UV 11090, uva11090

UV 11090, uva11090
Ultraviolet A 11090-Going in Cycle !!

Question Link

Given a directed graph, the loop with the smallest average weight of the ball

Idea: Binary + negative ring. Every time a binary value of mid is used to determine whether there is a ring smaller than mid, It is (w1 + w2 + w3 ...) /n <mid = w1-mid + w2-mid + w3-mid .... <0, so the edge weight is reduced to the mid value every second, and then the bellmanford judges the negative ring.

Code:

#include <cstdio>#include <cstring>#include <vector>#include <algorithm>#include <queue>using namespace std;typedef double Type;const int MAXNODE = 55;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 BellmanFrod {int n, m;vector<Edge> edges;vector<int> g[MAXNODE];bool inq[MAXNODE];Type d[MAXNODE];int p[MAXNODE];int cnt[MAXNODE];void init(int n) {this->n = n;for (int i = 0; i < n; i++) g[i].clear();edges.clear();}void add_Edge(int u, int v, Type dist) {edges.push_back(Edge(u, v, dist));m = edges.size();g[u].push_back(m - 1);}bool negativeCycle() {queue<int> Q;memset(inq, 0, sizeof(inq));memset(cnt, 0, sizeof(cnt));for (int i = 0; i < n; i++) {d[i] = 0; inq[i] = true; Q.push(i);}while (!Q.empty()) {int u = Q.front();Q.pop();inq[u] = false;for (int i = 0; i < g[u].size(); i++) {Edge& e = edges[g[u][i]];if (d[e.v] > d[u] + e.dist) {d[e.v] = d[u] + e.dist;p[e.v] = g[u][i];if (!inq[e.v]) {Q.push(e.v);inq[e.v] = true;if (++cnt[e.v] > n) return true;}}}}return false;}} gao;int T, n, m;bool judge(double mid) {for (int i = 0; i < gao.m; i++)gao.edges[i].dist -= mid;bool tmp = gao.negativeCycle();for (int i = 0; i < gao.m; i++)gao.edges[i].dist += mid;return tmp;}int main() {scanf("%d", &T);int cas = 0;while (T--) {scanf("%d%d", &n, &m);gao.init(n);int u, v;double dist;double Max = 0;while (m--) {scanf("%d%d%lf", &u, &v, &dist);u--; v--;Max = max(Max, dist);gao.add_Edge(u, v, dist);}printf("Case #%d: ", ++cas);if (!judge(Max + 1)) printf("No cycle found.\n");else {double l = 0, r = Max;for (int i = 0; i < 100; i++) {double mid = (l + r) / 2;if (!judge(mid)) l = mid;else r = mid;}printf("%.2lf\n", l);}}return 0;}