做最大流题目的时候会遇到一种需要用二分查找的题型：
(poj2455) 一张无向图中有 N 个点，M 条边，每条边都有一个权值，且每条边只能用一次，要求找出 T 条从 1 到 N 的路径，使这 T 条路径所经过的边中，权值的最大值最小。
转化为最大流模型：T就是最大流，每条边只能用一次在网络流中就是容量为1。然后二分查找（枚举），边权小于或等于mid的边就加一条容量为1的网络流的边。最后知道最大流ans与T相等的最小的mid就是所求。
在二分查找的时候，与一般的二分查找还是有区别的，一般不能有“ if(ans==T) break;” 这样的语句，因为这种语句使用的条件是函数严格递增,但是我们遇到的题目中很可能会有相邻的函数值相等的情况。
一般情况下，二分写成这样：
while(a<=b)
{
c=(a+b)/2;
……
if(ans>=sum) {res=c;b=c-1;}
else a=c+1;
}
res就是我们所求的答案。
其实这种题型的建图还是有套路可以找的，多做些题目就有思路了。
hdu3081 Marriage Match II 第一次做这种类型的题目可能会没思路。
1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6 const int N=220;
7 const int M=200000, INF=0x3f3f3f3f;
8 struct node
9 {
10 int to,next,w;
11 }edge[M];
12 int head[N],numh[N],h[N],cure[N],pre[N],f[N],vis[N][N];
13 int ans,tot,mid;
14 void SAP(int s, int e,int n)
15 {
16 int flow,u,tmp,neck,i;
17 ans=0;
18 memset(pre,-1,sizeof(pre));
19 memset(h,0,sizeof(h));
20 memset(numh,0,sizeof(numh));
21 for(i=1;i<=n;i++)
22 cure[i]=head[i];
23 numh[0]=n;
24 u=s;
25 while(h[s]<n)
26 {
27 if(u==e)
28 {
29 flow =INF;
30 for(i=s;i!=e;i=edge[cure[i]].to)
31 {
32 if(flow>edge[cure[i]].w)
33 {
34 neck=i;
35 flow =edge[cure[i]].w;
36 }
37 }
38 for(i=s;i!=e;i=edge[cure[i]].to)
39 {
40 tmp=cure[i];
41 edge[tmp].w-=flow;
42 edge[tmp^1].w+=flow;
43 }
44 ans+=flow;
45 u=neck;
46 }
47 for(i=cure[u];i!=-1;i=edge[i].next)
48 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
49 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
50 else
51 {
52 if(0==--numh[h[u]]) break; //GAPÓÅ»¯
53 cure[u]=head[u];
54 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
55 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
56 h[u]=tmp+1;
57 ++numh[h[u]];
58 if(u!=s) u=pre[u];
59 }
60 }
61 }
62 void addedge(int i,int j,int w)
63 {
64 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
65 edge[tot].to=i;edge[tot].w=0;edge[tot].next=head[j];head[j]=tot++;
66 }
67 int Find(int x){return x==f[x]?x:f[x]=Find(f[x]);}
68 void Link(int x,int y)
69 {
70 int a=Find(x),b=Find(y);
71 if(a!=b) {f[b]=a;}
72 }
73 int B[M],G[M];
74 int main()
75 {
76 //freopen("test.txt","r",stdin);
77 int cas,i,j,k,n,m,x,y,s,e,d,a,b;
78 scanf("%d",&cas);
79 while(cas--)
80 {
81 scanf("%d%d%d",&n,&m,&d);
82 for(i=1;i<=n;i++) f[i]=i;
83 s=2*n+1;e=s+1;
84 for(k=1;k<=m;k++)
85 scanf("%d%d",&G[k],&B[k]);
86 while(d--)
87 {
88 scanf("%d%d",&x,&y);
89 Link(x,y);
90 }
91 x=0,y=n;
92 while(x<=y)
93 {
94 mid=(x+y)/2;
95 tot=0;
96 memset(head,-1,sizeof(head));
97 memset(vis,0,sizeof(vis));
98 for(i=1;i<=n;i++){
99 addedge(s,i,mid);
100 addedge(i+n,e,mid);
101 }
102 for(i=1;i<=m;i++)
103 {
104 for(j=1;j<=n;j++)
105 {
106 a=Find(G[i]),b=Find(j);
107 if(a==b&&!vis[j][B[i]]) {addedge(j,B[i]+n,1);
108 vis[j][B[i]]=1;}
109 }
110 }
111 SAP(s,e,e);
112 if(ans>=n*mid) {d=mid;x=mid+1;}
113 else y=mid-1;
114 }
115 printf("%d\n",d);
