题目链接 HIT 2739
有上下界网络流
每条边至少经过一次,但是不限制经过次数,这么不就是有下界网络流的做法嘛,首先,将每个点的入度和出度确定下来,然后呢,入度减出度大于0的就和源点连接,入度减出度小于0的就和汇点连接,于是就建立起了有上下界网络流模型。
然后,判断“-1”,有入度无出度,或者有出度无入度的都是不可行的。
#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
//#include <unordered_map>
//#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
#define eps 1e-8
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
#define MP(a, b) make_pair(a, b)
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 1e2 + 7, maxM = 1e4 + 7;
int N, M, head[maxN], cnt, In_Out[maxN];
bool In[maxN], Ou[maxN];
struct Eddge
{
int nex, u, v; int flow, cost;
Eddge(int a=-1, int b=0, int c=0, int d=0, int f=0):nex(a), u(b), v(c), flow(d), cost(f) {}
} edge[maxM];
inline void addEddge(int u, int v, int f, int w)
{
edge[cnt] = Eddge(head[u], u, v, f, w);
head[u] = cnt++;
}
inline void _add(int u, int v, int f, int w) { addEddge(u, v, f, w); addEddge(v, u, 0, -w); }
struct MaxFlow_MinCost
{
int pre[maxN], S, T; int Flow[maxN], dist[maxN];
queue<int> Q;
bool inque[maxN];
inline bool spfa()
{
for(int i=0; i<=T; i++) { pre[i] = -1; dist[i] = INF; inque[i] = false; }
while(!Q.empty()) Q.pop();
Q.push(S); dist[S] = 0; inque[S] = true; Flow[S] = INF;
while(!Q.empty())
{
int u = Q.front(); Q.pop(); inque[u] = false;
int f, w;
for(int i=head[u], v; ~i; i=edge[i].nex)
{
v = edge[i].v; f = edge[i].flow; w = edge[i].cost;
if(f && dist[v] > dist[u] + w)
{
dist[v] = dist[u] + w;
Flow[v] = min(Flow[u], f);
pre[v] = i;
if(!inque[v])
{
inque[v] = true;
Q.push(v);
}
}
}
}
return ~pre[T];
}
inline int EK()
{
int sum_Cost = 0;
while(spfa())
{
int now = T, las = pre[now];
while(now ^ S)
{
edge[las].flow -= Flow[T];
edge[las ^ 1].flow += Flow[T];
now = edge[las].u;
las = pre[now];
}
sum_Cost += dist[T] * Flow[T];
}
return sum_Cost;
}
} MF;
void init()
{
cnt = 0; MF.S = 0; MF.T = N + 1;
for(int i=0; i<=MF.T; i++) head[i] = -1;
for(int i=0; i<N; i++) { In_Out[i] = 0; In[i] = Ou[i] = false; }
}
int main()
{
int Cas; scanf("%d", &Cas);
while(Cas--)
{
scanf("%d%d", &N, &M);
init();
int ans = 0;
for(int i=1, u, v, w; i<=M; i++)
{
scanf("%d%d%d", &u, &v, &w);
ans += w;
_add(u, v, INF, w);
Ou[u] = In[v] = true;
In_Out[u] --; In_Out[v] ++;
}
bool ok = true;
for(int i=0; i<N; i++)
{
if((!In[i] && Ou[i])|| (!Ou[i] && In[i])) { ok = false; break; }
}
if(!ok)
{
printf("-1\n");
continue;
}
for(int i=0; i<N; i++)
{
if(In_Out[i] > 0)
{
_add(MF.S, i, In_Out[i], 0);
}
else if(In_Out[i] < 0)
{
_add(i, MF.T, -In_Out[i], 0);
}
}
ans += MF.EK();
printf("%d\n", ans);
}
return 0;
}