図論初級アルゴリズム

図遍歴アルゴリズム----DFS&BFS...
 

public class GraphTraveler {
	
	LinkedList<Integer> open = new LinkedList<Integer>();
	
	public void bfs(Graph g, int start) {
		int n = g.getVolume();
		Graph tree = new Graph(n, false);
		boolean[] visited = new boolean[n];
		Arrays.fill(visited, false);
		open.add(start);
		visited[start] = true;
		while (!open.isEmpty()) {
			int now = open.poll();
			System.out.print(now + ", ");
			List<int[]> nexts = g.getAdjs(now);
			for (int[] e : nexts) {
				if (!visited[e[1]]) {
					open.add(e[1]);
					visited[e[1]] = true;
					tree.addEdge(e[0], e[1], e[2]);
				}
			}
		}
		System.out.println(tree);
	}

	public void dfs(Graph g, int start) {
		int n = g.getVolume();
		Graph tree = new Graph(n, false);
		boolean[] visited = new boolean[n];
		Arrays.fill(visited, false);
		open.add(start);
		visited[start] = true;
		while (!open.isEmpty()) {
			int now = open.pop();
			System.out.print(now + ", ");
			List<int[]> nexts = g.getAdjs(now);
			for (int[] e : nexts) {
				if (!visited[e[1]]) {
					open.push(e[1]);
					visited[e[1]] = true;
					tree.addEdge(e[0], e[1], e[2]);
				}
			}
		}
		System.out.println(tree);
	}
	
	public static void main(String[] args) {
		GraphTraveler t = new GraphTraveler();
		Graph g = new Graph(9, false);
		int[][] edges = {{0,1,4},{0,7,8},{1,2,8},{1,7,11},
				{2,3,7},{2,5,4},{2,8,2},{3,4,9},{3,5,14},
				{4,5,10},{5,6,2},{6,7,1},{6,8,6},{7,8,7}};
		for (int[] e : edges)
			g.addEdge(e[0], e[1], e[2]);
		System.out.println(g);
		System.out.println("----  BFS  ----");
		t.bfs(g, 4);
		System.out.println("----  DFS  ----");
		t.dfs(g, 4);
	}

}

 
 
最小生成ツリー---Prim&Kruskal...
 

public class GenericMST {
	
	public Graph prim(Graph g) {
		int n = g.getVolume();
		Graph tree = new Graph(n, g.isDirected());
		int[] cost = new int[n]; // cost[j]: min cost to tree
		int[] from = new int[n]; // e : (from[i], i)
		int[][] arcs = g.getArcs();
		for (int i = 0; i < n; i++) {
			cost[i] = arcs[i][0];
			from[i] = 0;
		}
		for (int i = 1; i < n; i++) {
			int min = Integer.MAX_VALUE;
			int k = 0;
			for (int j = 1; j < n; j++)
				if (cost[j] != -1 && cost[j] < min) {
					min = cost[j];
					k = j;
				}
			cost[k] = -1;
			for (int j = 1; j < n; j++)
				if (arcs[k][j] < cost[j]) {
					cost[j] = arcs[k][j];
					from[j] = k;
				}
		}
		for (int i = 0; i < n; i++)
			tree.addEdge(from[i], i, arcs[from[i]][i]);
		return tree;
	}

	public Graph kruskal(Graph g) {
		int n = g.getVolume();
		Graph tree = new Graph(n, g.isDirected());
		PriorityQueue<int[]> queue = new PriorityQueue<int[]>(32,
			new Comparator<int[]>() {
				public int compare(int[] e1, int[] e2) {
					return e1[2] - e2[2];
				}
		});
		List<int[]> edges = g.getEdges();
		DisjointSet set = new DisjointSet(n);
		for (int[] e : edges)
			queue.add(e);
		while (!queue.isEmpty()) {
			int[] e = queue.poll();
			if (set.find(e[0]) != set.find(e[1])) {
				tree.addEdge(e[0], e[1], e[2]);
				set.union(e[0], e[1]);
			}
		}
		return tree;
	}
	
	public static void main(String[] args) {
		Graph g = new Graph(9, false);
		/*int[][] edges = {{0,1,4},{0,7,8},{1,2,8},{1,7,11},
				{2,3,7},{2,5,4},{2,8,2},{3,4,9},{3,5,14},
				{4,5,10},{5,6,2},{6,7,1},{6,8,6},{7,8,7}};
		for (int[] e : edges)
			g.addEdge(e[0], e[1], e[2]);*/
		g.shuffle();
		System.out.println("----- Origine -----");
		System.out.println(g);
		GenericMST mst = new GenericMST();
		System.out.println("----- Kruskal -----");
		System.out.println(mst.kruskal(g));
		System.out.println("-----  Prim  ------");
		System.out.println(mst.prim(g));
	}

}

 
 
最短経路---Dijkstra&Floyed...
 