116 }
117 return 0;
118 }
hdu3277 Marriage Match III 与上面一题类似，多了拆点。拆点可以认为是把有N种属性的物品当为N个物品，但是他们之间还是有联系的。
1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6
7 const int N=800;
8 const int M=1100000, INF=10000000;
9 struct node
10 {
11 int to,next,w;
12 }edge[M];
13 int head[N],numh[N],h[N],cure[N],pre[N];
14 int ans,n,tot;
15 int f[N],G[M],B[M],mat[N][N];
16 void SAP(int s, int e,int n)
17 {
18 int flow,u,tmp,neck,i;
19 ans=0;
20 memset(pre,-1,sizeof(pre));
21 memset(h,0,sizeof(h));
22 memset(numh,0,sizeof(numh));
23 for(i=1;i<=n;i++)
24 cure[i]=head[i];
25 numh[0]=n;
26 u=s;
27 while(h[s]<n)
28 {
29 if(u==e)
30 {
31 flow =INF;
32 for(i=s;i!=e;i=edge[cure[i]].to)
33 {
34 if(flow>edge[cure[i]].w)
35 {
36 neck=i;
37 flow =edge[cure[i]].w;
38 }
39 }
40 for(i=s;i!=e;i=edge[cure[i]].to)
41 {
42 tmp=cure[i];
43 edge[tmp].w-=flow;
44 edge[tmp^1].w+=flow;
45 }
46 ans+=flow;
47 u=neck;
48 }
49 for(i=cure[u];i!=-1;i=edge[i].next)
50 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
51 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
52 else
53 {
54 if(0==--numh[h[u]]) break; //GAPÓÅ»¯
55 cure[u]=head[u];
56 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
57 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
58 h[u]=tmp+1;
59 ++numh[h[u]];
60 if(u!=s) u=pre[u];
61 }
62 }
63 }
64 void init()
65 {
66 for(int i=1;i<N;i++) f[i]=i;
67 memset(mat,0,sizeof(mat));
68 }
69 void addedge(int i,int j,int w)
70 {
71 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
72 edge[tot].to=i;edge[tot].w=0;edge[tot].next=head[j];head[j]=tot++;
73 }
74 int Find(int x){return x==f[x]?x:f[x]=Find(f[x]);}
75 void Link(int x,int y)
76 {
77 int a=Find(x),b=Find(y);
78 if(a!=b) f[b]=a;
79 }
80 int main()
81 {
82 //freopen("test.txt","r",stdin);
83 int m,n,f,i,j,k,cas,s,e;
84 scanf("%d",&cas);
85 while(cas--)
86 {
87 scanf("%d%d%d%d",&n,&m,&k,&f);
88 init();
89 s=3*n+1; e=s+1;
90 for(i=1;i<=m;i++)
91 {
92 scanf("%d%d",&G[i],&B[i]);
93 }
94 while(f--)
95 {
96 scanf("%d%d",&i,&j);
97 Link(i,j);
98 }
99 for(i=1;i<=m;i++)
100 {
101 int g=Find(G[i]);
102 mat[g][B[i]]=1;
103 }
104 int a=0,b=n,mid;
105 while(a<=b)
106 {
107 mid=(a+b)/2;
108 tot=0;
109 memset(head,-1,sizeof(head));
110 for(i=1;i<=n;i++)
111 {
112 addedge(s,i,mid);
113 addedge(i,i+n,k);
114 addedge(2*n+i,e,mid);
115 }
116 for(i=1;i<=n;i++)
117 {
118 for(j=1;j<=n;j++)
119 {
120 if(mat[Find(i)][j]) addedge(i,j+2*n,1);
121 else addedge(i+n,j+2*n,1);
122 }
123 }
124 SAP(s,e,e);
125 if(ans>=n*mid) {a=mid+1;f=mid;}
126 else b=mid-1;
127 }
128 printf("%d\n",f);
129 }
130 return 0;
131 }
poj2112 Optimal Milking 这种类型的基本题。
1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6 const int N =250, M=100000,INF=0x3f3f3f3f;
7 int Map[N][N], dist[N][N], pre[N];
8 void floyd(int n)
9 {
10 int i,j,k;
