update 22.2

BaconQiu · Oct 29, 2016 · 62a802f · 62a802f
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diff --git a/Chapter22_ElementaryGraphAlgorithms.md b/Chapter22_ElementaryGraphAlgorithms.md
@@ -45,4 +45,45 @@ in-degree:O(V+E)
 2. 缺点是HashTable更占空间？以及需要需要解决散列冲突问题？  
 3. 用搜索树替代，缺点是搜索时间效率降低。  
 
-##22.1  广度优先搜索  
+##22.1  广度优先搜索(BFS)  
+#####22.2-1 Show the d and π values that result from running breadth-first search on the directed graph of Figure 22.2(a), using vertex 3 as the source.  
+Vertex: 1, π: null, d:0  
+Vertex: 2, π:4, d:3  
+Vertex: 3, π: null, d:0  
+Vertex: 4, π:5, d:2  
+Vertex: 5, π:3, d:1  
+Vertex: 6, π:3, d:1  
+见[代码](https://github.com/zhuxiuwei/CLRS/blob/master/src/chap22_ElementaryGraphAlgo/BFS.java#L19)  
+
+#####22.2-2 Show the d and π values that result from running breadth-first search on the undirected graph of Figure 22.3, using vertex u as the source.  
+Vertex: r, d:1, π:s  
+Vertex: s, d:0, π: null  
+Vertex: t, d:2, π:w  
+Vertex: u, d:3, π:t  
+Vertex: v, d:2, π:r  
+Vertex: w, d:1, π:s  
+Vertex: x, d:2, π:w  
+Vertex: y, d:3, π:x  
+见[代码](https://github.com/zhuxiuwei/CLRS/blob/master/src/chap22_ElementaryGraphAlgo/BFS.java#L39)  
+
+#####22.2-4 What is the running time of BFS if its input graph is represented by an adjacency matrix and the algorithm is modified to handle this form of input?  
+从邻接表的O(V+E)变成O(v + v^2)，因为扫描所有邻居的时间从O(E)变成O(V^2)。  
+
+#####22.2-5 Argue that in a breadth-first search, the value d[u] assigned to a vertex u is independent of the order in which the vertices in each adjacency list are given. Using Figure 22.3 as an example, show that the breadth-first tree computed by BFS can depend on the ordering within adjacency lists.  
+见[代码](https://github.com/zhuxiuwei/CLRS/blob/master/src/chap22_ElementaryGraphAlgo/BFS.java#L61)  
+The order in adjacency list is different from [practice 22.2-2](https://github.com/zhuxiuwei/CLRS/blob/master/src/chap22_ElementaryGraphAlgo/BFS.java#L39), but the d in output are the same. π can be changed.  
+Output:  
+Vertex: r, d:1, π:s  
+Vertex: s, d:0, π: null  
+Vertex: t, d:2, π:w  
+Vertex: u, d:3, π:x <- π here is different from 22.2-2 output, but d not remains the same.  
+Vertex: v, d:2, π:r  
+Vertex: w, d:1, π:s  
+Vertex: x, d:2, π:w  
+Vertex: y, d:3, π:x  
+
+
+
+
+
+
diff --git a/src/chap22_ElementaryGraphAlgo/BFS.java b/src/chap22_ElementaryGraphAlgo/BFS.java
@@ -0,0 +1,110 @@
+package chap22_ElementaryGraphAlgo;
+
+import java.util.HashMap;
+import java.util.LinkedList;
+import java.util.List;
+import java.util.Map;
+import java.util.Queue;
+
+
+/**
+ * BFS。adjacent list.
+ * 161029
+ */
+public class BFS {
+
+	/**
+	 * practice 22.2-1
+	 */
+	public static void prac_22_2_1(){
+		//Graph of image 22-2(a).
