HDU 3572 작업 스케줄 (최대 흐름 문제, sap 알고리즘)

/*
  ： m   ，  n   ，       [si,ei]     ，  pi     。            ，
       m   。
  ：         ，      ，         。
       ，  ：              ，    s   t， s           ，     
  ；     t      ，   m；                ，   1。          。
  ：sap  ，      Dinic  。
sap      ：http://chuanwang66.iteye.com/blog/1450715
         ，         。
     ：       ，       ，        。
*/


//sap      

#include <iostream>
using namespace std;
const int nMax = 2000;
const int mMax = 500000;
const int INF = 0x7fffffff;
struct Edge
{
	int v, w, next;
	Edge(){}
	Edge(int v, int w, int next):v(v), w(w), next(next){}
}adj[mMax];
int ind;
int head[nMax];//         
int dis[nMax];//       
int vn[nMax];//        
int t, n, m;
int pi, si, ei;
int source, sink, NV;//  、  、    

void addEdge(int u, int v, int w)
{
	adj[ind] = Edge(v, w, head[u]);
	head[u] = ind ++;
	adj[ind] = Edge(u, 0, head[v]);
	head[v] = ind ++;
}

int dfs(int cur, int cost)
{
	if(cur == sink)
		return cost;
	int leave = cost;//leave         
	int MinDis = NV;
	for(int id = head[cur]; id != -1; id = adj[id].next)
	{
		int v = adj[id].v;
		if(adj[id].w)
		{
			if(dis[v] + 1 == dis[cur])
			{
				int MinFlow = min(leave, adj[id].w);//      ，      leave adj[id].w  ，  leave       
				MinFlow = dfs(v, MinFlow);//   v   sink          
				adj[id].w -= MinFlow;
				adj[id ^ 1].w += MinFlow;
				leave -= MinFlow;
				if(dis[source] >= NV) return cost - leave;//    -     
				if(leave == 0) break;
			}
			if(dis[v] < MinDis)//MinDis   cur          ，              。
				MinDis = dis[v];
		}
	}
	if(leave == cost)//         ，         
	{
		if((-- vn[dis[cur]]) == 0) dis[source] = NV;
		dis[cur] = MinDis + 1;
		vn[dis[cur]] ++;
	}
	return cost - leave;
}

int sap(int s, int e)
{
	source = s;
	sink = e;
	NV = e + 1;
	memset(dis, 0, sizeof(dis));
	memset(vn, 0, sizeof(vn));
	vn[0] = NV;
	int ans = 0;
	while(dis[source] < NV)//  dis[source] >= NV      
	{
		ans += dfs(s,INF);
	}
	return ans;
}

int main()
{
	//freopen("e://data.in", "r", stdin);
	int s, e;
	scanf("%d", &t);
	for(int cas = 1; cas <= t; cas ++)
	{
		int Max = 0;
		int sum = 0;
		s = 0;
		ind = 0;
		memset(head, -1, sizeof(head));
		scanf("%d %d", &n, &m);
		for(int i = 1; i <= n; ++ i)
		{
			scanf("%d %d %d", &pi, &si, &ei);
			sum += pi;
			addEdge(s, i, pi);
			Max = max(Max, ei);
			for(int j = si; j <= ei; ++ j)
				addEdge(i, n + j, 1);
		}
		e = n + Max + 1;
		for(int i = 1; i <= Max; ++ i)
			addEdge(n + i, e, m);
		int a;
		if((a = sap(s, e)) == sum)
			printf("Case %d: Yes

", cas);
		else
			printf("Case %d: No

", cas);
	}
	return 0;
}


//     

#include <iostream>
//#define TEST
using namespace std;

const int nMax = 2000;
const int mMax = 500000;
const int INF = 0x7fffffff;
struct Edge
{
	int u, v, w;
	int next;
	Edge(){}
	Edge(int u, int v, int w, int next):u(u), v(v), w(w), next(next){}
}adj[mMax];
int ind;
int dis[nMax];//  
int pre[nMax];//  
int head[nMax];//    
int flow[nMax];//       
int vn[nMax];//        
int cur[nMax];//   
int t, n, m;
int pi, si, ei;

void addEdge(int u, int v, int w)//        
{
	adj[ind] = Edge(u, v, w, head[u]);
	head[u] = ind ++;
	adj[ind] = Edge(v, u, 0, head[v]);
	head[v] = ind ++;
}

int sap(int s, int e, int n)//sap  ，      
{
	int u = s;
	int MaxFlow = 0;
	memset(dis, 0, sizeof(dis));
	flow[s] = INF;
	memset(vn, 0, sizeof(vn));
	pre[s] = -1;
	for(int i = 0; i < n; ++ i)
		cur[i] = head[i];//           
	while(d[s] < n)//         d[s] < n，                  ，  while(1)    
	{
		bool flag = false;
		if(u == e)
		{
			MaxFlow += flow[e];
			for(int v = pre[e]; v != -1; v = pre[v])
			{
				int id = cur[v];
				adj[id].w -= flow[e];//         
				adj[id ^ 1].w += flow[e];
				if(adj[id].w == 0) u = v;//      0   ，      0，            
			}
		}
		for(int id  = cur[u]; id != -1; id = adj[id].next)//     
		{
			int v = adj[id].v;
			if(adj[id].w > 0 && dis[v] + 1 == dis[u])
			{
				flag = true;
				pre[v] = u;
				flow[v] = min(flow[u], adj[id].w);
				cur[u] = id;
				u = v;
				break;
			}
		}
		if(!flag)//      ，      dis[u]  
		{
			if((-- vn[dis[u]]) == 0) break;//     
			int MinDis = n;//      ，  dis[v] 
			cur[u] = head[u];
			for(int id = head[u]; id != -1; id = adj[id].next)
			{
				int v = adj[id].v;
				if(adj[id].w > 0 && dis[v] < MinDis)//edge[i].w > 0        ，     
				{
					MinDis = dis[v];
					cur[u] = id;
				}
			}
			dis[u] = MinDis + 1;// dis[u]      
			vn[dis[u]] ++;
			if(u != s) u = pre[u];//  
		}
	}
	return MaxFlow;
}

int main()
{
	//freopen("e://data.in", "r", stdin);
	//freopen("e://data2.out", "w", stdout);
	int s, e;
	scanf("%d", &t);
	for(int cas = 1; cas <= t; cas ++)
	{
		int Max = 0;
		int sum = 0;
		s = 0;
		ind = 0;
		memset(head, -1, sizeof(head));
		scanf("%d %d", &n, &m);
		for(int i = 1; i <= n; ++ i)
		{
			scanf("%d %d %d", &pi, &si, &ei);
			sum += pi;
			addEdge(0, i, pi);
			Max = max(Max, ei);
			for(int j = si; j <= ei; ++ j)
				addEdge(i, n + j, 1);
		}
		e = n + Max + 1;
		for(int i = 1; i <= Max; ++ i)
			addEdge(n + i, e, m);
		if(sap(s, e, e + 1) == sum)
			printf("Case %d: Yes

", cas);
		else
			printf("Case %d: No

", cas);
	}
	return 0;
}