2395-Out of Hay

問題（外部リンク）

2395 -- Out of Hay

実装の概要

最終的に構成したいのは最小全域木ですが、今回は距離の総和ではなく全域木を構成する辺の中で最長のものの長さです。
そのため、クラスカル法の一部を変更し最大の距離を保存できるようにすることで解くことができます。

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] tmpArray = br.readLine().split(" ");

		//0 origin
		int n = Integer.parseInt(tmpArray[0]);
		int m = Integer.parseInt(tmpArray[1]);

		Edge edges[] = new Edge[m];

		for(int i = 0; i < m; i++){
			tmpArray = br.readLine().split(" ");
			int from = Integer.parseInt(tmpArray[0]) - 1;
			int to = Integer.parseInt(tmpArray[1]) - 1;
			int cost = Integer.parseInt(tmpArray[2]);

			edges[i] = new Edge(from,to, cost);
		}

		System.out.println(kruskal(edges, n));
	}


	static final int INF = Integer.MAX_VALUE;


	//辺の最大値を返すように仕様変更
	static int kruskal(Edge[] edges, int n){
		int numOfEdge = edges.length;

		Arrays.sort(edges);

		DisjointSet set = new DisjointSet(n);

		int longest = 0;

		for(int i = 0; i < numOfEdge ; i++){
			Edge tmpEdge = edges[i];

			if(!set.isSameSet(tmpEdge.from, tmpEdge.to)){
				set.union(tmpEdge.from, tmpEdge.to);
				longest = Math.max(tmpEdge.cost, longest);
			}
		}

		return longest;

	}
}

class DisjointSet {
    private int n;
    private int[] p;
    private int[] rank;

    public DisjointSet(int n){
        this.n = n;

        p = new int[n + 1];
        rank = new int[n + 1];

        for(int i = 1; i <= n; i++){
            makeSet(i);
        }
    }

    private void makeSet(int x){
        p[x] = x;
        rank[x] = 0;
    }

    public void union(int x, int y){
        link (findSet(x), findSet(y));
    }

    private int findSet(int x){
        if(x != p[x]){
            p[x] = findSet( p[x]);
        }
        return p[x];
    }

    public boolean isSameSet(int x, int y){
        return findSet(x) == findSet(y);
    }

    private void link(int x, int y){
        if(rank[x] > rank[y]){
            p[y] = x;
        }
        else {
            p[x] = y;
            if(rank[x] == rank[y]){
                rank[y]++;
            }
        }
    }
}

class Edge implements Comparable<Edge>{
	int from;
	int to;
	int cost;

	Edge(int from, int to, int cost){
		this.from = from;
		this.to = to;
		this.cost = cost;
	}

	@Override
	public int compareTo(Edge e) {
		return this.cost - e.cost;
	}
}