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zhuliu.cpp
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zhuliu.cpp
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#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
using namespace std;
/*
* 最小树形图(确定根,求有向图最小生成树)
* int型
* 复杂度O(NM)
* 点从0开始
*/
const int INF = 0x7fffffff;
const int MAXN = 1010;
const int MAXM = 40010;
struct Edge {
int u,v,cost;
};
Edge edge[MAXM];
int pre[MAXN],id[MAXN],visit[MAXN],in[MAXN];
int zhuliu(int root,int n,int m,Edge edge[]) { //返回最小树形图的边权和,若不存在返回-1
int res = 0,u,v;
while(1) {
for(int i = 0; i < n; i++)
in[i] = INF;
for(int i = 0; i < m; i++)
if(edge[i].u != edge[i].v && edge[i].cost < in[edge[i].v]) {
pre[edge[i].v] = edge[i].u;
in[edge[i].v] = edge[i].cost;
}
for(int i = 0; i < n; i++)
if(i != root && in[i] == INF)
return -1;//不存在最小树形图
int tn = 0;
memset(id,-1,sizeof(id));
memset(visit,-1,sizeof(visit));
in[root] = 0;
for(int i = 0; i < n; i++) {
res += in[i];
v = i;
while( visit[v] != i && id[v] == -1 && v != root) {
visit[v] = i;
v = pre[v];
}
if( v != root && id[v] == -1 ) {
for(int u = pre[v]; u != v ; u = pre[u])
id[u] = tn;
id[v] = tn++;
}
}
if(tn == 0)break;//没有有向环
for(int i = 0; i < n; i++)
if(id[i] == -1)
id[i] = tn++;
for(int i = 0; i < m;) {
v = edge[i].v;
edge[i].u = id[edge[i].u];
edge[i].v = id[edge[i].v];
if(edge[i].u != edge[i].v)
edge[i++].cost -= in[v];
else
swap(edge[i],edge[--m]);
}
n = tn;
root = id[root];
}
return res;
}
int main() {
int n,m;
scanf("%d%d",&n,&m);
for(int i=0; i<m; i++) {
int u,v,cost;
scanf("%d%d%d",&u,&v,&cost);
edge[i].u = u;
edge[i].v = v;
edge[i].cost = cost;
}
int ans = zhuliu(0,n,m,edge);
if(ans == -1)printf("No way!\n");
else printf("%d\n",ans);
return 0;
}