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拆点后转变变为指派问题,然后用费用流求解(719ms)#include<cstdio>
#include<climits>
#include<queue>
#include<cstring>
#include<cmath>
using namespace std;
#define ll long long
const int MAX_V = 2552;
struct edge
{
int to, cap, cost, rev;
edge(int t, int c, int co, int r):
to(t), cap(c), cost(co), rev(r){}
};
vector<edge> G[MAX_V];
int dist[MAX_V], prevv[MAX_V], preve[MAX_V], h[MAX_V], V, cost, flow, Z[51][51];
typedef pair<int, int> P;
inline void add_edge(int from, int to, int cap, int cost)
{
G[from].push_back(edge(to, cap, cost, G[to].size()));
G[to].push_back(edge(from, 0, -cost, G[from].size() - 1));
}
void min_cost_flow(int s, int t)
{
memset(h, 0, sizeof(h));
cost = 0,
flow = 0;
for (;;)
{
priority_queue<P, vector<P>, greater<P> > que;
que.push(P(0, s));
fill(dist, dist + MAX_V, INT_MAX);
dist[s] = 0;
for (int dis, v; !que.empty(); )
{
v = que.top().second, dis = que.top().first;
que.pop();
if (dis > dist[v])
continue;
for (int i = 0; i < G[v].size(); ++i)
{
edge& e = G[v][i];
if (e.cap && dist[e.to] > dis + e.cost + h[v] - h[e.to])
{
dist[e.to] = dis + e.cost + h[v] - h[e.to],
prevv[e.to] = v,
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if (dist[t] == INT_MAX)
return;
for (int v = 0; v <= V; ++v)
h[v] += dist[v];
int d = INT_MAX;
for (int v = t; v != s; v = prevv[v])
d = min(d, G[prevv[v]][preve[v]].cap);
flow += d,
cost += d * h[t];
for (int v = t; v != s; v = prevv[v])
{
edge& e = G[prevv[v]][preve[v]];
e.cap -= d,
G[v][e.rev].cap += d;
}
}
}
void solve()
{
int N, M, s = 0, t;
scanf("%d%d", &N, &M);
/*
points:
0: s
1 ~ N: toys
N * i + 1 ~ N * (i + 1): the i-th workshop
N * (M + 1) + 1: t
*/
t = N + N * M + 1,
V = t;
for (int i = 0; i <= V; ++i)
G[i].clear();
for (int i = 1; i <= N; ++i)
for (int j = 1; j <= M; ++j)
scanf("%d", &Z[i][j]);
for (int i = 1; i <= N; ++i)
add_edge(s, i, 1, 0);
for (int j = 1; j <= M; ++j)
{
for (int k = 1; k <= N; ++k)
{
add_edge(N * j + k, t, 1, 0);
for (int i = 1; i <= N; ++i)
add_edge(i, N * j + k, 1, k * Z[i][j]);
}
}
min_cost_flow(s, t);
printf("%.6f\n", (double)cost / N);
}
int main()
{
int t;
scanf("%d", &t);
while (t--)
solve();
return 0;
}
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