题意:N个点。M条边(2 <= N <= 1000 , 0 <= M <= 10^5),每一个点有个权值W(0 <= W <= 10^5),现要去除一些点(不能去掉点0),使得结点 0 与结点 N - 1 不连通,求去掉的点的最小权值和。
——>>这是很明显的最小点权割。。
建图方案:
1)将全部点 i 拆成 i 和 i + N。i -> i + N(容量为Wi)
2)原图中的边 i -> j 变成 i + N -> j(容量为无穷大)
3)0 -> 0 + N(由于原图中的边可能有涉及到0 -> x,这时会拆0)
接着,依据最小割最大流定理。求得最小割。。(又换命名法了我。囧。。)
#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using std::min;
using std::queue;
const int MAXN = 1000 * 2 + 10;
const int MAXM = 2 * (1000 + 100000) + 10;
const int INF = 0x3f3f3f3f;
struct EDGE
{
int to;
int cap;
int flow;
int nxt;
};
int N, M;
int hed[MAXN], nxt[MAXM], S, T;
int cur[MAXN], h[MAXN];
bool vis[MAXN];
int ecnt;
EDGE edge[MAXM];
void Init()
{
ecnt = 0;
memset(hed, -1, sizeof(hed));
}
void AddEdge(int u, int v, int cap)
{
edge[ecnt].to = v;
edge[ecnt].cap = cap;
edge[ecnt].flow = 0;
edge[ecnt].nxt = hed[u];
hed[u] = ecnt++;
}
bool Bfs()
{
queue<int> qu;
memset(vis, 0, sizeof(vis));
qu.push(S);
vis[S] = true;
h[S] = 0;
while (!qu.empty())
{
int u = qu.front();
qu.pop();
for (int e = hed[u]; e != -1; e = edge[e].nxt)
{
int v = edge[e].to;
if (!vis[v] && edge[e].flow < edge[e].cap)
{
h[v] = h[u] + 1;
vis[v] = true;
qu.push(v);
}
}
}
return vis[T];
}
int Dfs(int u, int cap)
{
if (u == T || cap == 0) return cap;
int flow = 0, subFlow;
for (int e = cur[u]; e != -1; e = edge[e].nxt)
{
cur[u] = e;
int v = edge[e].to;
if (h[v] == h[u] + 1 && (subFlow = Dfs(v, min(cap, edge[e].cap - edge[e].flow))) > 0)
{
flow += subFlow;
edge[e].flow += subFlow;
edge[e ^ 1].flow -= subFlow;
cap -= subFlow;
if (cap == 0) break;
}
}
return flow;
}
int Dinic()
{
int flow = 0;
while (Bfs())
{
memcpy(cur, hed, sizeof(hed));
flow += Dfs(S, INF);
}
return flow;
}
void Read()
{
int W;
scanf("%d%d", &N, &M);
for (int i = 1; i < N; ++i)
{
scanf("%d", &W);
AddEdge(i, i + N, W);
AddEdge(i + N, i, 0);
}
int P, Q;
for (int i = 0; i < M; ++i)
{
scanf("%d%d", &P, &Q);
AddEdge(P + N, Q, INF);
AddEdge(Q, P + N, 0);
}
AddEdge(0, N, INF);
AddEdge(N, 0, 0);
S = 0;
T = 2 * N - 1;
}
void Solve()
{
printf("%d\n", Dinic());
}
int main()
{
int T;
scanf("%d", &T);
while (T--)
{
Init();
Read();
Solve();
}
return 0;
}