11 for(i=1;i<=n;i++)
12 {
13 for(j=1;j<=n;j++)
14 {
15 dist[i][j]=Map[i][j];
16 }
17 }
18 for(k=1;k<=n;k++)
19 for(i=1;i<=n;i++)
20 for(j=1;j<=n;j++)
21 if(dist[i][k]!=INF&&dist[k][j]!=INF&&
22 dist[i][k]+dist[k][j]<dist[i][j])
23 {
24 dist[i][j]=dist[i][k]+ dist[k][j];
25 }
26 }
27 struct node
28 {
29 int to,next,w;
30 }edge[M];
31 int head[N],numh[N],h[N],cure[N];
32 int ans,tot;
33 void SAP(int s, int e,int n)
34 {
35 int flow,u,tmp,neck,i;
36 ans=0;
37 for(i=1;i<=n;i++)
38 cure[i]=head[i];
39 numh[0]=n;
40 u=s;
41 while(h[s]<n)
42 {
43 if(u==e)
44 {
45 flow =INF;
46 for(i=s;i!=e;i=edge[cure[i]].to)
47 {
48 if(flow>edge[cure[i]].w)
49 {
50 neck=i;
51 flow =edge[cure[i]].w;
52 }
53 }
54 for(i=s;i!=e;i=edge[cure[i]].to)
55 {
56 tmp=cure[i];
57 edge[tmp].w-=flow;
58 edge[tmp^1].w+=flow;
59 }
60 ans+=flow;
61 u=neck;
62 }
63 for(i=cure[u];i!=-1;i=edge[i].next)
64 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
65 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
66 else
67 {
68 if(0==--numh[h[u]]) break; //GAPÓÅ»¯
69 cure[u]=head[u];
70 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
71 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
72 h[u]=tmp+1;
73 ++numh[h[u]];
74 if(u!=s) u=pre[u];
75 }
76 }
77 }
78 void init()
79 {
80 tot=0;
81 memset(head,-1,sizeof(head));
82 memset(pre,-1,sizeof(pre));
83 memset(h,0,sizeof(h));
84 memset(numh,0,sizeof(numh));
85
86 }
87 void addedge(int i,int j,int w)
88 {
89 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
90 edge[tot].to=i;edge[tot].w=0;edge[tot].next=head[j];head[j]=tot++;
91 }
92 int main()
93 {
94 //freopen("test.txt","r",stdin);
95 int k,c,m,i,j,t,s,e,n,R,L,mid;
96 while(scanf("%d%d%d",&k,&c,&m)!=EOF)
97 {
98 n=k+c;
99 for(i=1;i<=n;i++)
100 for(j=1;j<=n;j++)
101 {
102 Map[i][j]=INF;
103 scanf("%d",&t);
104 if(i==j) continue;
105 if(t!=0) Map[i][j]=t;
106 }
107 floyd(n);
108 R=L=0;
109 for(i=1;i<=n;i++)
110 for(j=1;j<=n;j++)
111 if(dist[i][j]!=INF) R=max(R,dist[i][j]);
112 s=n+1;e=s+1;
113 while(L<=R)
114 {
115 mid=(R+L)/2;
116 init();
117 for(i=1;i<=k;i++) addedge(s,i,m);
118 for(i=1;i<=c;i++) addedge(i+k,e,1);
119 for(i=1;i<=k;i++)
120 for(j=k+1;j<=n;j++)
121 if(dist[i][j]<=mid) addedge(i,j,1);
122 SAP(s,e,e);
123 if(ans>=c) R=mid-1,t=mid;
124 else L=mid+1;
125 }
126 printf("%d\n",t);
127 }
128 return 0;
129 }
poj3228 Gold Transportation
1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6
7 const int N=410;
8 const int M=100000, INF=0x3f3f3f3f;
9 struct node
10 {
11 int to,next,w;
12 }edge[M];
13 int head[N],numh[N],h[N],cure[N],pre[N];
14 int ans,tot;
15 void SAP(int s, int e,int n)
16 {
17 int flow,u,tmp,neck,i;
18 ans=0;
19 for(i=1;i<=n;i++)
20 cure[i]=head[i];
21 numh[0]=n;
22 u=s;
23 while(h[s]<n)
24 {
25 if(u==e)
26 {
27 flow =INF;
28 for(i=s;i!=e;i=edge[cure[i]].to)
