ZOJ 1542 POJ 1861 Network Minimum Spanning Tree, longest side, Kruskal algorithm, zojkruskal

ZOJ 1542 POJ 1861 Network Minimum Spanning Tree, longest side, Kruskal algorithm, zojkruskal

Question connection: ZOJ 1542 POJ 1861 Network

Network Time Limit: 2 Seconds Memory Limit: 65536 KB Special Judge

Andrew is working as system administrator and is planning to establish a new network in his company. there will be N hubs in the company, they can be connected to each other using cables. since each worker of the company must have access to the whole network, each hub must be accessible by cables from any other hub (with possibly some intermediate hubs ).

Since cables of different types are available and shorter ones are cheaper, it is necessary to make such a plan of hub connection, that the maximum length of a single cable is minimal. there is another problem-not each hub can be connected to any other one because of compatibility problems and building geometry limitations. of course, Andrew will provide you all necessary information about possible hub connections.

You are to help Andrew to find the way to connect hubs so that all above conditions are satisfied.

Input

The first line of the input file contains two integer numbers: N-the number of hubs in the network (2 <= N <= 1000) and M-the number of possible hub connections (1 <= M <= 15000 ). all hubs are numbered from 1 to N. the following M lines contain information about possible connections-the numbers of two hubs, which can be connected and the cable length required to connect them. length is a positive integer number that does not exceed 10 ^ 6. there will be no more than one way to connect two hubs. A hub cannot be connected to itself. there will always be at least one way to connect all hubs.

Process to the end of file.

Output

Output first the maximum length of a single cable in your hub connection plan (the value you should minimize ). then output your plan: first output P-the number of cables used, then output P pairs of integer numbers-numbers of hubs connected by the corresponding cable. separate numbers by spaces and/or line breaks.

Sample Input

4 6
1 2 1
1 3 1
1 4 2
2 3 1
3 4 1
2 4 1

Sample Output

1
4
1 2
1 3
2 3
3 4

Analysis: calculates the value of the longest edge in the minimal spanning tree, and then outputs the selected edge. The Kruskal algorithm.

Code:

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <cstdlib>using namespace std;#define maxn 1010#define maxm 15002int n, m, maxlen, cnt;int parent[maxn], ans[maxn];struct edge{    int u, v, w;}EG[maxm];bool cmp(edge a, edge b){    return a.w < b.w;}int Find(int x){    if(parent[x] == -1) return x;    return Find(parent[x]);}void Kruskal(){    memset(parent, -1, sizeof(parent));    sort(EG, EG+m, cmp);    for(int i = 0; i < m; i++)    {        int t1 = Find(EG[i].u), t2 = Find(EG[i].v);        if(t1 != t2)        {            if(maxlen < EG[i].w)                maxlen = EG[i].w;            ans[cnt++] = i;            parent[t1] = t2;        }    }}int main(){    while(~scanf("%d%d", &n, &m))    {        for(int i = 0; i < m; i++)            scanf("%d%d%d", &EG[i].u, &EG[i].v, &EG[i].w);        maxlen = cnt = 0;        Kruskal();        printf("%d\n", maxlen);        printf("%d\n", cnt);        for(int i = 0; i < cnt; i++)            printf("%d %d\n", EG[ans[i]].u, EG[ans[i]].v);    }    return 0;}

Poj1861, my understanding: the minimum spanning tree with the smallest biggest edge, uses kruskal, and finally outputs this tree. There is no limit on the output of the tree.

This question is about the length of all edges and the smallest spanning tree, not the smallest spanning tree .. Take a look at the example given by it to understand.

The Minimum Spanning Tree uses the Kruskal algorithm graph G's smallest spanning tree T, using the C Language

# Include <cstdlib>
# Include <iostream>
# Include <queue>
Using namespace std;

//////////////////////////////////////// //////////////////////////////////////// ///////////////////////////////////////
// Description: and check the storage structure of the set.
// Tags: If the value is-1, it indicates the root node.
Struct DisjointSet
{
Int * arr; // The value is the subscript of the parent node.
Int number; // number of arr Elements
};

//////////////////////////////////////// //////////////////////////////////////// ///////////////////////////////////////
// Description: Initialize and query the set structure
// Input: number-elements... the remaining full text>