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POJ2135 来回最短路(简单费用流)

码农K 2022-07-27 阅读 64

题意:
      就是从1走到n然后再走回来,一条边只能走一次,要求路径最短。

思路:
      比较水,可以直接一遍费用流,不解释了,具体的看看代码,敲这个题就是为了练

练手,好久不敲了,怕比赛手生。

#include<queue>

#include<stdio.h>

#include<string.h>
#define N_node 1000 + 10

#define N_edge 40000 + 20

#define INF 100000000
using namespace std;
typedef struct

{

int from ,to ,cost ,flow ,next;

}STAR;
STAR E[N_edge];

int list[N_node] ,tot;

int mer[N_edge];

int s_x[N_node];
void add(int a ,int b ,int c ,int d)

{

E[++tot].from = a;

E[tot].to = b;

E[tot].cost = c;

E[tot].flow = d;

E[tot].next = list[a];

list[a] = tot;



E[++tot].from = b;

E[tot].to = a;

E[tot].cost = -c;

E[tot].flow = 0;

E[tot].next = list[b];

list[b] = tot;

}
bool Spfa(int s ,int t ,int n)

{

int mark[N_node] = {0};

for(int i = 0 ;i <= n ;i ++) s_x[i] = INF;

mark[s] = 1 ,s_x[s] = 0;

queue<int>q;

q.push(s);

memset(mer ,255 ,sizeof(mer));

while(!q.empty())

{

int xin ,tou = q.front();

q.pop();

mark[tou] = 0;

for(int k = list[tou] ;k ;k = E[k].next)

{

xin = E[k].to;

if(s_x[xin] > s_x[tou] + E[k].cost && E[k].flow)

{

s_x[xin] = s_x[tou] + E[k].cost;

mer[xin] = k;

if(!mark[xin])

{

mark[xin] = 1;

q.push(xin);

}

}

}

}

return mer[t] != -1;

}
int M_C_Flow(int s ,int t ,int n)

{

int maxflow = 0 ,mincost = 0 ,minflow;

while(Spfa(s ,t ,n))

{

minflow = INF;

for(int i = mer[t] ;i + 1 ;i = mer[E[i].from])

if(minflow > E[i].flow) minflow = E[i].flow;

for(int i = mer[t] ;i + 1 ;i = mer[E[i].from])

{

E[i].flow -= minflow;

E[i^1].flow += minflow;

mincost += minflow * E[i].cost;

}

maxflow += minflow;

}

return mincost;

}
int main ()

{

int n ,m ,i ,a ,b ,c;

while(~scanf("%d %d" ,&n ,&m))

{

memset(list ,0 ,sizeof(list)) ,tot = 1;

for(i = 1 ;i <= m ;i ++)

{

scanf("%d %d %d" ,&a ,&b ,&c);

add(a ,b ,c ,1);

add(b ,a ,c ,1);

}

add(0 ,1 ,0 ,2);

add(n ,n + 1 ,0 ,2);

printf("%d\n" ,M_C_Flow(0 ,n + 1 ,n + 1));

}

return 0;

}


   
   
   
   
    










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