29 {
30 if(flow>edge[cure[i]].w)
31 {
32 neck=i;
33 flow =edge[cure[i]].w;
34 }
35 }
36 for(i=s;i!=e;i=edge[cure[i]].to)
37 {
38 tmp=cure[i];
39 edge[tmp].w-=flow;
40 edge[tmp^1].w+=flow;
41 }
42 ans+=flow;
43 u=neck;
44 }
45 for(i=cure[u];i!=-1;i=edge[i].next)
46 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
47 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
48 else
49 {
50 if(0==--numh[h[u]]) break; //GAP优化
51 cure[u]=head[u];
52 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
53 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
54 h[u]=tmp+1;
55 ++numh[h[u]];
56 if(u!=s) u=pre[u];
57 }
58 }
59 }
60 void init()
61 {
62 tot=0;
63 memset(head,-1,sizeof(head));
64 memset(pre,-1,sizeof(pre));
65 memset(h,0,sizeof(h));
66 memset(numh,0,sizeof(numh));
67
68 }
69 void addedge(int i,int j,int w)
70 {
71 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
72 edge[tot].to=i;edge[tot].w=0;edge[tot].next=head[j];head[j]=tot++;
73 }
74 struct ND
75 {
76 int u,v,w;
77 }e[M];
78 int g[N],p[N];
79 int main()
80 {
81 //freopen("test.txt","r",stdin);
82 int n,m,i,j,k,s,E,a,b,c,sum,res,s1;
83 while(scanf("%d",&n)!=EOF)
84 {
85 if(!n) break;
86 sum=0;s1=0;
87 for(i=1;i<=n;i++) {scanf("%d",&g[i]); sum+=g[i]; }
88 for(i=1;i<=n;i++) {scanf("%d",&p[i]); s1+=p[i];}
89 scanf("%d",&m);
90 a=INF; b=0;
91 int t=0;
92 while(m--){
93 scanf("%d%d%d",&i,&j,&k);
94 e[t].u=i;e[t].v=j;e[t].w=k;t++;
95 a=min(a,k); b=max(b,k);
96 }
97 if(sum>s1) {printf("No Solution\n");continue;}
98 s=n+1; E=s+1;res=-1;
99 while(a<=b)
100 {
101 c=(a+b)/2;
102 init();
103 for(i=1;i<=n;i++)
104 {
105 if(g[i])addedge(s,i,g[i]);
106 if(p[i])addedge(i,E,p[i]);
107 }
108 for(i=0;i<t;i++)
109 if(e[i].w<=c) addedge(e[i].u,e[i].v,INF),addedge(e[i].v,e[i].u,INF);
110 SAP(s,E,E);
111 if(ans>=sum) {res=c;b=c-1;}
112 else a=c+1;
113 }
114 if(res==-1) printf("No Solution\n");
115 else printf("%d\n",res);
116 }
117 return 0;
118 }
poj2455 Secret Milking Machine
1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6 const int N=210;
7 const int M=100000, INF=0x3f3f3f3f;
8 struct node
9 {
10 int to,next,w;
11 }edge[M];
12 struct ND
13 {
14 int u,v,w;
15 }e[40010];
16 int head[N],numh[N],h[N],cure[N],pre[N];
17 int ans,tot;
18 void SAP(int s, int e,int n)
19 {
20 int flow,u,tmp,neck,i;
21 ans=0;
22 for(i=1;i<=n;i++)
23 cure[i]=head[i];
24 numh[0]=n;
25 u=s;
26 while(h[s]<n)
27 {
28 if(u==e)
29 {
30 flow =INF;
31 for(i=s;i!=e;i=edge[cure[i]].to)
32 {
33 if(flow>edge[cure[i]].w)
34 {
35 neck=i;
36 flow =edge[cure[i]].w;
37 }
38 }
39 for(i=s;i!=e;i=edge[cure[i]].to)
40 {
41 tmp=cure[i];
42 edge[tmp].w-=flow;
43 edge[tmp^1].w+=flow;
44 }
45 ans+=flow;
46 u=neck;
47 }
48 for(i=cure[u];i!=-1;i=edge[i].next)
49 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