+		Vertex<Integer> v1 = new Vertex<Integer>(1), v2 = new Vertex<Integer>(2), v3 = new Vertex<Integer>(3), v4 = new Vertex<Integer>(4), v5 = new Vertex<Integer>(5), v6 = new Vertex<Integer>(6);
+		List<Vertex<Integer>> l1 = new LinkedList<Vertex<Integer>>(); l1.add(v2); l1.add(v4);
+		List<Vertex<Integer>> l2 = new LinkedList<Vertex<Integer>>(); l2.add(v5);
+		List<Vertex<Integer>> l3 = new LinkedList<Vertex<Integer>>(); l3.add(v6); l3.add(v5);
+		List<Vertex<Integer>> l4 = new LinkedList<Vertex<Integer>>(); l4.add(v2);
+		List<Vertex<Integer>> l5 = new LinkedList<Vertex<Integer>>(); l5.add(v4);
+		List<Vertex<Integer>> l6 = new LinkedList<Vertex<Integer>>(); l6.add(v6);
+		Map<Vertex<Integer>, List<Vertex<Integer>>> g = new HashMap<Vertex<Integer>, List<Vertex<Integer>>>();
+		g.put(v1, l1); g.put(v2, l2); g.put(v3, l3); g.put(v4, l4); g.put(v5, l5); g.put(v6, l6);
+		System.out.println("=========== prac_22_2_1: After BFS: ==============");
+		bfs(g, v3);
+		for(Vertex<Integer> key: g.keySet())
+			System.out.println(key);
+	}
+
+	/**
+	 * practice 22.2-2
+	 */
+	public static void prac_22_2_2(){
+		//Graph of image 22-3(a).
+		Vertex<Character> r = new Vertex<Character>('r'), s = new Vertex<Character>('s'), t = new Vertex<Character>('t'), u = new Vertex<Character>('u'), v = new Vertex<Character>('v'), w = new Vertex<Character>('w'), x = new Vertex<Character>('x'), y = new Vertex<Character>('y');
+		List<Vertex<Character>> rl = new LinkedList<Vertex<Character>>(); rl.add(s); rl.add(v);
+		List<Vertex<Character>> sl = new LinkedList<Vertex<Character>>(); sl.add(r); sl.add(w);
+		List<Vertex<Character>> tl = new LinkedList<Vertex<Character>>(); tl.add(u); tl.add(w); tl.add(x);
+		List<Vertex<Character>> ul = new LinkedList<Vertex<Character>>(); ul.add(t); ul.add(x); ul.add(y);
+		List<Vertex<Character>> vl = new LinkedList<Vertex<Character>>(); vl.add(r); 
+		List<Vertex<Character>> wl = new LinkedList<Vertex<Character>>(); wl.add(s); wl.add(t); wl.add(x);
+		List<Vertex<Character>> xl = new LinkedList<Vertex<Character>>(); xl.add(t); xl.add(u); xl.add(y);
+		List<Vertex<Character>> yl = new LinkedList<Vertex<Character>>(); yl.add(u); yl.add(x);
+		Map<Vertex<Character>, List<Vertex<Character>>> g = new HashMap<Vertex<Character>, List<Vertex<Character>>>();
+		g.put(r, rl); g.put(s, sl); g.put(t, tl); g.put(u, ul); g.put(v, vl); g.put(w, wl); g.put(x, xl); g.put(y, yl);
+		System.out.println("=========== prac_22_2_2: After BFS: ==============");
+		bfs(g, s);
+		for(Vertex<Character> key: g.keySet())
+			System.out.println(key);
+	}
+
+	/**
+	 * practice 22.2-5
+	 */
+	public static void prac_22_2_5(){
+		//Graph of image 22-3(a).
