Bzoj 1001 [BeiJing2006] Wolf catches rabbits

Title Link: http://www.lydsy.com/JudgeOnline/problem.php?id=1001

The shortest-cut conversion is a classic problem.

The title looks like a minimum cut, and a look at the definition of cut and min cut:

Cut: For a graph, divide all vertices into two sets S and T=v-s, where the source point S is in the set S, and the meeting point T is in the set T. If you remove the "starting point in S, the end point in T", you cannot reach T from S. Such a set partition (S,T) is called a s-t cut, its capacity is the starting point in S, and the end point is the capacity of all sides in T.

Minimum cut: The smallest cut in the figure.

Maximum flow theorem by minimum cut:

For any network has a single origin and single destination node, the maximum possible flow from origin to destination E Quals the minimum cut value for all cuts in the network.

So you run the biggest stream and you come out? But V,e can reach 1e3, I know the fastest network flow algorithm ISAP all to O (v^2 E), so the network flow is not OK.

Such a diagram is called a s-t plan, so the graph is the shortest way to its dual graph.

Concrete view of Dong Zhou's "Two poles connecting"--analysis of the application of maximum minimum theorem in the competition of informatics

1 /*2 * Problem:bzoj 10013 * AUTHOR:SHJWUDP4 * Created time:2015/3/26 Thursday 16:36:425 * File name:233.cpp6 * state:accepted7 * Memo: Network flow, Shortest path8  */9#include <iostream>Ten#include <cstdio> One#include <cstring> A#include <algorithm> -#include <queue> -   the using namespacestd; -   - Const intinf=0x7f7f7f7f; -   + Const intmaxa=1e3+7; - Const intmaxb=maxa*maxa*2; + Const intmaxc=maxa*maxa*3; A   at structEdge { -     intV, NT; -     intW; - } EDGES[MAXC]; -   - intHEAD[MAXB], edgenum; in   - intN, M; to ints, t; +   - voidInitintN) { theMemset (Head,-1,sizeof(head[0]) * (n+3)); *edgenum=0; $ }Panax Notoginseng voidAddedge (intUintVintW) { -edges[edgenum].v=v; theedges[edgenum].w=W; +Edges[edgenum].nt=Head[u]; Ahead[u]=edgenum++; the } + namespaceDijkstra { -     structHeapnode { $         intd, u; $Heapnode (intDintu):d (d), U (u) {} -         BOOL operator< (Constheapnode& RHS)Const { -             returnD >RHS.D; the         } -     };Wuyi   the     intN; -     intd[maxa*maxa<<1]; Wu     BOOLdone[maxa*maxa<<1]; -     intGoints) { Aboutmemset (D,0x7f,sizeof(d[0]) * (n+3)); $memset (Done,0,sizeof(done[0]) * (n+3)); -d[s]=0; done[s]=1; -Priority_queueQ; -Q.push (Heapnode (0, s)); A          while(!Q.empty ()) { +Heapnode x=Q.top (); Q.pop (); the              for(intI=HEAD[X.U]; ~i; I=Edges[i].nt) { -edge& e=Edges[i]; $                 if(d[e.v]>d[x.u]+e.w) { thed[e.v]=d[x.u]+E.W; the                     if(!DONE[E.V]) { thedone[e.v]=1; the Q.push (Heapnode (d[e.v], e.v)); -                     } in                 } the             } the         } About         returnD[t]>=inf?0:d [t]; the     } the } the intMain () { + #ifndef Online_judge -Freopen ("inch","R", stdin); the     //freopen ("Out", "w", stdout);Bayi #endif the      while(~SCANF ("%d%d", &n, &M)) { theS= (n1) * (M-1)*2+1; T= (n1) * (M-1)*2+2; -Init (dijkstra::n= (n1) * (M-1)*2+2); -         intx; the          for(intI=0; i<n; i++) the              for(intj=0; j<m-1; J + +) { thescanf"%d", &x); theAddedge (i==0? s: ((i-1) * (M-1) +j) <<1|1, i==n-1? t: (I* (M-1) +j) <<1, x); -             } the          for(intI=0; i<n-1; i++) the              for(intj=0; j<m; J + +) { thescanf"%d", &x);94Addedge (j==m-1? s: (I* (M-1) +j) <<1|1, j==0? t: (I* (M-1) + (J-1)) <<1, x); the             } the          for(intI=0; i<n-1; i++) the              for(intj=0; j<m-1; J + +) {98scanf"%d", &x); AboutAddedge ((i* (M-1) +j) <<1, (i* (M-1) +j) <<1|1, x); -             }101          102printf"%d\n", Dijkstra::go (s));103     }104     return 0; the}

Bzoj 1001

Bzoj 1001 [BeiJing2006] Wolf catches rabbits