50 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
51 else
52 {
53 if(0==--numh[h[u]]) break; //GAP优化
54 cure[u]=head[u];
55 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
56 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
57 h[u]=tmp+1;
58 ++numh[h[u]];
59 if(u!=s) u=pre[u];
60 }
61 }
62 }
63 void init()
64 {
65 tot=0;
66 memset(head,-1,sizeof(head));
67 memset(pre,-1,sizeof(pre));
68 memset(h,0,sizeof(h));
69 memset(numh,0,sizeof(numh));
70 }
71 void addedge(int i,int j,int w)
72 {
73 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
74 edge[tot].to=i;edge[tot].w=w;edge[tot].next=head[j];head[j]=tot++;
75 }
76 bool cmp(const ND &a, const ND &b)
77 {
78 return a.w<b.w;
79 }
80 int main()
81 {
82 //freopen("test.txt","r",stdin);
83 int n,p,T,i,j,k,R,L,m,s;
84 scanf("%d%d%d",&n,&p,&T);
85 R=0;L=INF;
86 for(i=0;i<p;i++)
87 {
88 scanf("%d%d%d",&e[i].u,&e[i].v,&e[i].w);
89 k=e[i].w;
90 R=max(R,k);
91 L=min(L,k);
92 }
93 sort(e,e+p,cmp);
94 while(L<=R)
95 {
96 init();
97 m=(L+R)/2;
98 for(i=0;i<p;i++)
99 {
100 if(e[i].w>m)break;
101 addedge(e[i].u,e[i].v,1);
102 }
103 SAP(1,n,n);
104 if(ans>=T) {s=m; R=m-1;}
105 else L=m+1;
106 }
107 printf("%d\n",m);
108 return 0;
109 }
poj2391 Ombrophobic Bovines
此题是这种类型中较难的题目，综合性挺高的。需要用floyd求任意两点之间的最短距离，然后二分查找。最烦的是超出了int范围，需要修改好几处。并且最不顺心的是习惯上用的二分查找在这里过不了。
1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6 const int N =500,M=1000000;
7 const long long INF=0x3f3f3f3f3f3f;
8 long long Map[N][N], dist[N][N],ans;
9 void floyd(int n)
10 {
11 int i,j,k;
12 for(i=1;i<=n;i++)
13 {
14 for(j=1;j<=n;j++)
15 {
16 dist[i][j]=Map[i][j];
17 }
18 }
19 for(k=1;k<=n;k++)
20 for(i=1;i<=n;i++)
21 for(j=1;j<=n;j++)
22 if(dist[i][k]!=INF&&dist[k][j]!=INF&&
23 dist[i][k]+dist[k][j]<dist[i][j])
24 {
25 dist[i][j]=dist[i][k]+ dist[k][j];
26 }
27 }
28 struct node
29 {
30 int to,next,w;
31 }edge[M];
32 int head[N],numh[N],h[N],cure[N],pre[N];
33 int tot;
34 void SAP(int s, int e,int n)
35 {
36 int u,tmp,neck,i;
37 long long flow;
38 ans=0;
39 for(i=1;i<=n;i++)
40 cure[i]=head[i];
41 numh[0]=n;
42 u=s;
43 while(h[s]<n)
44 {
45 if(u==e)
46 {
47 flow =INF;
48 for(i=s;i!=e;i=edge[cure[i]].to)
49 {
50 if(flow>edge[cure[i]].w)
51 {
52 neck=i;
53 flow =edge[cure[i]].w;
54 }
55 }
56 for(i=s;i!=e;i=edge[cure[i]].to)
57 {
58 tmp=cure[i];
59 edge[tmp].w-=flow;
60 edge[tmp^1].w+=flow;
61 }
62 ans+=flow;
63 u=neck;
64 }
65 for(i=cure[u];i!=-1;i=edge[i].next)
66 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
67 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
68 else
69 {
70 if(0==--numh[h[u]]) break; //GAP优化
71 cure[u]=head[u];
72 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
73 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
74 h[u]=tmp+1;
75 ++numh[h[u]];
76 if(u!=s) u=pre[u];
77 }
78 }
