HDU 3491 Thieves(經典拆點建圖,割點)
阿新 • • 發佈:2019-01-05
題目地址
題意:有一群小偷要從s點逃到t點,告訴你這個城市的道路圖,並且告訴你每個關鍵點要多少警察才不會讓小偷逃走,問你最少要多少警察才能阻止小偷逃走(小偷會知道警察的佈局)
思路:明顯的最小割點的題目,解決這類割點問題一般都是進行拆點建圖,把每個點拆成兩個點(i,i+n)和一條容量為代價的邊,然後道路的起點就是該起點的出點(x+n),終點就是該終點的入點(y),容量為inf無限大,這樣就不會去割邊了,最後以為最小割等於最大流,所以跑一邊最大流就好了。
#include <iostream>
#include <cstring>
#include <string>
#include <queue>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <cmath>
#include <cstdio>
#include <algorithm>
#include <iomanip>
#define N 40010
#define M 100010
#define LL __int64
#define inf 0x3f3f3f3f
#define lson l,mid,ans<<1
#define rson mid+1,r,ans<<1|1
#define getMid (l+r)>>1
#define movel ans<<1
#define mover ans<<1|1
using namespace std;
const LL mod = 1000000007;
int head[N], level[N];
int n, m, cnt;
struct node {
int to;
int cap;//剩餘流量
int next;
}edge[2 * M];
struct Dinic {
void init() {
memset (head, -1, sizeof(head));
cnt = 0;
}
void add(int u, int v, int cap) {//有向圖
edge[cnt].to = v, edge[cnt].cap = cap, edge[cnt].next = head[u], head[u] = cnt++;
edge[cnt].to = u, edge[cnt].cap = 0, edge[cnt].next = head[v], head[v] = cnt++;//反向邊
}
bool bfs(int s, int t) {//建立分層圖
memset(level, -1, sizeof(level));
queue<int>q;
level[s] = 0;//源點的層次最高
q.push(s);
while (!q.empty()) {
int u = q.front();
q.pop();
for (int i = head[u]; i != -1; i = edge[i].next) {
int v = edge[i].to;
if (edge[i].cap > 0 && level[v] < 0) {
level[v] = level[u] + 1;
q.push(v);
}
}
}
return level[t] != -1;
}
int dfs(int u, int t, int num) {//找增廣路
if (u == t) {//找到了匯點返回當前的最小值,在這條路徑上分別減去最小值
return num;
}
for (int i = head[u]; i != -1; i = edge[i].next) {
int v = edge[i].to;
if (edge[i].cap > 0 && level[u] < level[v]) {
int d = dfs(v, t, min(num, edge[i].cap));
if (d > 0) {
edge[i].cap -= d;
edge[i ^ 1].cap += d;//反向邊加值
return d;
}
}
}
level[u] = -1;
return 0;
}
int minflow(int s, int t) {//源點和匯點
int sum = 0, num;
while (bfs(s, t)) {
while (num = dfs(s, t, inf), num > 0) {//當前層次圖不斷的找增廣路
sum += num;
}
}
return sum;
}
}dc;
int main() {
cin.sync_with_stdio(false);
int T;
int a, b;
int s, t;
cin >> T;
while (T--) {
dc.init();
cin >> n >> m >> s >> t;
dc.add(s, s + n, inf);
dc.add(t, t + n, inf);
for (int i = 1; i <= n; i++) {
cin >> a;
dc.add(i, i + n, a);
}
for (int i = 0; i < m; i++) {
cin >> a >> b;
dc.add(a + n, b, inf);
dc.add(b + n, a, inf);
}
cout << dc.minflow(s, t + n) << endl;
}
return 0;
}