首页 > ACM题库 > HDU-杭电 > HDU 3311-Dig The Wells-动态规划-[解题报告]HOJ
2014
03-16

HDU 3311-Dig The Wells-动态规划-[解题报告]HOJ

Dig The Wells

问题描述 :

You may all know the famous story “Three monks”. Recently they find some places around their temples can been used to dig some wells. It will help them save a lot of time. But to dig the well or build the road to transport the water will cost money. They do not want to cost too much money. Now they want you to find a cheapest plan.

输入:

There are several test cases.
Each test case will starts with three numbers n , m, and p in one line, n stands for the number of monks and m stands for the number of places that can been used, p stands for the number of roads between these places. The places the monks stay is signed from 1 to n then the other m places are signed as n + 1 to n + m. (1 <= n <= 5, 0 <= m <= 1000, 0 <=p <= 5000)
Then n + m numbers followed which stands for the value of digging a well in the ith place.
Then p lines followed. Each line will contains three numbers a, b, and c. means build a road between a and b will cost c.

输出:

There are several test cases.
Each test case will starts with three numbers n , m, and p in one line, n stands for the number of monks and m stands for the number of places that can been used, p stands for the number of roads between these places. The places the monks stay is signed from 1 to n then the other m places are signed as n + 1 to n + m. (1 <= n <= 5, 0 <= m <= 1000, 0 <=p <= 5000)
Then n + m numbers followed which stands for the value of digging a well in the ith place.
Then p lines followed. Each line will contains three numbers a, b, and c. means build a road between a and b will cost c.

样例输入:

3 1 3
1 2 3 4
1 4 2
2 4 2
3 4 4 
4 1 4
5 5 5 5 1
1 5 1
2 5 1
3 5 1
4 5 1

样例输出:

6
5

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<queue>
#include<algorithm>
#define INF 999999999
#define MAX 1010
#define MAX_STATUS 1<<6
using namespace std;

struct EDGE
{
	int v ,w;
	int next;
}edges[MAX*13];

struct NODE
{
	int x ,y;
};

int head[MAX] ,cnt;

int n ,m ,p;
int value[MAX];

int status;//表示0~n号节点都被选择时的状态+1
int dis[MAX][MAX_STATUS] ,situation[MAX] ,vis[MAX][MAX_STATUS] ,dp;
//dis[i][j]表示以i节点为根选择点集状态为j时的最小值;situation[i]表示i节点对应的状态;vis[i][j]表示i节点为点集j时是否在队列中
queue<NODE> q;

void init()
{
	memset(head,-1,sizeof(head));
	memset(vis,0,sizeof(vis));
	memset(situation,0,sizeof(situation));
	cnt = 0;
	status = 1<<(n + 1);
	for(int i = 0;i <= n + m;i++)
	{
		for(int j = 0;j <= status;j++)
		{
			dis[i][j] = INF;
		}
	}
	for(int i = 0;i <= n;i++)
	{
		situation[i] = 1<<i;
		dis[i][situation[i]] = 0;
	}
}

void add_edges(int u ,int v ,int w)
{
	edges[cnt].v = v;
	edges[cnt].w = w;
	edges[cnt].next = head[u];
	head[u] = cnt;
	cnt++;

	edges[cnt].v = u;
	edges[cnt].w = w;
	edges[cnt].next = head[v];
	head[v] = cnt;
	cnt++;
}

void SPFA()
{
	NODE temp ,newd;
	while(!q.empty())
	{
		temp = q.front();
		q.pop();
		vis[temp.x][temp.y] = 0;
		for(int i = head[temp.x];i!=-1;i = edges[i].next)
		{
			int v ,situ;
			v = edges[i].v;
			situ = temp.y | situation[v];
			if(dis[temp.x][temp.y] + edges[i].w < dis[v][situ])
			{
				 dis[v][situ] = dis[temp.x][temp.y] + edges[i].w;
				 if(situ==temp.y && !vis[v][situ])
				 {
					 newd.x = v;
					 newd.y = situ;
					 q.push(newd);
					 vis[v][situ] = 1;
				 }
			}
		}
	}
}

void Steiner_Tree()
{
	NODE  temp;
	for(int i = 0;i < status;i++)
	{
		for(int j = 0;j <= n + m;j++)
		{
			for(int k = i;k;k = (k - 1) & i)
			{
				dis[j][i] = min(dis[j][i],dis[j][k|situation[j]]+dis[j][(i-k)|situation[j]]);
			}
			if(dis[j][i]!=INF)
			{
				temp.x = j;
				temp.y = i;
				q.push(temp);
				vis[j][i] = 1;
			}
		}
		SPFA();
	}
}

int DP()
{
	dp = INF;
	for(int j = 0;j <= n+m;j++)
	{
	        dp = min(dp,dis[j][status-1]);
	}
    return dp;
}

int main()
{
	int u ,v ,w;
	while(~scanf("%d%d%d",&n,&m,&p))
	{
		init();
		for(int i = 1;i <= m + n;i++)
		{
			scanf("%d",&value[i]);
			add_edges(0,i,value[i]);
		}
		for(int i = 0;i < p;i++)
		{
			scanf("%d%d%d",&u,&v,&w);
			add_edges(u,v,w);
		}
		Steiner_Tree();
		printf("%d\n",DP());
	}
	return 0;
}

参考:http://blog.csdn.net/catalyst1314/article/details/20574927