hdu4966 最小树形图+虚根

/*

辛辛苦苦调试半天，

过了样例，竟然没有ac！！

网上对比了ac代码，感觉添加一个虚根就能ac

但是想不明白为什么

*/

/*

第二天想了下，知道了为什么wa：因为从等级0连到其他课程等级i的不止一门课，如果不加虚根，仅仅是通过判断L1[i]==0来决定根节点显然是会错的

添加根节点能保证生成的是最小树形图

*/

我的代码

/*
hdu4966
第i门课从0到a[i]个等级，从最开始所有课都是0级，目标所有课到最高级
M条路，如果第i门课达到L1[i]，那么通过M后，第j门课到达L2[i]
N，M
a[i] .. a[N]
接下来M行c[i], L1[i], d[i], L2[i], money[i]
边权当然是money，每门课拆成a[i]个等级(500个点)
每门课的a[i]到a[i]-1连一条权值为0的边 
增加一个超级源点，和每门课level 0连在一起 
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#define MAXN 505
#define INF 0x3f3f3f
using namespace std;
struct Edge{
    int u,v,cost;
}edge[MAXN*MAXN];
int a[MAXN];//等级 
int V[MAXN][MAXN];//点集
int c[MAXN],L1[MAXN],d[MAXN],L2[MAXN],money[MAXN]; 
int pre[MAXN],id[MAXN],vis[MAXN],in[MAXN];
int zhuliu(int root,int n,int m){
    int res=0;
    int 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;
        
        int tn=0;
        memset(id,-1,sizeof id);
        memset(vis,-1,sizeof vis);
        in[root]=0;
        for(int i=0;i<n;i++){
            res+=in[i];
            v=i;
            while(v!=root && id[v]==-1 && vis[v]!=i){
                vis[v]=i;
                v=pre[v];
            }
            if(id[v]==-1 && v!=root){
                for(int u=pre[v];u!=v;u=pre[u])
                    id[u]=tn;
                id[v]=tn++;
            }
        }
        
        if(tn==0)
            break;
        for(int i=0;i<n;i++)
            if(id[i]==-1)
                id[i]=tn++;
        for(int i=0;i<m;i++){//第四步，更新一次边集 
            int u=edge[i].u;
            int v=edge[i].v;
            edge[i].u=id[u];
            edge[i].v=id[v];
            if(id[u] != id[v])
                edge[i].cost-=in[v]; 
        }
        n=tn;
        root=id[root];        
    }
    return res; 
}
int totm;
void addedge(int u,int v,int w){
    edge[totm].u=u;
    edge[totm].v=v;
    edge[totm].cost=w;
    totm++;
}
int main(){
    int n,m,totn;
    while(scanf("%d%d",&n,&m) && n && m){
        totn=totm=0;
        memset(V,0,sizeof V);
        for(int i=1;i<=n;i++){
            scanf("%d",&a[i]);
            for(int j=0;j<=a[i];j++){
                V[i][j]=totn++; 
                if(j!=0)
                    addedge(V[i][j],V[i][j-1],0);
            }
        }
        int sum=0,root=0;
        for(int i=1;i<=m;i++){
            scanf("%d%d%d%d%d",&c[i],&L1[i],&d[i],&L2[i],&money[i]);
            if(L1[i]==0)
                root=c[i];
            addedge(V[c[i]][L1[i]],V[d[i]][L2[i]],money[i]);
            sum+=money[i];
        }
        
        if(root==0){
            printf("-1
");
            continue;
        }
        
        int ans=zhuliu(root,totn,totm);
            printf("%d
",ans);
    }
    return 0;
}

 ac代码

#include <cstdio>
#include <cstring>
#include <iostream>
 
using namespace std;
 
const int maxn = 555, maxm = 500 * 2000, inf = 1e9;
 
struct Edge{
    int u, v, w;
    Edge(){}
    Edge(int u, int v, int w):
    u(u), v(v), w(w){}
}e[maxm];
int ec;
int lev[55], begid[55], endid[55];
int N;
 
int mincost[maxn], pre[maxn];
bool makeMin(int root){
    for(int i = 1; i <= N; i++) mincost[i] = inf;
    for(int i = 0; i < ec; i++){
        if(e[i].u == e[i].v) continue;
        int v = e[i].v;
        if(mincost[v] > e[i].w){
            mincost[v] = e[i].w;
            pre[v] = e[i].u;
        }    
    }
    for(int i = 1; i <= N; i++){
        if(i == root) continue;
        if(mincost[i] == inf) return false;
    }
    return true;
}
 
int vis[maxn];
int id[maxn];
bool existCircle(int root, int &res){
    memset(vis, -1, sizeof(vis));
    memset(id, -1, sizeof(id));
    int ind = 1;
    mincost[root] = 0;
    for(int i = 1; i <= N; i++){
        int v = i;
        res += mincost[i];
        while(vis[v] != i && v != root && id[v] == -1) {
            vis[v] = i, v = pre[v];
        }
        if(v != root && id[v] == -1){
            for(int u = pre[v]; u != v; u = pre[u]) id[u] = ind;
            id[v] = ind++;
        }
    }
    if(ind == 1) return false;
    for(int i = 1; i <= N; i++)
        if(id[i] == -1) id[i] = ind++;
    N = ind - 1;
    return true;
}
 
void update(){
    for(int i = 0; i < ec; i++){
        int v = e[i].v;
        e[i].u = id[e[i].u];
        e[i].v = id[e[i].v];
        if(e[i].u == e[i].v) continue;
        e[i].w -= mincost[v];            
    }
}
 
int DMST(int root){
    int res = 0;
    while(1){
        if(!makeMin(root)) return -1;
        if(!existCircle(root, res)) return res;
        update();
        root = id[root];
    }
    return -1;
}
 
int main(){
//    freopen("in", "r", stdin);
//    freopen("out", "w", stdout);
    int n, m;
    while(scanf("%d%d", &n, &m), n&&m){
        for(int i = 1; i <= n; i++) scanf("%d", lev+i);    
        lev[0] = 1, begid[0] = 0;    
        for(int i = 1; i <= n; i++) begid[i] = begid[i-1] + lev[i-1] + 1;
        N = begid[n] + lev[n];        
        int c, l, d, r, w;
        int root = 1;
        ec = 0;
        for(int i = 1; i <= n; i++)
        e[ec++] = Edge(root, begid[i], 0);
        for(int i = 1; i <= n; i++){
            for(int j = 1; j <= lev[i]; j++){
                int u = begid[i] + j, v = u - 1;
                e[ec++] = Edge(u, v, 0);
            }
        }
        for(int i = 0; i < m; i++){
            scanf("%d%d%d%d%d", &c, &l, &d, &r, &w);
            int v = begid[d] + r;
            for(int j = l, u = begid[c] + l; j <= lev[c]; u++, j++){
                e[ec++] = Edge(u, v, w);    
            }
        }    
        int ans = DMST(root);
        if(~ans) printf("%d
", ans);
        else puts("-1");
    }
    return 0;
}