UVA 11865 - Stream My Contest(最小树形图)

UVA 11865 - Stream My Contest

题目链接

题意：给定一些有向边，每个边有一个花费和一个带宽，给定一个金额，要求一个有向生成树使得金额足够，并且带宽最小值尽量大，求出这个最大值

思路：二分带宽，然后就是最小树形图了

代码：

#include <cstdio>#include <cstring>const int MAXNODE = 65;const int MAXEDGE = 10005;typedef long long Type;const Type INF = 0x3f3f3f3f3f3f3f;struct Edge {int u, v, kbps;Type dist;Edge() {}Edge(int u, int v, Type dist, int kbps = 0) {this->u = u;this->v = v;this->dist = dist;this->kbps = kbps;}void read() {scanf("%d%d%d%lld", &u, &v, &kbps, &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 edgeint 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++) { //judgeif (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 circleans += 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;typedef long long ll;Edge e[MAXEDGE];int t, n, m;ll c;bool judge(int mid) {gao.init(n);for (int i = 0; i < m; i++) {if (e[i].kbps < mid) continue;gao.add_Edge(e[i]);}ll tmp = gao.dir_mst(0);if (tmp == -1) return false;return tmp <= c;}int main() {scanf("%d", &t);while (t--) {scanf("%d%d%lld", &n, &m, &c);for (int i = 0; i < m; i++)e[i].read();int l = 0, r = 1000001;if (!judge(l)) printf("streaming not possible.\n");else {while (l < r) {int mid = (l + r) / 2;if (judge(mid)) l = mid + 1;else r = mid;}printf("%d kbps\n", l - 1);}}return 0;}