zoukankan      html  css  js  c++  java
  • POJ 1258 Agri-Net(最小生成树 Prim+Kruskal)

    题目链接: 传送门

    Agri-Net

    Time Limit: 1000MS     Memory Limit: 10000K

    Description

    Farmer John has been elected mayor of his town! One of his campaign promises was to bring internet connectivity to all farms in the area. He needs your help, of course.
    Farmer John ordered a high speed connection for his farm and is going to share his connectivity with the other farmers. To minimize cost, he wants to lay the minimum amount of optical fiber to connect his farm to all the other farms.
    Given a list of how much fiber it takes to connect each pair of farms, you must find the minimum amount of fiber needed to connect them all together. Each farm must connect to some other farm such that a packet can flow from any one farm to any other farm.
    The distance between any two farms will not exceed 100,000.

    Input

    The input includes several cases. For each case, the first line contains the number of farms, N (3 <= N <= 100). The following lines contain the N x N conectivity matrix, where each element shows the distance from on farm to another. Logically, they are N lines of N space-separated integers. Physically, they are limited in length to 80 characters, so some lines continue onto others. Of course, the diagonal will be 0, since the distance from farm i to itself is not interesting for this problem.

    Output

    For each case, output a single integer length that is the sum of the minimum length of fiber required to connect the entire set of farms.

    Sample Input

    4
    0 4 9 21
    4 0 8 17
    9 8 0 16
    21 17 16 0
    

    Sample Output

    28
    

    Prim算法O(V^2)

    #include<iostream>
    #include<cstdio>
    #include<cstring>
    using namespace std;
    const int INF = 0x3f3f3f3f;
    const int MAX_V = 105;
    int edge[MAX_V][MAX_V];
    int dis[MAX_V];
    bool vis[MAX_V];
    int N;
    
    int prim()
    {
    	memset(dis,INF,sizeof(dis));
    	memset(vis,false,sizeof(vis));
    	for (int i = 1;i <= N;i++)
    	{
    		dis[i] = edge[i][1];
    	}
    	dis[1] = 0;
    	vis[1] = true;
    	int sum = 0;
    	for (int i = 1;i < N;i++)
    	{
    		int tmp = INF,pos;
    		for (int j = 1;j <= N;j++)
    		{
    			if(!vis[j] && tmp > dis[j])
    			{
    				tmp = dis[j];
    				pos = j;
    			}
    		}
    		if (tmp == INF) return 0;
    		vis[pos] = true;
    		sum += dis[pos];
    		for(int j = 1;j <= N;j++)
    		{
    			if (!vis[j] && edge[pos][j] < dis[j])
    			{
    				dis[j] = edge[pos][j];
    			}
    		}
    	}
    	return sum;
    }
    
    
    int main()
    {
    	while (~scanf("%d",&N))
    	{
    		for (int i = 1;i <= N;i++)
    		{
    			for (int j = 1;j <= N;j++)
    			{
    				scanf("%d",&edge[i][j]);
    			}
    		}
    		int res = prim();
    		printf("%d
    ",res);
    	}
    	return 0;
    }
    

    Prim算法O(ElogV)

    #include<iostream>
    #include<vector>
    #include<queue>
    #include<utility>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    typedef __int64 LL;
    typedef pair<int,int>pii;  //first  最短距离  second 顶点编号 
    const int INF = 0x3f3f3f3f;
    const int MAX = 105;
    struct edge{
    	int to,cost;
    	edge(int t,int c):to(t),cost(c){}
    };
    vector<edge>G[MAX];
    int N,dis[MAX];
    bool vis[MAX];
    
    
    int prim()
    {
    	int res = 0;
    	priority_queue<pii,vector<pii>,greater<pii> >que;
    	memset(dis,INF,sizeof(dis));
    	memset(vis,false,sizeof(vis));
    	dis[1] = 0;
    	que.push(pii(0,1));
    	while (!que.empty())
    	{
    		pii p = que.top();
    		que.pop();
    		int v = p.second;
    		if (vis[v] || p.first > dis[v])	continue;
    		vis[v] = true;
    		res += dis[v];
    		for (int i = 0;i < G[v].size();i++)
    		{
    			edge e = G[v][i];
    			if (dis[e.to] >  e.cost)
    			{
    				dis[e.to] = e.cost;
    				que.push(pii(dis[e.to],e.to));
    			}
    		}
    		
