Edmonds–Karp算法
计算机科学中, Edmonds–Karp算法通过实现Ford–Fulkerson算法来计算网络中的最大流,其时间复杂度为。该算法由Yefim (Chaim) Dinic 在1970年最先提出并由Jack Edmonds和理察·卡普在1972年独立发表。[1]
C++實作
以下是关于 Edmonds-Karp 算法的 C++ 语言描述:
struct Main {
struct Edge {
int u, v, Capacity, Flow;
Edge (int u, int v, int Capacity, int Flow) :
u(u), v(v), Capacity(Capacity), Flow(Flow) {}
};
struct Edmonds_Karp {
vector<Edge> Edges;
vector<int> Graph[MAXN]; // 保存下标
int n,
Augment[MAXN], Previous[MAXN];
// 当起点到 Augment[i] 的可改进量;
void Initialise(int n)
{
for (int i = 0; i < n; ++i)
G[i].clear();
Edges.clear();
}
void Add(int u, int v, int Capacity)
{
Edges.push_back(Edge(u, v, Capacity, 0));
Edges.push_back(Edge(v, u, 0, 0));
int m = Edges.size() - 1;
Graph[u].push_back(m - 1);
Graph[v].push_back(m);
}
};
int MaxFlow(int s, int t)
{
int FlowSum = 0;
while (1) {
memset(Augment, 0, sizeof Augment);
queue<int> Travel;
Travel.push(s);
Augment[s] = INT_MAX;
while (!Travel.empty()) {
int From = Travel.front();
Travel.pop();
for (int i = 0; i < Graph[From].size(); ++i) {
Edge &Temp = Edges[Graph[From][i]];
if (!Augment[Temp.v] && Temp.Capacity > Temp.Flow) {
Previous[Temp.v] = Graph[From][i];
Augment[Temp.v] = min(Augment[From], Temp.Capacity - Temp.Flow);
Travel.push(Temp.v);
}
}
if (Augment[t]) break;
}
if (!Augment[t]) break;
for (int i = t; i != s; i = Edges[Previous[i]].From) {
Edges[Previous[i]].Flow += Augment[t];
Edges[Previous[i] ^ 1].Flow -= Augment[t];
}
FlowSum += Augment[t];
}
return flow;
}
Main(void) {}
};
参考资料
- Edmonds, Jack; Karp, Richard M. . Journal of the ACM (Association for Computing Machinery). 1972, 19 (2): 248–264. doi:10.1145/321694.321699 (英语).
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