1034 Head of a Gang (30 分)

知识点：并查集 DFS

版本4

注意：顶点数可能达到2000，另外权值是所有边的总和，不同的思路有可能计算成了两倍，需要除2后再与K比较。
由于节点在插入的过程中，每两个点的通话时间的动态变化的，所以需要先把通话时长计算出来以后再进行合并。
同时按照权值最大的节点作为根节点的原则。
总结：这道题用并查集也可以在做，但是推荐使用DFS。先用邻接矩阵存起来，同时需要记录点权。然后直接深搜，把所有条件都放在形参中。简单易操作。

#include <cstdio>
#include <iostream>
#include <vector>
#include <cstring>
#include <queue> 
#include <unordered_map>
#include <algorithm>
using namespace std;
unordered_map<string, int> SI;
unordered_map<int, string> IS;
typedef pair<string, int> PSI;
const int N = 2005;
int cost[N], member[N], root[N], total[N];
struct node{
	int u, v;
}E[N];
int find(int x){
	if(x != root[x]) root[x] = find(root[x]);
	return root[x];
}
int main(){
	int n, K, t, u, v, id = 0;
	scanf("%d%d", &n, &K);
	string p, q;
	memset(cost, 0, sizeof cost);
	for(int i = 0; i < N; i++){
		member[i] = 1;
		root[i] = i;
	}
	for(int i = 0; i < n; i++){
		cin>>p>>q>>t;
		//第一个人 
		if(SI.count(p)) u = SI[p];
		else{
			u = id++;
			SI[p] = u;
			IS[u] = p;
		}
		//第二个人
		if(SI.count(q)) v = SI[q];
		else{
			v = id++;
			SI[q] = v;
			IS[v] = q;
		}
		cost[u] += t;
		cost[v] += t;
		E[i]= {u, v};		
	}
	for(int i = 0; i < N; i++) total[i] = cost[i];
	for(int i = 0; i < n; i++){
		u = E[i].u , v = E[i].v;
		int faU = find(u);
		int faV = find(v);
		if(faU != faV){
			if(cost[faU] > cost[faV]){
				root[faV] = faU;
				member[faU] += member[faV];
				total[faU] += total[faV];
			}else {
				root[faU] = faV;
				member[faV] += member[faU];
				total[faV] += total[faU];
			}
		}
	}
	int num = 0;
	vector<PSI> res;
	for(int i = 0; i < id; i++){
//		printf("%dth root = %d, member = %d, cost = %d, total = %d\n", i, root[i], member[i], cost[i], total[i]);
		if(root[i] == i && member[i] > 2 && total[i]/2.0 > K){
			res.push_back({IS[i], member[i]});
			num++;
		}
	}
	cout<<num<<endl;
	sort(res.begin(), res.end());
	for(auto it: res){
		cout<<it.first<<" "<<it.second<<endl;
	}
	return 0;
} 

版本3

还有2个测试点没过
22分
求指点

#include<bits/stdc++.h>
using namespace std;
const int  maxn = 3005;
int f[maxn],val[maxn];
map<int, string> IS;
map<string, int> SI;
int person=1;
struct node{
	int a,cnt,total,tag,mm;
}E[maxn];
void init(){
	for(int i=0;i<maxn;i++){
		f[i] = i;
		E[i].a=E[i].cnt=E[i].total=E[i].mm=0;
		val[i] = 0;
	}
}
int find(int x){
	if(x == f[x]) return x;
	return f[x] = find(f[x]);
}
bool cmp(node a, node b){
	if(a.tag != b.tag) return a.tag > b.tag;
	else return a.a < b.a;
}
int change(string str){ 
	if(SI.find(str) != SI.end()) return SI[str];
	else{
		SI[str] = person;
		IS[person] = str;
		return person++;
	}
}
int main(){
	int n,m,x,a,b;
	string str1,str2;
	init();
	cin>>n>>m;
	for(int i=0;i<n;i++){
		cin>>str1>>str2>>x;
		a = change(str1);
		b = change(str2);
		int fa = find(a);
		int fb = find(b);
		val[a] += x;  
		val[b] += x;
		if(fa != fb) f[fa] = fb;
			
