UVA 1660 Cable TV Network——最小割求点连通度
2018-03-04 17:29
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拆点法,一个点拆出的两个点之间建一条容量为1的有向边,题目中所给的边都是容量为INF的边,然后枚举任意两点间的最小割(其实只需要枚举0和其余点之间的最小割就可以)#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int maxn = 500;
const int INF = 0x3f3f3f3f;
struct Edge {
int to, cap, rev;
Edge(int x=0, int y=0, int z=0) : to(x), cap(y), rev(z) {}
};
vector<Edge> G[maxn];
int level[maxn], iter[maxn];
void addedge(int u, int v, int cap) {
G[u].push_back(Edge(v, cap, G[v].size()));
G[v].push_back(Edge(u, 0, G[u].size()-1));
}
void bfs(int s) {
memset(level, -1, sizeof(level));
queue<int> q;
level[s] = 0;
q.push(s);
while (!q.empty()) {
int v = q.front(); q.pop();
for (int i = 0; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && level[e.to] < 0) {
level[e.to] = level[v] + 1;
q.push(e.to);
}
}
}
}
int dfs(int v, int t, int f) {
if (v == t) return f;
for (int &i = iter[v]; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && level[v] < level[e.to]) {
int d = dfs(e.to, t, min(f, e.cap));
if (d > 0) {
e.cap -= d;
G[e.to][e.rev].cap += d;
return d;
}
}
}
return 0;
}
int max_flow(int s, int t) {
int flow = 0;
while (true) {
bfs(s);
if (level[t] < 0) return flow;
memset(iter, 0, sizeof(iter));
int f;
while ((f = dfs(s, t, INF)) > 0) flow += f;
}
}
int n, m, u[maxn], v[maxn];
void init() {
for (int i = 0; i < maxn; i++) G[i].clear();
for (int i = 0; i < n; i++) addedge(i, i + n, 1);
for (int i = 0; i < m; i++) {
addedge(u[i]+n, v[i], INF);
addedge(v[i]+n, u[i], INF);
}
}
int main() {
while (~scanf("%d %d", &n, &m)) {
for (int i = 0; i < m; i++) scanf(" (%d,%d)", &u[i], &v[i]);
int ans = INF;
for (int i = 1; i < n; i++) {
init();
ans = min(ans, max_flow(n, i));
}
if (ans >= INF) ans = n;
printf("%d\n", ans);
}
return 0;
}
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int maxn = 500;
const int INF = 0x3f3f3f3f;
struct Edge {
int to, cap, rev;
Edge(int x=0, int y=0, int z=0) : to(x), cap(y), rev(z) {}
};
vector<Edge> G[maxn];
int level[maxn], iter[maxn];
void addedge(int u, int v, int cap) {
G[u].push_back(Edge(v, cap, G[v].size()));
G[v].push_back(Edge(u, 0, G[u].size()-1));
}
void bfs(int s) {
memset(level, -1, sizeof(level));
queue<int> q;
level[s] = 0;
q.push(s);
while (!q.empty()) {
int v = q.front(); q.pop();
for (int i = 0; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && level[e.to] < 0) {
level[e.to] = level[v] + 1;
q.push(e.to);
}
}
}
}
int dfs(int v, int t, int f) {
if (v == t) return f;
for (int &i = iter[v]; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && level[v] < level[e.to]) {
int d = dfs(e.to, t, min(f, e.cap));
if (d > 0) {
e.cap -= d;
G[e.to][e.rev].cap += d;
return d;
}
}
}
return 0;
}
int max_flow(int s, int t) {
int flow = 0;
while (true) {
bfs(s);
if (level[t] < 0) return flow;
memset(iter, 0, sizeof(iter));
int f;
while ((f = dfs(s, t, INF)) > 0) flow += f;
}
}
int n, m, u[maxn], v[maxn];
void init() {
for (int i = 0; i < maxn; i++) G[i].clear();
for (int i = 0; i < n; i++) addedge(i, i + n, 1);
for (int i = 0; i < m; i++) {
addedge(u[i]+n, v[i], INF);
addedge(v[i]+n, u[i], INF);
}
}
int main() {
while (~scanf("%d %d", &n, &m)) {
for (int i = 0; i < m; i++) scanf(" (%d,%d)", &u[i], &v[i]);
int ans = INF;
for (int i = 1; i < n; i++) {
init();
ans = min(ans, max_flow(n, i));
}
if (ans >= INF) ans = n;
printf("%d\n", ans);
}
return 0;
}
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