优先队列2

1. 题目1：关于工作安排， 每个工作有权重weight和时长length这样两个属性，要求如何安排时间使得$sum_j^n W_j C_j$的值最小。假设一共n个工作，$W_j$为第j个工作的权重，$C_j$为到第j个工作工作完成的时长(加上之前的工作时长)。

贪心算法有这样两个思路: 按照 (1) weight-length 和 (2)weight/length 的从大到小的思路进行排列，故可以用到优先队列。

1.1 优先队列按照存储工作的weight-length的从大到小的属性排列，按照从大到小的值对$sum_j^n W_j C_j $进行计算。代码如下

#include <iostream>
#include <vector>
#include <sstream>
#include <fstream>
#include <stack>
#include <queue>
#include <algorithm>
using namespace std;


class Job
{
public:
    int index;  //工作号
    int weight; //权重
    int length; //工作时长
    int we_le; //weight-length
};
/***********优先队列Job类自定义比较函数**********/
class mycompare
{
    bool reverse;
public:
    mycompare(const bool & re = false)
    {reverse = re;}
    bool operator() (Job &a, Job &b) const
    {
        if(reverse) return (a.we_le > b.we_le);//实现从小到大的排列
        else {
            if(a.we_le == b.we_le) 
            {
                return (a.weight < b.weight); // 如果相等，则选择weight大的排在前
            } else {
                return (a.we_le < b.we_le); //从大到小
            }
        }
    }
};
/*************工作安排*******************/
class JobShedule
{
public:
    JobShedule()
    {
        ifstream fin("t.txt");
        string line;
        stringstream stream;
        if(getline(fin,line))
        {
            stream.clear();
            stream << line;
            stream >> count;
        }
        int cnt = 0;
        while(getline(fin, line))
        {
            int _len, _wei;
            stream.clear();
            stream << line;
            stream >> _wei;
            stream >> _len;
            jobs[cnt].index = cnt + 1;
            jobs[cnt].length = _len;
            jobs[cnt].weight = _wei;
            jobs[cnt].we_le = _wei - _len;
            mypq.push(jobs[cnt]);
            cnt++;
        }    
    }


/*************计算总的带权重的工作时间**************/    
    void calc_time()
    {
        ofstream fout;
        fout.open("output.txt");
        while(!mypq.empty())                
        {
            Job tmp = mypq.top();
            mypq.pop();
            curLength += tmp.length;
            time += tmp.weight * curLength;
            fout << "tmp time:: " << time << endl;
        }
    }

public:
    int count;
    long long time = 0;
    int curLength = 0;
    Job jobs[12];
    //优先队列，按照工作的weight-length排列队列。
    priority_queue <Job, vector< Job > ,mycompare> mypq;
};

int main()
{
    JobShedule jobsh;
    jobsh.calc_time();
    cout << "total time:" << jobsh.time << endl;
    return 0;
}

1.2 如果按照工作的weight/length从大到小排列。

class Job
{
public:
    int index;
    int weight;
    int length;
    float ratio; //按照weight/length
};
/*************自定义比较函数，按照ratio从大到小排列***************/
class mycompare
{
    bool reverse;
public:
    mycompare(const bool & re = false)
    {reverse = re;}
    bool operator() (Job &a, Job &b) const
    {
        if(reverse) return (a.ratio > b.ratio);//实现从小到大的排列
        else {
            if(a.ratio == b.ratio) 
            {
                return (a.weight < b.weight); // 如果相等，则选择weight大的排在前
            } else {
                return (a.ratio < b.ratio); //从大到小
            }
        }
    }
};

2.prim算法的简单实现，代码比较烂。对cost的最小值进行选取。

#include <iostream>
#include <string>
#include <stack>
#include <fstream>
#include <sstream>
#include <ctime>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
/**********边表************/
class EdgeNode
{
public:
    int adjvex;
    int cost;
    int head;
    EdgeNode *next;
    EdgeNode(int _head, int _adj, int _cost,EdgeNode *n = NULL) : head(_head), adjvex(_adj), cost(_cost), next(n) {}
};
/*=========顶点表============*/
class VertexNode
{
public:
    int data;
    EdgeNode *firstEdge;
    VertexNode()
    {
        firstEdge = NULL;
    }
};
/*********自定义比较函数(优先队列使用)************/
class mycompare
{
    bool reverse;
public:
    mycompare(const bool &re = true)
    {
        reverse = re;    
    }
    bool operator() (EdgeNode *a, EdgeNode *b) const
    {
        //从小到大排列， 优先队列,!mycompare，按照cost的从小到大排列
        if(reverse) return (a->cost > b->cost); 
        else {
            return (a->cost < b->cost);
            //从小到大排列， 优先队列,!mycompare，按照cost的从大到小排列
        }

