uva 10806 Dijkstra, Dijkstra. (最小费最大流)

uva 10806 Dijkstra, Dijkstra.题目大意:你和你的伙伴想要越狱。你的伙伴先去探路,等你的伙伴到火车站后,他会打电话给你(电话是藏在蛋糕里带进来的),然后你就可以跑去火车站了,那里有人接应你。但是,因为你的伙伴跑去火车站的时候穿的是囚服,所以,他经过的街道都被戒严了,你必须从其他街道跑过去。如果你可以到达火车站,请输出你和你的伙伴在路上花费的最短时间,如果不能请“Back to jail”。解题思路:最小费最大流。设置一个超级源点连向监狱(起点1), 容量为2(两个人),设置一个超级汇点,使火车站(终点n)连向他,容量为2(两个人),其余街道皆为无向(即正向反向都要考虑),且容量为1(每条街道只能跑一次)。最后求最大流,若最大流为2则输出最小费,否则回监狱准备下次越狱吧。;ll;const int N = 105;const int INF = 0x3f3f3f3f;int n, m, s, t;int a[N], pre[N], d[N], inq[N]; struct Edge{int from, to, cap, flow;ll cos;};vector<Edge> edges;vector<int> G[3 * N];void init() {for (int i = 0; i < 3 * N; i++) G[i].clear();edges.clear();}void addEdge(int from, int to, int cap, int flow, ll cos) {edges.push_back((Edge){from, to, cap, 0, cos});edges.push_back((Edge){to, from, 0, 0, -cos});int m = edges.size();G[from].push_back(m – 2);G[to].push_back(m – 1);}void input() {int from, to;ll cost;for (int i = 0; i < m; i++) {scanf(“%d %d %lld”, &from, &to, &cost);addEdge(from, to, 1, 0, cost);addEdge(to, from, 1, 0, cost);}addEdge(0, 1, 2, 0, 0);addEdge(n, n + 1, 2, 0, 0);}int BF(int s, int t, int& flow, ll& cost) {queue<int> Q;memset(inq, 0, sizeof(inq));memset(a, 0, sizeof(a));memset(pre, 0, sizeof(pre));for (int i = 0; i <= 2 * n + 1; i++) d[i] = INF;d[s] = 0;a[s] = INF;inq[s] = 1;int flag = 1;pre[s] = 0;Q.push(s);while (!Q.empty()) {int u = Q.front(); Q.pop();inq[u] = 0;for (int i = 0; i < G[u].size(); i++) {Edge &e = edges[G[u][i]];if (e.cap > e.flow && d[e.to] > d[u] + e.cos) {d[e.to] = d[u] + e.cos;a[e.to] = min(a[u], e.cap – e.flow);pre[e.to] = G[u][i];if (!inq[e.to]) {inq[e.to] = 1;Q.push(e.to);}}}flag = 0;}if (d[t] == INF) return 0;flow += a[t];cost += (ll)d[t] * (ll)a[t];for (int u = t; u != s; u = edges[pre[u]].from) {edges[pre[u]].flow += a[t];edges[pre[u]^1].flow -= a[t];}return 1;}int MCMF(int s, int t, ll& cost) {int flow = 0;cost = 0;while (BF(s, t, flow, cost));return flow;}int main() {while (scanf(“%d”, &n) != EOF) {if (n == 0) break;scanf(“%d”, &m);s = 0, t = n + 1;init();input();ll cost = 0;int ans = MCMF(s, t, cost);if (ans == 1) printf(“Back to jail\n”);else printf(“%lld\n”, cost);}return 0;}

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uva 10806 Dijkstra, Dijkstra. (最小费最大流)

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