	}

	for(int i=0;i<maxn;i++){ //筛选 
		int d = find(i);  
		if(val[i]!=0){ 
			if(E[d].mm < val[i]){
				E[d].mm = val[i];
				E[d].a = i;
			} 
			E[d].total += val[i];
			E[d].cnt++;
		}
	}
	
	int k=0;
	for(int i=0;i<maxn;i++){
		if(E[i].cnt > 2 && E[i].total/2 > m){
			k++;
			E[i].tag=1;
		}else 
			E[i].tag = 0;
	}
	sort(E,E+maxn,cmp);
	cout<<k<<endl;
	for(int i=0;i<k; i++){
		cout<<IS[E[i].a]<<" "<<E[i].cnt<<endl;
	}
	return 0;
}

版本2

DFS

#include<iostream>
#include<string>
#include<map>
#include<algorithm>
#define N 2010
using  namespace std;
map<string,int> string2int;
map<int,string> int2string;
map<string,int> gang;
int G[N][N]={0},w[N]={0};
bool vis[N] = {false};
int idNum = 1;
int k;
int change(string s){
	if(string2int[s] == 0){
		string2int[s] = idNum;
		int2string[idNum]=s;
		return idNum++;
	}else{
		return string2int[s];
	}
}
void DFS(int u,int &h,int &m,int &t){
	m++;
	vis[u] = true;
	if(w[u] > w[h]){
		h = u;
	}
	for(int v=1;v < idNum;v++){
		if(G[u][v] > 0){ //如果有边 
			t += G[u][v];
			G[u][v]=G[v][u] = 0;
			if(vis[v]==false){
				DFS(v,h,m,t);
			}
		}
	}
}
void DFSTrave(){
	for(int i=1; i<idNum;i++){
		if(vis[i]==false){
			int head = i,numMem=0,totalV=0;//头目，总人数，总边权
			DFS(i,head,numMem,totalV);
			if(numMem > 2 && totalV > k){
				gang[int2string[head]] = numMem;
			} 
		}
	}
}
int main(){	
    int n,d;
	string str1,str2;
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>str1>>str2>>d;
		int id1 = change(str1);
		int id2 = change(str2);
		w[id1] += d;  //点权 
		w[id2] += d;  
		G[id1][id2] += d; //边权 
		G[id2][id1] += d; 	
		}
	DFSTrave(); 
	cout<<gang.size()<<endl;
	map<string,int>::iterator it;
		for(it = gang.begin();it !=gang.end();it++){
			cout<<it->first<<" "<<it->second<<endl;
	}
	return 0;
}

版本1

DFS

#include<iostream>
#include<string>
#include<map>
#include<algorithm>
#define N 2010
using  namespace std;
map<string,int> string2int;
map<int,string> int2string;
map<string,int> gang;

int G[N][N]={0},w[N]={0};

bool vis[N] = {false};
int idNum = 1;
int k;
int change(string s){
	if(string2int[s] == 0){
		string2int[s] = idNum;
		int2string[idNum]=s;
		return idNum++;
	}else{
		return string2int[s];
	}
}
void DFS(int i, int &cnt, int &mxi, int& cost){
	cnt++; cost += w[i];
	if(w[i] > w[mxi]) mxi = i;
	for(int j = 1; j < idNum; j++){
		if(!vis[j] && G[i][j]){
			vis[j] = 1;
			DFS(j, cnt, mxi, cost);
		}
	}
}
void DFST(){
	for(int i = 1; i < idNum; i++){
		if(!vis[i]) {
			vis[i] = 1;
			int cnt = 0, mxi = i, cost = 0;
			DFS(i, cnt, mxi, cost);
			if(cnt > 2 && cost/2.0 > k) gang[int2string[mxi]] = cnt;
		}
	}
}

int main(){	
    int n, d;
	string str1,str2;
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>str1>>str2>>d;
		int id1 = change(str1);
		int id2 = change(str2);
		w[id1] += d;  //点权 
		w[id2] += d;  
		G[id1][id2] += d; //边权 
		G[id2][id1] += d; 	
		}
	DFST(); 
	cout<<gang.size()<<endl;
	map<string,int>::iterator it;
		for(it = gang.begin();it !=gang.end();it++){
			cout<<it->first<<" "<<it->second<<endl;
	}
	return 0;
}