Medium HDU 4370 0 or 1, modelling +dijkstra.

Description

Given a n*n matrix C ij (1<=i,j<=n), We want to find a n*n matrix X ij (1<=i,j<=n), which is 0 or 1.

Besides,x IJ meets the following conditions:

1.X 12+x 13+ ... X 1n=1
2.X 1n+x 2n+ ... X N-1n=1
3.for each I (1<i<n), Satisfies∑x ki (1<=k<=n) =∑x ij (1<=j<=n).

For example, if N=4,we can get the following equality:

X 12+x 13+x 14=1
X 14+x 24+x 34=1
X 12+x 22+x 32+x 42=x 21+x 22+x 23+x 24
X 13+x 23+x 33+x 43=x 31+x 32+x 33+x 34

Now, we want to know the minimum of∑c ij*x ij (1<=i,j<=n) can get.

The problem can be converted to the shortest path. The problem can be 1.1 points of analysis, the first is to select the first row of the K after the choice of a K line, so the edge of the 1->k edge of the first row of the value of K, and then the shortest way to find 1->n is good ...

There is, however, a special case where 1 and the other form a ring, N and the other form a ring. So the answer is two rings of the and, and the shortest short of the small one ...

The code is as follows:

#include <stdio.h>#include<string.h>#include<iostream>#include<algorithm>#include<vector>#include<queue>#include<Set>#include<map>#include<string>#include<math.h>#include<stdlib.h>#include<time.h>using namespacestd;Const intmaxn= -;Const intinf=10e8;voidDijkstra (intCOST[][MAXN],intLowcost[],intNintstart) {Priority_queue<int>que; intT;  for(intI=1; i<=n;++i) lowcost[i]=INF;    Que.push (start);  while(!Que.empty ()) {T=Que.top ();        Que.pop ();  for(intI=1; i<=n;++i)if(i!=t)if(Lowcost[t]==inf | | lowcost[i]>lowcost[t]+Cost[t][i]) {Lowcost[i]= (Lowcost[t]==inf?)0: lowcost[t]) +Cost[t][i];                Que.push (i); }    }}intMAP1[MAXN][MAXN];intANS[MAXN];intMain () {//freopen ("In.txt", "R", stdin); //freopen ("OUT.txt", "w", stdout);    intN; intt1,t2;  while(~SCANF ("%d",&N)) { for(intI=1; i<=n;++i) for(intj=1; j<=n;++j) scanf ("%d",&Map1[i][j]); Dijkstra (Map1,ans,n,1); T1=Ans[n]; T2=ans[1];        Dijkstra (Map1,ans,n,n); T2+=Ans[n]; printf ("%d\n", Min (t1,t2)); }        return 0;}

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Medium HDU 4370 0 or 1, modelling +dijkstra.