HDU 6611 K Subsequence （最小费用最大流）

最新推荐文章于 2021-07-28 20:12:48 发布

原创最新推荐文章于 2021-07-28 20:12:48 发布 · 217 阅读

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本文深入探讨了最小成本最大流算法的实现细节，通过具体的代码示例展示了如何在图中寻找最小成本路径以达到最大流的目标。文章涵盖了算法的初始化、边的添加以及核心的最小成本最大流求解过程。

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#include <iostream>
#include <stdio.h>
#include <queue>
#include <cstring> 
#include <algorithm>
#define il inline
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int maxn = 1e4;
const int INF = 0x7fffffff;
struct edge {
	int to, capacity, cost, rev;
	edge() {}
	edge(int to, int _capacity, int _cost, int _rev) :to(to), capacity(_capacity), cost(_cost), rev(_rev) {}
};
struct Min_Cost_Max_Flow {
	int V, H[maxn + 5], dis[maxn + 5], PreV[maxn + 5], PreE[maxn + 5];
	vector<edge> G[maxn + 5];
	//调用前初始化
	void Init(int n) {
		V = n;
		for (int i = 0; i <= V; ++i)G[i].clear();
	}
	//加边
	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));
	}
	//flow是自己传进去的变量，就是最后的最大流，返回的是最小费用
	int Min_cost_max_flow(int s, int t, int f, int& flow) {
		int res = 0; fill(H, H + 1 + V, 0);
		while (f) {
			priority_queue <pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > q;
			fill(dis, dis + 1 + V, INF);
			dis[s] = 0; q.push(pair<int, int>(0, s));
			while (!q.empty()) {
				pair<int, int> now = q.top(); q.pop();
				int v = now.second;
				if (dis[v] < now.first)continue;
				for (int i = 0; i < G[v].size(); ++i) {
					edge& e = G[v][i];
					if (e.capacity > 0 && dis[e.to] > dis[v] + e.cost + H[v] - H[e.to]) {
						dis[e.to] = dis[v] + e.cost + H[v] - H[e.to];
						PreV[e.to] = v;
						PreE[e.to] = i;
						q.push(pair<int, int>(dis[e.to], e.to));
					}
				}
			}
			if (dis[t] == INF)break;
			for (int i = 0; i <= V; ++i)H[i] += dis[i];
			int d = f;
			for (int v = t; v != s; v = PreV[v])d = min(d, G[PreV[v]][PreE[v]].capacity);
			f -= d; flow += d; res += d*H[t];
			for (int v = t; v != s; v = PreV[v]) {
				edge& e = G[PreV[v]][PreE[v]];
				e.capacity -= d;
				G[v][e.rev].capacity += d;
			}
		}
		return res;
	}
	int Max_cost_max_flow(int s, int t, int f, int& flow) {
		int res = 0;
		fill(H, H + 1 + V, 0);
		while (f) {
			priority_queue <pair<int, int> > q;
			fill(dis, dis + 1 + V, -INF);
			dis[s] = 0;
			q.push(pair<int, int>(0, s));
			while (!q.empty()) {
				pair<int, int> now = q.top(); q.pop();
				int v = now.second;
				if (dis[v] > now.first)continue;
				for (int i = 0; i < G[v].size(); ++i) {
					edge& e = G[v][i];
					if (e.capacity > 0 && dis[e.to] < dis[v] + e.cost + H[v] - H[e.to]) {
						dis[e.to] = dis[v] + e.cost + H[v] - H[e.to];
						PreV[e.to] = v;
						PreE[e.to] = i;
						q.push(pair<int, int>(dis[e.to], e.to));
					}
				}
			}
			if (dis[t] == -INF)break;
			for (int i = 0; i <= V; ++i)H[i] += dis[i];
			int d = f;
			for (int v = t; v != s; v = PreV[v])d = min(d, G[PreV[v]][PreE[v]].capacity);
			f -= d; flow += d;
			res += d*H[t];
			for (int v = t; v != s; v = PreV[v]) {
				edge& e = G[PreV[v]][PreE[v]];
				e.capacity -= d;
				G[v][e.rev].capacity += d;
			}
		}
		return res;
	}
};
Min_Cost_Max_Flow MCMF;
int a[2005];
int main()
{
	int T;
	scanf("%d",&T);
	while(T--)
	{
		int n,k;
		scanf("%d %d",&n,&k);
		int s1 = 0,s2 = 2*n+1,t=2*n+2;
		MCMF.Init(t);
		for(int i=1;i<=n;i++){
			scanf("%d",&a[i]);
			MCMF.Add_Edge(i,i+n,1,-a[i]);
		}
		for(int i=1;i<=n;i++){
			for(int j=i+1;j<=n;j++)
				if(a[j]>=a[i])MCMF.Add_Edge(i+n,j,1,0); 
		}
		for(int i=1;i<=n;i++)MCMF.Add_Edge(s2,i,1,0),MCMF.Add_Edge(i+n,t,1,0);
		MCMF.Add_Edge(s1,s2,k,0);
		int flow = 0;
		printf("%d\n",-MCMF.Min_cost_max_flow(s1,t,INF,flow));
	}
	return 0;
}