 if aa>bb then 122 exit(bb); 123 exit(aa); 124 end; { min } 125 function dfs(now,minf: longint ):longint; 126 var 127 i,j : longint; 128 tmp : longint; 129 begin 130 if now=t then 131 exit(minf); 132 for i:=f[now] to f[now+1]-1 do 133 if d[y[i]]=d[x[i]]+1 then 134 if c[i]>0 then 135 begin 136 tmp:=dfs(y[i],min(minf,c[i])); 137 if tmp<>0 then 138 begin 139 dec(c[i],tmp); 140 for j:=f[y[i]] to f[y[i]+1]-1 do 141 if y[j]=now then 142 begin 143 inc(c[j],tmp); 144 break; 145 end; 146 exit(tmp); 147 end; 148 end; 149 exit(0); 150 end; { dfs } 151 procedure dinic(); 152 var 153 tmp : longint; 154 begin 155 while bfs(s) do 156 begin 157 tmp:=dfs(s,oo); 158 while tmp<>0 do 159 begin 160 dec(answer,tmp); 161 tmp:=dfs(s,oo); 162 end; 163 end; 164 end; { dinic } 165 procedure print; 166 begin 167 writeln(answer); 168 end; { print } 169 begin 170 assign(input,'profit.in');reset(input); 171 assign(output,'profit.out');rewrite(output); 172 init(); 173 sort(1,tot); 174 make; 175 dinic(); 176 print(); 177 close(input); 178 close(output); 179 end.
第三个算法：前向星存储+SAP 最大点3s++ 加上inline，1.8s
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1 {$inline on} 2 program profit(input,output); 3 const 4 oo = 199500714; 5 var 6 f,x,y,c : array[0..500000] of longint; 7 h,vh : array[0..100000] of longint; 8 s,t : longint; 9 n,m : longint; 10 answer : int64; 11 tot : longint; 12 tmpflow : longint; 13 can : boolean; 14 procedure add(xx,yy,cc: longint ); inline; 15 begin 16 inc(tot); 17 x[tot]:=xx; 18 y[tot]:=yy; 19 c[tot]:=cc; 20 end; { add } 21 procedure init; inline; 22 var 23 i,xx,yy,cc : longint; 24 begin 25 readln(n,m); 26 s:=0; 27 t:=m+n+1; 28 for i:=1 to n do 29 begin 30 read(cc); 31 add(s,i,cc); 32 add(i,s,0); 33 end; 34 readln; 35 answer:=0; 36 for i:=1 to m do 37 begin 38 readln(xx,yy,cc); 39 add(xx,i+n,oo); 40 add(i+n,xx,0); 41 add(yy,i+n,oo); 42 add(i+n,yy,0); 43 add(i+n,t,cc); 44 add(t,i+n,0); 45 inc(answer,cc); 46 end; 47 end; { init } 48 procedure swap(var aa,bb :longint ); inline; 49 var 50 tt : longint; 51 begin 52 tt:=aa; 53 aa:=bb; 54 bb:=tt; 55 end; { swap } 56 procedure sort(p,q :longint ); inline; 57 var 58 i,j,mid : longint; 59 begin 60 i:=p; 61 j:=q; 62 mid:=x[(i+j)>>1]; 63 repeat 64 while x[i]<mid do 65 inc(i); 66 while x[j]>mid do 67 dec(j); 68 if i<=j then 69 begin 70 swap(x[i],x[j]); 71 swap(y[i],y[j]); 72 swap(c[i],c[j]); 73 inc(i); 74 dec(j); 75 end; 76 until i>j; 77 if i<q then sort(i,q); 78 if j>p then sort(p,j); 79 end; { sort } 80 procedure make; inline; 81 var 82 i : longint; 83 begin 84 fillchar(f,sizeof(f),0); 85 for i:=1 to tot do 86 if f[x[i]]=0 then 87 f[x[i]]:=i; 88 f[t+1]:=tot+1; 89 for i:=t downto s do 90 if f[i]=0 then 91 f[i]:=f[i+1]; 92 end; { make } 93 procedure dfs(now : longint ); inline; 94 var 95 min,tmp : longint; 96 i,j : longint; 97 begin 98 min:=t; 99 tmp:=tmpflow; 100 if now=t then 101 begin 102 can:=true; 103 dec(answer,tmpflow); 104 exit; 105 end; 106 for i:=f[now] to f[now+1]-1 do 107 if c[i]>0 then 108 begin 109 if h[y[i]]+1=h[now] then 110 begin 111 if c[i]<tmpflow then 112 tmpflow:=c[i]; 113 dfs(y[i]); 114 if h[s]>=t+1 then 115 exit; 116 if can then 117 break; 118 tmpflow:=tmp; 119 end; 120 if h[y[i]]<min then 121 min:=h[y[i]]; 122 end; 123 if not can then 124 begin 125 dec(vh[h[now]]); 126 if vh[h[now]]=0 then 127 h[s]:=t+1; 128 h[now]:=min+1; 129 inc(vh[h[now]]); 130 end 131 else 132 begin 133 dec(c[i],tmpflow); 134 for j:=f[y[i]] to f[y[i]+1]-1 do 135 if y[j]=now then 136 begin 137 inc(c[j],tmpflow); 138 break; 139 end; 140 end; 141 end; { dfs } 142 procedure SAP(); inline; 143 begin 144 fillchar(h,sizeof(h),0); 145 fillchar(vh,sizeof(vh),0); 146 vh[0]:=t+1; 147 while h[s]<t+1 do 148 begin 149 tmpflow:=oo; 150 can:=false; 151 dfs(s); 152 end; 153 end; { SAP } 154 procedure print; inline; 155 begin 156 writeln(answer); 157 end; { print } 158 begin 159 assign(input,'profit.in');reset(input); 160 assign(output,'profit.out');rewrite(output); 161 init(); 162 sort(1,tot); 163 make; 164 SAP; 165 print(); 166 close(input); 167 close(output); 168 end.
