題目連結

最小樹形圖講解

  一道最小樹形圖的裸題，我們只需要對於在同一學科的由高等級逐一指向低等級的邊建為0權值即可，另外的邊，建立成有向邊即可。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
int N, M, a[55], b[55][501], num_V, num_E, tot;
struct Eddge
{
    int u, v, val;
    Eddge(int a=0, int b=0, int c=0):u(a), v(b), val(c) {}
}edge[250005];
int vis[1005], id[1005], pre[1005], in[1005];
int Dir_MST(int root, int V, int E)
{
    int ans = 0;
    while(true)
    {
        for(int i=0; i<V; i++) in[i] = INF;
        for(int i=1; i<=E; i++)
        {
            int u = edge[i].u, v = edge[i].v;
            if(u != v && edge[i].val < in[v])
            {
                in[v] = edge[i].val;
                pre[v] = u;
            }
        }
        for(int i=0; i<V; i++)
        {
            if(i == root) continue;
            if(in[i] == INF) return -1;
        }
        int cnt = 0;
        memset(id, -1, sizeof(id)); memset(vis, -1, sizeof(vis));
        in[root] = 0;
        for(int i=0; i<V; i++)
        {
            ans += in[i];
            int v = i;
            while(vis[v] != i && id[v] == -1 && v != root)
            {
                vis[v] = i;
                v = pre[v];
            }
            if(v != root && id[v] == -1)
            {
                for(int u = pre[v]; u != v; u = pre[u]) id[u] = cnt;
                id[v] = cnt++;
            }
        }
        if(cnt == 0) break;
        for(int i=0; i<V; i++) if(id[i] == -1) id[i] = cnt++;
        for(int i=1; i<=E; i++)
        {
            int u = edge[i].u, v = edge[i].v;
            edge[i].u = id[u];  edge[i].v = id[v];
            if(id[u] != id[v]) edge[i].val -= in[v];
        }
        V = cnt;
        root = id[root];
    }
    return ans;
}
void init()
{
    num_E = num_V = 0;
}
int main()
{
    while(scanf("%d%d", &N, &M) && (N || M))
    {
        init();
        for(int i=1; i<=N; i++)
        {
            scanf("%d", &a[i]);
            b[i][0] = ++num_V;
            for(int j=1; j<=a[i]; j++)
            {
                b[i][j] = ++num_V;
                edge[++num_E] = Eddge(num_V, num_V-1, 0);
            }
        }
        for(int i=1, e1, e2, e3, e4, e5; i<=M; i++)
        {
            scanf("%d%d%d%d%d", &e1, &e2, &e3, &e4, &e5);
            if(e2 == 0) edge[++num_E] = Eddge(0, b[e1][e2], 0);
            edge[++num_E] = Eddge(b[e1][e2], b[e3][e4], e5);
        }
        printf("%d\n", Dir_MST(0, num_V + 1, num_E));
    }
    return 0;
}