pss407·2020년 8월 30일
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## 입력

The input consists of one to 100 data sets, followed by a final line containing only 0. Each data set starts with a line containing only a number n, which is the number of villages, 1 < n < 27, and the villages are labeled with the first n letters of the alphabet, capitalized. Each data set is completed with n-1 lines that start with village labels in alphabetical order. There is no line for the last village. Each line for a village starts with the village label followed by a number, k, of roads from this village to villages with labels later in the alphabet. If k is greater than 0, the line continues with data for each of the k roads. The data for each road is the village label for the other end of the road followed by the monthly maintenance cost in aacms for the road. Maintenance costs will be positive integers less than 100. All data fields in the row are separated by single blanks. The road network will always allow travel between all the villages. The network will never have more than 75 roads. No village will have more than 15 roads going to other villages (before or after in the alphabet). In the sample input below, the first data set goes with the map above.

## 출력

The output is one integer per line for each data set: the minimum cost in aacms per month to maintain a road system that connect all the villages. Caution: A brute force solution that examines every possible set of roads will not finish within the one minute time limit.

## 예제 입력 1

9
A 2 B 12 I 25
B 3 C 10 H 40 I 8
C 2 D 18 G 55
D 1 E 44
E 2 F 60 G 38
F 0
G 1 H 35
H 1 I 35
3
A 2 B 10 C 40
B 1 C 20
0

## 예제 출력 1

216
30

## 풀이

이 문제는 최소 비용 신장 트리를 구하는 문제로 Prim 알고리즘을 이용해서 풀었다. Prim 알고리즘은 우선순위 큐와 일반 큐 두 개를 이용해서 구현했다.

import java.io.BufferedReader;
import java.io.IOException;
import java.util.ArrayList;
import java.util.PriorityQueue;
import java.util.Queue;

public class Main {
static boolean[] visited;
static ArrayList<Node>[] nodeList;

public static void main(String[] args) throws IOException {

while(true) {
if(N==0)
break;

nodeList = new ArrayList[N+1];
for(int i=1; i<N+1; i++) {
nodeList[i] = new ArrayList<>();
}
visited = new boolean[N+1];

for(int i=0; i<N-1; i++) {
int start = input[0].charAt(0) - 64;
int m = Integer.parseInt(input[1]);

for(int j=1; j<=m; j++) {
int end = input[j*2].charAt(0) - 64;
int cost = Integer.parseInt(input[j*2+1]);
}
}

System.out.println(MST());
}
}

public static int MST() {
PriorityQueue<Node> pq = new PriorityQueue<>();
ArrayList<Node> tempList;
Node tempNode;

while(!queue.isEmpty()) {
int currentNode = queue.poll();
visited[currentNode] = true;
tempList = nodeList[currentNode];

for(int i=0; i<tempList.size(); i++) {
if(!visited[tempList.get(i).end]) {
}
}

while(!pq.isEmpty()) {
tempNode = pq.poll();

if(!visited[tempNode.end]) {
visited[tempNode.end]=true;
break;
}
}
}
}

static class Node implements Comparable<Node>{
int start;
int end;
int cost;

public Node(int start, int end, int cost) {
this.start = start;
this.end = end;
this.cost = cost;
}

@Override
public int compareTo(Node node) {
return this.cost > node.cost ? 1 : -1;
}
}
}
👶🏻Jr. Programmer