+		Vertex<Character> r = new Vertex<Character>('r'), s = new Vertex<Character>('s'), t = new Vertex<Character>('t'), u = new Vertex<Character>('u'), v = new Vertex<Character>('v'), w = new Vertex<Character>('w'), x = new Vertex<Character>('x'), y = new Vertex<Character>('y');
+		List<Vertex<Character>> rl = new LinkedList<Vertex<Character>>(); rl.add(v); rl.add(s); 
+		List<Vertex<Character>> sl = new LinkedList<Vertex<Character>>(); sl.add(w); sl.add(r); 
+		List<Vertex<Character>> tl = new LinkedList<Vertex<Character>>(); tl.add(x); tl.add(w); tl.add(u);
+		List<Vertex<Character>> ul = new LinkedList<Vertex<Character>>(); ul.add(y); ul.add(x); ul.add(t); 
+		List<Vertex<Character>> vl = new LinkedList<Vertex<Character>>(); vl.add(r); 
+		List<Vertex<Character>> wl = new LinkedList<Vertex<Character>>(); wl.add(x); wl.add(t); wl.add(s); 
+		List<Vertex<Character>> xl = new LinkedList<Vertex<Character>>(); xl.add(y); xl.add(u); xl.add(t); 
+		List<Vertex<Character>> yl = new LinkedList<Vertex<Character>>(); yl.add(x); yl.add(u); 
+		Map<Vertex<Character>, List<Vertex<Character>>> g = new HashMap<Vertex<Character>, List<Vertex<Character>>>();
+		g.put(r, rl); g.put(s, sl); g.put(t, tl); g.put(u, ul); g.put(v, vl); g.put(w, wl); g.put(x, xl); g.put(y, yl);
+		System.out.println("=========== prac_22_2_5: After BFS: ==============");
+		bfs(g, s);
+		for(Vertex<Character> key: g.keySet())
+			System.out.println(key);
+	}
+
+	/**
+	 * BFS. p344.
+	 * @param grahp The graph.
+	 * @param s Source vertex.
+	 */
+	public static <E> void bfs(Map<Vertex<E>, List<Vertex<E>>> grahp, Vertex<E> s){
+		Queue<Vertex<E>> q = new LinkedList<Vertex<E>>();
+		s.color = COLOR.GREY;
+		q.offer(s);
+		while(!q.isEmpty()){
+			Vertex<E> v = q.poll();
+			List<Vertex<E>> neighbors = grahp.get(v);
+			for(Vertex<E> neighbor: neighbors){
+				if(neighbor.color == COLOR.WHITE){
+					q.offer(neighbor);
+					neighbor.π = v;
+					neighbor.d = v.d + 1;
+					neighbor.color = COLOR.GREY;
+				}
+			}
+			v.color = COLOR.BLACK;
+		}
+	}
+
+	public static void main(String[] args) {
+		prac_22_2_1();
+		prac_22_2_2();
+		prac_22_2_5();
+	}
+
+}
diff --git a/src/chap22_ElementaryGraphAlgo/Vertex.java b/src/chap22_ElementaryGraphAlgo/Vertex.java
@@ -0,0 +1,49 @@
+package chap22_ElementaryGraphAlgo;
+/**
+ * Vertex of graph. 160929
+ * Used by BFS, DSF, etc.
+ */
+public class Vertex<T> {
+	public T value;
+	public Vertex<T> π;
+	public int d;	//
+	public COLOR color;
+
+	public Vertex(T value){
+		this.value = value;
+		this.π = null;
+		this.d = 0;
+		this.color = COLOR.WHITE;
+	}
+
+	@Override
+	public String toString(){
+		if(π != null)
+			return "Vertex: " + value + ", d:" + d + ", π:" + π.value;
+		else
+			return "Vertex: " + value + ", d:" + d + ", π: null";
+
+	}
+
+	@Override
+	public boolean equals(Object obj){
+		if(obj == null)
+			return false;
+
+		if(!(obj instanceof Vertex))
+			return false;
+
+		@SuppressWarnings({ "rawtypes" })
+		Vertex o = (Vertex)obj;
+		return o.value == this.value;	//Assume value is unique in a Graph.
+	}
+
+	@Override
+	public int hashCode(){
+		int res = 17;
+		res = res * 31 + value.hashCode();
+		return res;
+	}
+}
+
+enum COLOR{WHITE, GREY, BLACK}