zoj 3204 字典序最小的最小生成树的输出

Connect them

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Time Limit: 1 Second      Memory Limit: 32768 KB

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You have n computers numbered from 1 to n and you want to connect them to make a small local area network (LAN). All connections are two-way (that is connecting computers i and j is the same as connecting computers j and i). The cost of connecting computer i and computer j is c_ij. You cannot connect some pairs of computers due to some particular reasons. You want to connect them so that every computer connects to any other one directly or indirectly and you also want to pay as little as possible.

Given n and each c_ij , find the cheapest way to connect computers.

Input

There are multiple test cases. The first line of input contains an integer T (T <= 100), indicating the number of test cases. Then T test cases follow.

The first line of each test case contains an integer n (1 < n <= 100). Then n lines follow, each of which contains n integers separated by a space. The j-th integer of the i-th line in these n lines is c_ij, indicating the cost of connecting computers i and j (c_ij = 0 means that you cannot connect them). 0 <= c_ij <= 60000, c_ij = c_ji, c_ii = 0, 1 <= i, j <= n.

Output

For each test case, if you can connect the computers together, output the method in in the following fomat:

i₁ j₁ i₁ j₁ ......

where i_k i_k (k >= 1) are the identification numbers of the two computers to be connected. All the integers must be separated by a space and there must be no extra space at the end of the line. If there are multiple solutions, output the lexicographically smallest one (see hints for the definition of "lexicography small") If you cannot connect them, just output "-1" in the line.

Sample Input

230 2 32 0 53 5 020 00 0

Sample Output

1 2 1 3-1

Hints:
A solution A is a line of p integers: a₁, a₂, ...a_p.
Another solution B different from A is a line of q integers: b₁, b₂, ...b_q.
A is lexicographically smaller than B if and only if:
(1) there exists a positive integer r (r <= p, r <= q) such that a_i = b_i for all 0 < i < r and a_r < b_r 
OR
(2) p < q and a_i = b_i for all 0 < i <= p

此题关键在最小生成树的输出要按照字典序最小的输出，用kruscal算法求解。

#include<iostream>#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;#define maxn 110int Father[maxn];struct Edge{    int from;    int to;    int w;}edge[maxn*maxn],path[maxn*maxn];int n,tol,cnt;void addedge(int u,int v,int w){    edge[tol].from=u;    edge[tol].to=v;    edge[tol].w=w;    tol++;}bool cmp1(Edge a,Edge b){    if(a.w!=b.w)return a.w<b.w;    else if(a.from!=b.from)    return a.from<b.from;    else    return a.to<b.to;}bool cmp2(Edge a,Edge b){    if(a.from!=b.from)    return a.from<b.from;    else    return a.to<b.to;}//ksuscal求最小生产树int find(int x){    if(Father[x]==-1)return x;    return Father[x]=find(Father[x]);}void kruscal(){    memset(Father,-1,sizeof(Father));    cnt=0;    for(int i=0;i<tol;i++)    {        int u=edge[i].from;        int v=edge[i].to;        int t1=find(u);        int t2=find(v);        if(t1!=t2)        {            path[cnt++]=edge[i];            Father[t1]=t2;        }    }}int main(){    int cas;    cin>>cas;    while(cas--)    {        tol=0;        cin>>n;        int val;        for(int i=0;i<n;i++)        {            for(int j=0;j<n;j++)            {                cin>>val;                if(j<=i||val==0)continue;                addedge(i,j,val);            }        }        sort(edge,edge+tol,cmp1);        kruscal();        if(cnt!=n-1)        {            cout<<"-1"<<endl;        }        else        {            sort(path,path+cnt,cmp2);            for(int i=0;i<cnt-1;i++)            cout<<path[i].from+1<<" "<<path[i].to+1<<" ";            cout<<path[cnt-1].from+1<<" "<<path[cnt-1].to+1<<endl;        }    }    return 0;}