    }

};
/*********无向图的数据结构*************/
class Graph 
{
public:
/*********初始化图的邻接表数据***************/
    Graph()
    {
        ifstream fin("pp.txt");
        string line;
        stringstream stream;
        if(getline(fin, line))
        {
            stream.clear();
            stream << line;
            stream >> numVertexes;
            stream >> numEdges;
        }
        init_adjList();
        while(getline(fin, line))
        {
            int vertex, adjacent,  _cost;
            stream.clear();
            stream << line;
            stream >> vertex;
            stream >> adjacent;
            stream >> _cost;
            addEdge(vertex, adjacent, _cost);            
        }
    }
/********初始化邻接表的顶点表*******/
    void init_adjList()
    {
        adjList.resize(numVertexes);
        for(int i = 0; i < numVertexes; i++)
        {    
            adjList[i].data = i;
        }        
    }


/************加边，头插法*****************/
    void addEdge(int a, int b, int _cost)
    {
        EdgeNode *enode1 = new EdgeNode(a-1, b-1, _cost, NULL);
        EdgeNode *enode2 = new EdgeNode(b-1, a-1, _cost, NULL);
        adjList[a-1].data = a-1;
        enode1->next = adjList[a-1].firstEdge;
        adjList[a-1].firstEdge = enode1;
        adjList[b-1].data = b-1;
        enode2->next = adjList[b-1].firstEdge;
        adjList[b-1].firstEdge = enode2;
    }
/************打印看结果************/
    void print()
    {
        ofstream fout;
        fout.open("primoutput.txt");
        for(int i = 0; i < numVertexes; i++)
        {
            fout << "vertex:" << adjList[i].data << " adj:" ;
            EdgeNode *tmp = new EdgeNode(0, 0, 0 );
            tmp = adjList[i].firstEdge;
            while(tmp)
            {
                fout << tmp->adjvex << "cost: " << tmp->cost << " ";
                tmp = tmp->next;
            }
            fout << endl;
        }
    }
/*********************************/
public:
    int numVertexes; //顶点数目
    int numEdges;     //边数目
    vector<VertexNode> adjList;   //图的邻接表
};
/***********prim算法实现**********/
class Prims
{
public:
    Prims(Graph graph)
    {
        int s = 0;
        length = graph.numVertexes; //顶点数目
        tree.resize(length); 
        marked.push_back(s); //将初始顶点加入最小生成树中
        pq.push(graph.adjList[s].firstEdge); //将初始顶点的第一条边加入队列
        while(!pq.empty())
        {
            EdgeNode *p = new EdgeNode(0,0,0);
            p = graph.adjList[s].firstEdge;
            while(p)
            {
                if(!is_marked(p->adjvex))
                {
                    pq.push(p);
                }
                p = p->next;
            }

            EdgeNode *p1 = new EdgeNode(0,0,0);
            p1 = pq.top();
            pq.pop();
            s = p1->adjvex;
            if(!is_marked(s)) //如果没有加入进最小生成树
            {
                marked.push_back(p1->adjvex);
                tree[p1->head].push_back(p1->adjvex); //将边加入最小生成数
                sum += p1->cost;  //cost的累加
            }
        
        }

    }
/*******************判断是否加入最小生成树***************/    
    bool is_marked(int a)
    {
    
        for(int i = 0; i < marked.size(); i++)
        {
            if(marked[i] == a)
            {
                return true;
            }
        }
        return false;
    }
/***************输出看结果**************/
    void write()
    {
        ofstream fout;
        fout.open("tree.txt");
        for(int i = 0; i < length; i++)
        {
            fout << "tree[" << i << "]: " ;
            for(int j = 0; j < tree[i].size(); j++)
            {
                fout << tree[i][j] << " ";
            }
            fout << endl;
        }
    }


public:
    int length;
    int sum = 0;
    vector<int> marked;//最小生成树木的顶点表
    vector<vector<int> > tree; //最小生成树的边 ,数组存储
    priority_queue<EdgeNode*, vector<EdgeNode*>, mycompare> pq; //优先队列
};


int main()
{
    Graph graph;
    graph.print();
    Prims _prims(graph);
    _prims.write();
    cout << "sum: " << _prims.sum << endl;
    return 0;
}