【模板】网络最大流(EK、Dinic、ISAP)(网络流)/洛谷P3376
题目链接
https://www.luogu.com.cn/problem/P3376
题目大意
输入格式
第一行包含四个正整数 \(n,m,s,t\),分别表示点的个数、有向边的个数、源点序号、汇点序号。
接下来\(m\)行,每行包含三个正整数 \(u_i,v_i,w_i\),表示第 \(i\) 条有向边从 \(u_i\) 出发,到达 \(v_i\),边权为 \(w_i\)(即该边最大流量为 \(w_i\) )。
输出格式
一行,包含一个正整数,即为该网络的最大流。
题目解析
(待补充,咕咕咕。。。)
参考代码
\(EK\)
#include <bits/stdc++.h>
using namespace std;
const int N = 205;
const long long INF = (1LL << 32);
struct Edge{
int from, to;
long long cap, flow;
};
int n, m, s, t;
long long a[N];
int p[N];
vector <Edge> e;
vector <int> G[N];
void addEdge(int from, int to, int cap, int i)
{
e.push_back((Edge){from, to, cap, 0});
e.push_back((Edge){to, from, 0, 0});
G[from].push_back(i << 1);
G[to].push_back((i << 1)+1);
}
long long maxflow()
{
long long flow = 0;
while (1)
{
memset(a, 0, sizeof(a));
a[s] = INF;
queue <int> q;
q.push(s);
while (!q.empty())
{
int x = q.front();
q.pop();
for (int i=0; i<G[x].size(); ++i)
{
Edge &b = e[G[x][i]];
if (!a[b.to] && b.cap > b.flow)
{
p[b.to] = G[x][i];
a[b.to] = min(a[x], b.cap-b.flow);
q.push(b.to);
}
}
if (a[t]) break;
}
if (!a[t]) break;
for (int u=t; u!=s; u=e[p[u]].from)
{
e[p[u]].flow += a[t];
e[p[u]^1].flow -= a[t];
}
flow += a[t];
}
return flow;
}
int main()
{
int u, v, w;
scanf("%d%d%d%d", &n, &m, &s, &t);
for (int i=0; i<m; ++i)
{
scanf("%d%d%d", &u, &v, &w);
addEdge(u, v, w, i);
}
printf("%lld\n", maxflow());
return 0;
}
\(Dinic\)
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int INF = 2147483647;
const int N = 205;
struct Edge{
int from, to, cap, flow;
};
int cur[N], depth[N];
int n, m, s, t;
vector <Edge> e;
vector <int> G[N];
void addEdge(int u, int v, int w, int i)
{
e.push_back((Edge){u, v, w, 0});
e.push_back((Edge){v, u, 0, 0});
G[u].push_back(i);
G[v].push_back(i^1);
}
int BFS()
{
queue <int> Q;
memset(depth, 0, sizeof depth);
depth[s] = 1;
Q.push(s);
while (!Q.empty())
{
int u = Q.front(); Q.pop();
for (int i = 0; i < G[u].size(); ++i) {
Edge& b = e[G[u][i]];
if (!depth[b.to] && b.cap > b.flow)
{
depth[b.to] = depth[u] + 1;
Q.push(b.to);
}
}
}
return depth[t];
}
int DFS(int x, int a)
{
if (x == t || !a) return a;
int flow = 0;
for (int& i = cur[x]; i < G[x].size(); ++i) {
Edge& b = e[G[x][i]];
if (depth[b.to] == depth[x]+1 && b.cap > b.flow)
{
if (int c = DFS(b.to, min(a, b.cap - b.flow)))
{
b.flow += c;
e[G[x][i]^1].flow -= c;
flow += c;
a -= c;
if (!a) break;
}
}
}
return flow;
}
ll maxFlow_Dinic()
{
ll ans = 0;
while (BFS()) {
memset(cur, 0, sizeof cur);
ans += DFS(s, INF);
}
return ans;
}
int main()
{
scanf("%d%d%d%d", &n, &m, &s, &t);
for (int i = 0; i < m; ++i) {
int u, v, w;
scanf("%d%d%d", &u, &v, &w);
addEdge(u, v, w, i << 1);
}
printf("%lld\n", maxFlow_Dinic());
return 0;
}
\(ISAP\)
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 205;
const int INF = 2147483647;
struct Edge {
int from, to, cap, flow;
};
int n, m, s, t, cnt, gap[N], cur[N], dep[N];
vector <int> G[N];
vector <Edge> e;
void addEdge(int u, int v, int w, int i)
{
e.push_back((Edge){u, v, w, 0});
e.push_back((Edge){v, u, 0, 0});
G[u].push_back(i);
G[v].push_back(i^1);
}
void init()
{
memset(gap, 0, sizeof gap);
memset(cur, 0, sizeof cur);
memset(dep, 0, sizeof dep);
++gap[dep[t] = 1];
queue <int> Q;
Q.push(t);
while (!Q.empty()) {
int x=Q.front(); Q.pop();
for (int i = 0; i < G[x].size(); i++)
{
int v = e[G[x][i]].to;
if (!dep[v])
{
++gap[dep[v] = dep[x]+1];
Q.push(v);
}
}
}
}
int augment(int x, int a)
{
if (x == t || !a) return a;
int flow = 0;
for (int &i=cur[x]; i < G[x].size(); i++)
{
Edge& b = e[G[x][i]];
if (dep[x] == dep[b.to] + 1 && b.cap > b.flow) {
int tmp = augment(b.to, min(a, b.cap - b.flow));
flow += tmp;
a -= tmp;
b.flow += tmp;
e[G[x][i]^1].flow -= tmp;
if (!a) return flow;
}
}
if (!(--gap[dep[x]])) dep[s] = cnt+1;
++gap[++dep[x]], cur[x] = 0;
return flow;
}
ll maxFlow_ISAP()
{
cnt = n; //Num_of_nodes -> cnt
init();
ll ans = 0;
while (dep[s] <= cnt) ans += augment(s, INF);
return ans;
}
int main()
{
scanf("%d%d%d%d", &n, &m, &s, &t);
for (int i = 0; i < m; i++) {
int u, v, w;
scanf("%d%d%d", &u, &v, &w);
addEdge(u, v, w, i << 1);
}
printf("%lld\n", maxFlow_ISAP());
return 0;
}
感谢支持!