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UVA - 1658 Admiral (最小费用最大流)

2015-08-26 15:12 453 查看
最短路对应费用,路径数量对应流量。为限制点经过次数,拆点为边。跑一次流量为2的最小费用最大流。

最小费用最大流和最大流EK算法是十分相似的,只是把找增广路的部分换成了求费用的最短路。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

const int maxv = 2000+5;
const int maxe = 22000+5;

struct Edge
{
int v,cap,cost,nxt;
void IN(int V,int C,int c,int N)
{
v = V; cap = C; cost = c; nxt = N;
}
}edges[maxe];

int head[maxv],ecnt,vcnt;

void AddEdge(int u,int v,int C,int c)
{
edges[ecnt].IN(v,C,c,head[u]);
head[u] = ecnt++;
edges[ecnt].IN(u,0,-c,head[v]);
head[v] = ecnt++;
}
const int INF = 0x3f3f3f3f;
int S,T;
bool vis[maxv];
int d[maxv],p[maxv],a[maxv];
bool spfa()
{
memset(d,0x3f,sizeof(int)*vcnt);
memset(vis,0,sizeof(bool)*vcnt);

queue<int> q; q.push(S); d[S] = 0;
a[S] = INF;
while(q.size()){
int u = q.front(); q.pop();
vis[u] = false;
for(int i = head[u]; ~i; i = edges[i].nxt){
Edge &e = edges[i];
if(e.cap&& d[e.v] > d[u]+e.cost){
d[e.v] = d[u] + e.cost;
p[e.v] = i;
a[e.v] = min(a[u],e.cap);
if(!vis[e.v]) { q.push(e.v); vis[e.v] = true; }
}
}
}
return d[T] != INF;
}

ll MinCostMaxFlow()
{
ll cost = 0;
while(spfa()){
cost += d[T];
for(int i = T; i != S; i = edges[p[i]^1].v){
edges[p[i]].cap -= a[T];
edges[p[i]^1].cap += a[T];
}
}
return cost;
}

int pin[maxv],pout[maxv];

int main()
{
//freopen("in.txt","r",stdin);
int v,e;
int S = 0; T = 1;
while(~scanf("%d%d",&v,&e)){

vcnt = 2; ecnt = 0;
pin[1] = pout[1] = vcnt++;
pin[v] = pout[v] = vcnt++;
for(int i = 2; i < v; i++) {
pin[i] = vcnt++;
pout[i] = vcnt++;
}
memset(head,-1,sizeof(int)*(vcnt));
AddEdge(S,pin[1],2,0);
AddEdge(pout[v],T,2,0);
for(int i = 2; i < v; i++) AddEdge(pin[i],pout[i],1,0);
while(e--){
int u,v,c; scanf("%d%d%d",&u,&v,&c);
AddEdge(pout[u],pin[v],1,c);
}
printf("%lld\n",MinCostMaxFlow());
}
return 0;
}
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