79 }
80 void init()
81 {
82 tot=0;
83 memset(head,-1,sizeof(head));
84 memset(pre,-1,sizeof(pre));
85 memset(h,0,sizeof(h));
86 memset(numh,0,sizeof(numh));
87
88 }
89 void addedge(int i,int j,int w)
90 {
91 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
92 edge[tot].to=i;edge[tot].w=0;edge[tot].next=head[j];head[j]=tot++;
93 }
94 int c[N],x[N];
95 int main()
96 {
97 //freopen("test.txt","r",stdin);
98 int n,m,i,j,k;
99 long long res,L,R,mid,s1,s2,w;
100 while(scanf("%d%d",&n,&m)!=EOF){
101 for(i=1;i<=n;i++)
102 {
103 Map[i][i]=0;
104 for(j=i+1;j<=n;j++)
105 Map[j][i]=Map[i][j]=INF;
106 }
107 s1=s2=0;
108 for(i=1;i<=n;i++)
109 {
110 scanf("%d%d",&x[i],&c[i]);
111 s1+=x[i];s2+=c[i];
112 }
113
114 while(m--)
115 {
116 scanf("%d%d%I64d",&i,&j,&w);
117 Map[i][j]=Map[j][i]=min(w,Map[i][j]);
118 }
119 if(s1>s2) {printf("-1\n");continue;}
120 for(i=1;i<=n;i++)
121 if(x[i]>c[i]) break;
122 if(i>n) {printf("0\n");continue;}
123 floyd(n);
124 int s=2*n+1,e=s+1;
125 L=0,res=-1,R=INF;
126 while(L<R)
127 {
128 init();
129 mid=(R+L)/2;
130 for(i=1;i<=n;i++)
131 {
132 addedge(i,i+n,INF);
133 addedge(s,i,x[i]);
134 addedge(i+n,e,c[i]);
135 for(j=1;j<=n;j++)
136 {
137 if(i==j) continue;
138 if(dist[i][j]<=mid) addedge(i,j+n,INF);
139 }
140 }
141 SAP(s,e,e);
142 if(ans>=s1) {res=mid; R=mid;}
143 else L=mid+1;
144 }
145 printf("%I64d\n",res);
146 }
147 return 0;
148 }
我的代码中最大流算法都是用的优化的SAP算法，因为他的时间复杂度低。并且我已经习惯了这代码。
SAP模版：
1 const int N=110;
2 const int M=2*N*N, INF=0x3f3f3f3f;
3 struct node
4 {
5 int to,next,w;
6 }edge[M];
7 int head[N],numh[N],h[N],cure[N],pre[N];
8 int ans,tot;
9 void SAP(int s, int e,int n)
10 {
11 int flow,u,tmp,neck,i;
12 ans=0;
13 for(i=1;i<=n;i++)
14 cure[i]=head[i];
15 numh[0]=n;
16 u=s;
17 while(h[s]<n)
18 {
19 if(u==e)
20 {
21 flow =INF;
22 for(i=s;i!=e;i=edge[cure[i]].to)
23 {
24 if(flow>edge[cure[i]].w)
25 {
26 neck=i;
27 flow =edge[cure[i]].w;
28 }
29 }
30 for(i=s;i!=e;i=edge[cure[i]].to)
31 {
32 tmp=cure[i];
33 edge[tmp].w-=flow;
34 edge[tmp^1].w+=flow;
35 }
36 ans+=flow;
37 u=neck;
38 }
39 for(i=cure[u];i!=-1;i=edge[i].next)
40 if(edge[i].w && h[u]==h[edge[i].to]+1) break;
41 if(i!=-1) {cure[u]=i;pre[edge[i].to]=u;u=edge[i].to;}
42 else
43 {
44 if(0==--numh[h[u]]) break; //GAP优化
45 cure[u]=head[u];
46 for(tmp=n,i=head[u];i!=-1;i=edge[i].next)
47 if(edge[i].w) tmp=min(tmp, h[edge[i].to]);
48 h[u]=tmp+1;
49 ++numh[h[u]];
50 if(u!=s) u=pre[u];
51 }
52 }
53 }
54 void init()
55 {
56 tot=0;
57 memset(head,-1,sizeof(head));
58 memset(pre,-1,sizeof(pre));
59 memset(h,0,sizeof(h));
60 memset(numh,0,sizeof(numh));
61
62 }
63 void addedge(int i,int j,int w)
64 {
65 edge[tot].to=j;edge[tot].w=w;edge[tot].next=head[i];head[i]=tot++;
66 edge[tot].to=i;edge[tot].w=0;edge[tot].next=head[j];head[j]=tot++;
67 }
时间： 2024-11-02 06:36:35