uva-321-暴力枚举-隐式图搜索

Posted 2021-01-14 shuiyonglewodezzzzz

题意：给你n个房间,有许多灯的控制开关,i房间灯的开关在j房间,未开灯的房间不能进,i房间和j房间之间如果没有门,也不能从i进入到j,开始房间是1，并且灯是开着的,问你是否能够走到最后一个房间n,并且此时其他房间的灯都是关着的.如果存在多个解,输出操作步数最小的操作序列.

范围：n<=10,

解题思路:设状态为,当前的房间编号+当前其他房间灯的状态.所以总的状态为N*2^N,最大值10*1024，裸枚举.

注意，这道题目每次枚举都必须从房间编码1-N,要不然会wa，而且,PE也wa.使用了位标志房间灯的状态.

#include <iostream>
#include<map>
#include<memory.h>
#include<stdio.h>
#include<string>
#include<queue>
#include<vector>
using namespace std;
const int  MAXN = 11;

class Node
{
public:
    vector<string>step;
    int cur;
    int curStepNum;
    int lights;
    Node()
    {
        //step.reserve(65535);
    }
    bool operator <(const Node& node) const
    {
        return curStepNum > node.curStepNum;
    };
};
int conn[MAXN][MAXN];
int contro[MAXN][MAXN];
int r, d, s;
int states[10][1025];
priority_queue<Node>q;
int perLights[10] = {
    1 << 0,1 << 1,1 << 2 ,1 << 3 ,1 << 4 ,1 << 5 ,
    1 << 6,1 << 7,1 << 8 ,1 << 9 };



void read()
{
    int ss, ee;
    for (int i = 0;i < d;i++)
    {
        cin >> ss >> ee;
        //start with 0
        conn[ss - 1][ee - 1] = 1;
        conn[ee - 1][ss - 1] = 1;
    }
    for (int i = 0;i < s;i++)
    {
        cin >> ss >> ee;
        contro[ss - 1][ee - 1] = 1;
    }
}
Node bfs()
{
    Node node;
    node.cur = 0;
    node.curStepNum = 0;
    node.lights = 1;
    q.push(node);
    //init node 只有0房间是亮的
    states[0][1] = 1;
    while (q.empty() == false)
    {
        node = q.top();
        q.pop();
        int curIndex = node.cur;
        //cur lights state
        int curLights = node.lights;
        int curStepNum = node.curStepNum;
        //判断是不是终点
        if ((curIndex == r - 1) && curLights == perLights[r - 1])
        {
            return node;
        }
    
        //枚举灯的状态
        for (int i = 0;i < 10; i++)
        {
            if (contro[curIndex][i] == 0)
                continue;
            if (i == curIndex)
                continue;
            //控制的灯
            int nextControLightIndex = i;
            string desc = "";
            int nextLight = 0;
            if ((curLights & perLights[nextControLightIndex]) == perLights[nextControLightIndex])
            {
                //关闭next房间的灯
                nextLight = (curLights ^ perLights[nextControLightIndex]);
                if (states[curIndex][nextLight] == 1)
                    //repeat
                    continue;
                desc = "- Switch off light in room " + std::to_string(nextControLightIndex + 1);
                desc += ".";
            }
            else
            {
                //打开next房间的灯
                nextLight = curLights | perLights[nextControLightIndex];
                if (states[curIndex][nextLight] == 1)
                    //repeat
                    continue;
                desc = "- Switch on light in room " + std::to_string(nextControLightIndex + 1);
                desc += ".";
            }
            Node newNode;
            newNode.curStepNum = curStepNum + 1;
            newNode.cur = curIndex;
            newNode.lights = nextLight;
            newNode.step = node.step;
            newNode.step.push_back(desc);
            //push to queue
            q.push(newNode);
            states[curIndex][nextLight] = 1;
        }
        //end curIndex enum lights state
        //start door
        for (int i = 0;i < 10;i++)
        {
            if (curIndex == i)
                continue;
            if (conn[curIndex][i] == 0)
                continue;
            int nextDoor = i;
            if ((perLights[nextDoor] & curLights) == 0)
                //灯是灭的,不能进
                continue;
            if (states[nextDoor][curLights] == 1)
                //已经看到过,不能进
                continue;
            //灯是开着的,能进
            Node newNode;
            newNode.cur = nextDoor;
            newNode.curStepNum = curStepNum + 1;
            newNode.lights = curLights;
            newNode.step = node.step;
            string desc = "- Move to room " + std::to_string(nextDoor + 1);
            desc += ".";
            newNode.step.push_back(desc);
            states[nextDoor][curLights] = 1;
            q.push(newNode);
        }
    }
    node.cur = -1;
    return node;
}
int main()
{
    int t = 0;
    while (cin >> r >> d >> s)
    {
        if (r == d && d == s && r == 0)
            break;
        memset(conn, 0, sizeof(conn));
        memset(contro, 0, sizeof(conn));
        memset(states, 0, sizeof(states));
        while (q.empty() == false)
            q.pop();
        read();
        
        cout << "Villa #";
        cout << t + 1 << endl;
        if (r == 1)
        {
            cout << "The problem can be solved in " << 0 << " steps:" << endl;

        }
        else
        {
            Node node = bfs();
            //cout << "test" << endl;
            if (node.cur == -1)
            {
                cout << "The problem cannot be solved." << endl;
            }
            else
            {
                cout << "The problem can be solved in " << node.curStepNum << " steps:" << endl;
                vector<string> b = node.step;
                for (int i = 0;i <= b.size() - 1;i++)
                    cout << b[i] << endl;;
            }
        }
        t++;
        cout << endl;
    }


}