最大流 增广路算法+最小费用最大流

cap>flow代表连通，cap==flow代表不连通

最大流

不停的寻找s连通至t的路径，更新..直到找不到路径

注:p[u] ^ 1和p[u]互为方向边

#include<iostream>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
const int maxn = 1005;
const int inf = 0x3f3f3f3f;

struct Edge {
int from,to,cap,flow;
Edge() = default;
Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}
};
vector<Edge> edges;
vector<int> G[maxn];
int a[maxn], p[maxn];//起点到i的可改进量，最短路树上p的入弧编号
void add_Edge(int from, int to, int cap) {
edges.push_back(Edge(from, to, cap, 0));
edges.push_back(Edge(to, from, 0, 0));
int m = edges.size();
G[from].push_back(m - 2);
G[to].push_back(m - 1);
}
int Maxflow(int s, int t) {
int flow = 0;
while (1) {
memset(a, 0, sizeof(a));
queue<int> Q;
Q.push(s);
a[s] = inf;
while (!Q.empty()) {
int x = Q.front(); Q.pop();
for (auto y : G[x]) {
if (!a[edges[y].to] && edges[y].cap > edges[y].flow)
p[edges[y].to] = y, a[edges[y].to] = min(a[x], edges[y].cap - edges[y].flow)
, Q.push(edges[y].to);
}
if (a[t]) break;
}
if (!a[t]) break;
flow += a[t];
for (int u = t; u != s; u = edges[p[u]].from)
edges[p[u]].flow += a[t], edges[p[u] ^ 1].flow -= a[t];
}
return flow;
}

最小费用最大流

由于cost可能为负，故用BellmanFord寻找s至t的最短路径，然后更新…直到不连通

#include<iostream>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
const int maxn = 1005;
const int inf = 0x3f3f3f3f;
struct Edge {
int from,to,cap,flow,cost;
Edge() = default;
Edge(int u,int v,int c,int f,int d):from(u),to(v),cap(c),flow(f),cost(d){}
};
vector<Edge> edges;
vector<int> G[maxn];
int a[maxn], p[maxn],d[maxn],inq[maxn],n;//起点到i的可改进量，最短路树上p的入弧编号
void add_Edge(int from, int to, int cap,int cost) {
edges.push_back(Edge(from, to, cap, 0,cost));
edges.push_back(Edge(to, from, 0, 0,-cost));
int m = edges.size();
G[from].push_back(m - 2);
G[to].push_back(m - 1);
}
bool BellmanFord(int s, int t, int &flow, int &cost) {
for (int i = 0; i < n; ++i)
d[i] = inf;
memset(inq, 0, sizeof(inq));
d[s] = 0, inq[s] = 1, p[s] = 0, a[s] = inf;
//memset(a, 0, sizeof(a));
queue<int> Q;
Q.push(s);
a[s] = inf;
while (!Q.empty()) {
int u = Q.front(); Q.pop();
inq[u] = 0;
for (auto x : G[u])
if (edges[x].cap > edges[x].flow && d[edges[x].to] < d[u] + edges[x].cost) {
d[edges[x].to] = d[u] + edges[x].cost, p[edges[x].to] = x
, a[edges[x].to] = min(a[u], edges[x].cap - edges[x].flow);
if (!inq[edges[x].to]) inq[edges[x].to] = 1, Q.push(edges[x].to);
}
}
if (d[t]==inf) return false;
flow += a[t];
cost += d[t] * a[t];
for (int u = t; u != s; u = edges[p[u]].flow)
edges[p[u]].flow += a[t], edges[p[u] ^ 1].flow -= a[t];
return true;
}
int MincostMaxflow(int s, int t, int &cost) {
int flow = 0; cost = 0;
while (BellmanFord(s, t, flow, cost));
return flow;
}