HDU 3072 Intelligence System
题意:给定有向图,边有权值,求保留一些边,从一点出发,能传递到其他所有点的最小代价,保证有解
思路:先缩点,然后从入度为0的点作为起点(因为题目保证有解,所以必然有一个且只有一个入度为0的点),然后做一下最小树形图即可
代码:
#include <cstdio> #include <cstring> #include <vector> #include <algorithm> #include <stack> using namespace std; const int MAXNODE = 50005; const int MAXEDGE = 100005; typedef int Type; const Type INF = 0x3f3f3f3f; struct Edge { int u, v; Type dist; Edge() {} Edge(int u, int v, Type dist) { this->u = u; this->v = v; this->dist = dist; } }; struct Directed_MST { int n, m; Edge edges[MAXEDGE]; int vis[MAXNODE]; int pre[MAXNODE]; int id[MAXNODE]; Type in[MAXNODE]; void init(int n) { this->n = n; m = 0; } void add_Edge(int u, int v, Type dist) { edges[m++] = Edge(u, v, dist); } void add_Edge(Edge e) { edges[m++] = e; } Type dir_mst(int root) { Type ans = 0; while (true) { for (int i = 0; i < n; i++) in[i] = INF; for (int i = 0; i < m; i++) { //find min edge int u = edges[i].u; int v = edges[i].v; if (edges[i].dist < in[v] && u != v) { in[v] = edges[i].dist; pre[v] = u; } } for (int i = 0; i < n; i++) { //judge 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 < n; i++) { //find circle 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 < n; i++) if (id[i] == -1) id[i] = cnt++; for (int i = 0; i < m; i++) { int v = edges[i].v; edges[i].u = id[edges[i].u]; edges[i].v = id[edges[i].v]; if (edges[i].u != edges[i].v) edges[i].dist -= in[v]; } n = cnt; root = id[root]; } return ans; } } gao; const int N = 50005; vector<Edge> g[N]; int n, m; int pre[N], dfn[N], sccno[N], sccn, dfs_clock; stack<int> S; void dfs_scc(int u) { pre[u] = dfn[u] = ++dfs_clock; S.push(u); for (int i = 0; i < g[u].size(); i++) { int v = g[u][i].v; if (!pre[v]) { dfs_scc(v); dfn[u] = min(dfn[u], dfn[v]); } else if (!sccno[v]) dfn[u] = min(dfn[u], pre[v]); } if (dfn[u] == pre[u]) { sccn++; while (1) { int x = S.top(); S.pop(); sccno[x] = sccn; if (x == u) break; } } } void find_scc() { dfs_clock = sccn = 0; memset(pre, 0, sizeof(pre)); memset(sccno, 0, sizeof(sccno)); for (int i = 0; i < n; i++) if (!pre[i]) dfs_scc(i); } int in[N]; int main() { while (~scanf("%d%d", &n, &m)) { for (int i = 0; i < n; i++) g[i].clear(); int u, v, val; while (m--) { scanf("%d%d%d", &u, &v, &val); g[u].push_back(Edge(u, v, val)); } find_scc(); gao.init(sccn); memset(in, 0, sizeof(in)); for (int u = 0; u < n; u++) { for (int j = 0; j < g[u].size(); j++) { int v = g[u][j].v; if (sccno[u] == sccno[v]) continue; in[sccno[v]]++; gao.add_Edge(sccno[u] - 1, sccno[v] - 1, g[u][j].dist); } } for (int i = 1; i <= sccn; i++) { if (!in[i]) { printf("%d\n", gao.dir_mst(i - 1)); break; } } } return 0; }
时间: 2024-10-10 13:46:30