ACM-ICPC 2018 瀋陽賽區網路預賽 F題 Fantastic Graph (有源匯的上下界可行流)
阿新 • • 發佈:2018-12-09
題意
給你兩個集合X,Y,X集合有N個點,Y集合有M個點,輸入一個上下界down,up,現在有K條邊,輸入K條邊(u,v)。每選擇一條邊(u,v),u和v點的權值就+1,問能否通過選擇一些邊(每條邊只能選一次)使得所有點的權值都在[down,up]之間。
思路
有源匯的上下界可行流。
建立源點s,t。
①s向X集合每一個點連邊,上下界為[down,up]
②Y集合向 t 連邊, 上下界為[down,up]
③題目中的邊,上下界為[0,1]
然後跑有源匯的上下界可行流即可。
//#include<bits/stdc++.h> #include <iostream> #include <cstdio> #include <cstring> #include <cmath> #include <vector> #include <queue> using namespace std; const int MAXN = 1e5 + 5; const int INF = 0x3f3f3f3f; struct Edge { int from, to, cap, flow; //起點,終點,容量,流量 Edge(int u, int v, int c, int f) : from(u), to(v), cap(c), flow(f) {} }; struct Dinic { int n, m, s, t; //結點數,邊數(包括反向弧),源點s,匯點t vector<Edge> edges; //邊表。edges[e]和edges[e^1]互為反向弧 vector<int> G[MAXN]; //鄰接表,G[i][j]表示結點i的第j條邊在edges陣列中的序號 int d[MAXN]; //從起點到i的距離(層數差) int cur[MAXN]; //當前弧下標 bool vis[MAXN]; //BFS分層使用 void init(int n) { this->n = n; edges.clear(); for (int i = 0; i <= n; i++) G[i].clear(); } void AddEdge(int from, int to, int cap) { edges.push_back(Edge(from, to, cap, 0)); edges.push_back(Edge(to, from, 0, 0)); m = edges.size(); G[from].push_back(m - 2); G[to].push_back(m - 1); } bool BFS()//構造分層網路 { memset(vis, 0, sizeof(vis)); queue<int> Q; d[s] = 0; vis[s] = true; Q.push(s); while (!Q.empty()) { int x = Q.front(); Q.pop(); for (int i = 0; i < G[x].size(); i++) { Edge& e = edges[G[x][i]]; if (!vis[e.to] && e.cap > e.flow) { vis[e.to] = true; d[e.to] = d[x] + 1; Q.push(e.to); } } } return vis[t]; } int DFS(int x, int a)//沿阻塞流增廣 { if (x == t || a == 0) return a; int flow = 0, f; for (int& i = cur[x]; i < G[x].size(); i++)//從上次考慮的弧 { Edge& e = edges[G[x][i]]; if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0)//多路增廣 { e.flow += f; edges[G[x][i]^1].flow -= f; flow += f; a -= f; if (a == 0) break; } } return flow; } int MaxFlow(int s, int t) { this->s = s; this->t = t; int flow = 0; while (BFS()) { memset(cur, 0, sizeof(cur)); flow += DFS(s, INF); } return flow; } }solve; int n, m, k, down, up, sum[MAXN]; int main() { int CASE = 1; while (~scanf("%d%d%d", &n, &m, &k)) { int tot = 0; memset(sum, 0, sizeof(sum)); scanf("%d%d", &down, &up); int s = 0, t = n+m+1, vs = n+m+2, vt = n+m+3; solve.init(vt); solve.AddEdge(t, s, INF); for (int i = 1; i <= n; i++) { solve.AddEdge(s, i, up-down); sum[s] -= down; sum[i] += down; } for (int i = 1; i <= m; i++) { solve.AddEdge(i+n, t, up-down); sum[i+n] -= down; sum[t] += down; } while (k--) { int u, v; scanf("%d%d", &u, &v); solve.AddEdge(u, v+n, 1); } for (int i = s; i <= t; i++) { if (sum[i] < 0) solve.AddEdge(i, vt, -sum[i]); else solve.AddEdge(vs, i, sum[i]), tot += sum[i]; } printf("Case %d: ", CASE++); int ans = solve.MaxFlow(vs, vt); if (ans == tot) printf("Yes\n"); else printf("No\n"); } return 0; } /* 3 3 7 2 3 1 2 2 3 1 3 3 2 3 3 2 1 2 1 3 3 7 3 4 1 2 2 3 1 3 3 2 3 3 2 1 2 1 */