public class ShortestPath {

	public void dijkstra(Graph g, int s) {
		int n = g.getVolume();
		int[][] arcs = g.getArcs();
		boolean[] find = new boolean[n];
		int[] cost = new int[n];
		ArrayList[] paths = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			find[i] = false;
			cost[i] = arcs[s][i];
			paths[i] = new ArrayList();
		}
		find[s] = true;
		cost[s] = 0;
		for (int i = 1; i < n; i++) {
			int min = Integer.MAX_VALUE;
			int k = -1;
			for (int j = 0; j < n; j++)
				if (!find[j] && cost[j] < min) {
					min = cost[j];
					k = j;
				}
			find[k] = true;
			paths[k].add(k);
			for (int j = 0; j < n; j++)
				if (arcs[k][j] < Integer.MAX_VALUE &&
					!find[j] && arcs[k][j] + min < cost[j]) {
					cost[j] = arcs[k][j] + min;
					paths[j] = (ArrayList) paths[k].clone();
				}
		}
		for (int i = 0; i < n; i++)
			System.out.println(cost[i] + " -- " + paths[i]);
	}
	
	public void floyed(Graph g) {
		int n = g.getVolume();
		int[][] arcs = g.getArcs();
		int[][] cost = new int[n][n];
		int[][] path = new int[n][n];
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++) {
				cost[i][j] = (i == j) ? 0 : arcs[i][j];
				path[i][j] = -1;
			}
		for (int k = 0; k < n; k++)
			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					if (cost[i][k] < Integer.MAX_VALUE && 
						cost[k][j] < Integer.MAX_VALUE &&
						cost[i][k] + cost[k][j] < cost[i][j]) {
						cost[i][j] = cost[i][k] + cost[k][j];
						path[i][j] = k;
					}
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++) {
				System.out.format("(%d,%d) %3d: %d", i, j, cost[i][j], i);
				showPath(path, i, j);
				System.out.println();
			}
				
	}
	
	public void showPath(int[][] path, int i, int j) {
		int k = path[i][j];
		if (k == -1) {
			System.out.print("->" + j);
			return;
		}
		showPath(path, i, k);
		showPath(path, k, j);
	}
	
	public static void main(String[] args) {
		ShortestPath sp = new ShortestPath();
		Graph g = new Graph(5, true);
		/*int[][] edges = {{0,1,10},{0,3,5},{1,2,1},{1,3,2},
				{2,4,4},{3,1,3},{3,2,9},{3,4,2},{4,0,7},{4,2,6}};*/
		int[][] edges = {{0,1,3},{0,2,8},{0,4,-4},{1,3,1},
				{1,4,7},{2,1,4},{3,0,2},{3,2,-5},{4,3,6}};
		for (int[] e : edges)
			g.addEdge(e[0], e[1], e[2]);
		System.out.println(g);
		/*System.out.println("---- Dijkstra ----");
		sp.dijkstra(g, 0);*/
		System.out.println("----  Floyed  ----");
		sp.floyed(g);
	}

}

 
 
図の表示...
 

public class Graph {

	private int n;
	private boolean directed;
	private int[][] arcs;
	
	public Graph(int n, boolean directed) {
		this.n = n;
		this.directed = directed;
		arcs = new int[n][n];
		for (int[] arc : arcs)
			Arrays.fill(arc, Integer.MAX_VALUE);
	}
	
	public void addEdge(int from, int to, int weight) {
		if (from < 0 || from >= n || to < 0 || to >= n || from == to)
			return;
		if (arcs[from][to] < Integer.MAX_VALUE)
			return;
		arcs[from][to] = weight;
		if (!directed)
			arcs[to][from] = weight;
	}
	
	public List<int[]> getAdjs(int from) {
		List<int[]> adjs = new ArrayList<int[]>();
		if (from >= 0 && from < n) {
			for (int w, to = 0; to < n; to++)
				if ((w = arcs[from][to]) < Integer.MAX_VALUE)
					adjs.add(new int[]{from, to, w});
		}
		return adjs;
	}
	
	public List<int[]> getEdges() {
		List<int[]> edges = new ArrayList<int[]>();
		for (int i = 0; i < n; i++)
			for (int w, j = (directed) ? 0 : i + 1; j < n; j++)
				if ((w = arcs[i][j]) < Integer.MAX_VALUE)
					edges.add(new int[]{i, j, w});
		return edges;
	}
	
	public int getVolume() {
		return n;
	}
	
	public boolean isDirected() {
		return directed;
	}
	
	public int[][] getArcs() {
		return arcs;
	}
	
	public void shuffle() {
		Random r = new Random();
		for (int k = 0; k < 3 * n; k++)
			addEdge(r.nextInt(n), r.nextInt(n), 1 + r.nextInt(20));
	}
	
	public String toString() {
		StringBuilder buf = new StringBuilder();
		for (int i = 0; i < n; i++) {
			buf.append(i + " -> ");
			for (int j = 0; j < n; j++)
				if (arcs[i][j] < Integer.MAX_VALUE)
					buf.append("(" + j + "," + arcs[i][j] + ") ");
			buf.append("
");
		}
		return buf.toString();
	}

}

 
 
Kruskalアルゴリズムで使用され、セットを調べます.
 

public class DisjointSet {

	private int[] set;
	
	public DisjointSet(int n) {
		set = new int[n];
		for (int i = 0; i < n; i++)
			set[i] = -1;
	}
	
	public void union(int x, int y) {
		int r1 = find(x);
		int r2 = find(y);
		if (r1 == r2)
			return;
		if (set[r2] < set[r1])
			set[r1] = r2;
		else {
			if (set[r2] == set[r1])
				set[r1]--;
			set[r2] = r1;
		}
	}
	
	public int find(int x) {
		if (set[x] < 0)
			return x;
		return set[x] = find(set[x]);
	}
	
}