    	}
    	return res;
    } 
    
    
    int main()
    {
    	while (~scanf("%d",&N))
    	{
    		int tmp;
    		for (int i = 1;i <= N;i++)
    		{
    			G[i].clear();
    			for (int j = 1;j <= N;j++)
    			{
    				scanf("%d",&tmp);
    				G[i].push_back(edge(j,tmp));
    			}
    		}
    		int res = prim();
    		printf("%d
    ",res);
    	}
    	return 0;
    }
    

    Kruskal算法O(ElogV)

    #include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    const int INF = 0x3f3f3f3f;
    const int MAX = (105*105-105)/2;
    struct Edge{
    	int u,v,w;
    };
    int N,father[MAX],rk[MAX];
    struct Edge edge[MAX];
    
    bool cmp(Edge x,Edge y)
    {
    	return x.w < y.w;
    }
    
    
    void init()
    {
    	memset(father,0,sizeof(father));
    	memset(rk,0,sizeof(rk));
    	for (int i = 0;i <= N;i++)
    	{
    		father[i] = i;
    	}
    }
    
    int find(int x)
    {
    	int r = x;
    	while (father[r] != r)
    	{
    		r = father[r];
    	}
    	int i = x,j;
    	while (i != r)
    	{
    		j = father[i];
    		father[i] = r;
    		i = j;
    	}
    	return r;
    }
    /*int find(int x)
    {
    	return x == father[x]?x:father[x] = find(father[x]);
    }*/
    
    void unite(int x,int y)
    {
    	int fx,fy;
    	fx = find(x);
    	fy = find(y);
    	if (fx == fy)	return;
    		if (rk[fx] < rk[fy])
    		{
    			father[fx] = fy;
    		}
    		else
    		{
    			father[fy] = fx;
    			if (rk[x] == rk[y])
    			{
    				rk[x]++;
    			}
    		}
    	
    }
    
    /*void unite(int x,int y)
    {
    	int fx = find(x),fy = find(y);
    	if (fx != fy)
    	{
    		father[fx] = fy;
    	}
    }*/
    
    
    int main()
    {
    	while (~scanf("%d",&N))
    	{
    		int tmp,cnt = 0,sum = 0;
    		for (int i = 1;i <= N;i++)
    		{
    			for (int j = 1;j <= N;j++)
    			{
    				scanf("%d",&tmp);
    				if (i < j)
    				{
    					edge[cnt].u = i;
    					edge[cnt].v = j;
    					edge[cnt].w = tmp;
    					cnt++;
    				}
    			}
    		}
    		init();
    		sort(edge,edge+cnt,cmp);
    		for (int i = 0;i < cnt;i++)
    		{
    			int x,y;
    			x = find(edge[i].u);
    			y = find(edge[i].v);
    			if (x != y)
    			{
    				unite(x,y);
    				sum += edge[i].w;
    			}
    		}
    		printf("%d
    ",sum);
    	}
    	return 0;
    }
    
  • 相关阅读:
    剑指 Offer——13. 调整数组顺序使奇数位于偶数前面
    剑指 Offer——3. 从尾到头打印链表
    剑指 Offer——2. 替换空格
    剑指 Offer——1. 二维数组中的查找
    LeetCode 905. Sort Array By Parity 按奇偶校验排列数组
    LeetCode 448. Find All Numbers Disappeared in an Array找到所有数组中消失的元素
    SSH 代码笔记
    anaconda3安装caffe
    opencv多版本安装
    人脸文章与数据库
  • 原文地址:https://www.cnblogs.com/ZhaoxiCheung/p/5702131.html
Copyright © 2011-2022 走看看