update 22.1

Chapter22_ElementaryGraphAlgorithms.md

@@ -27,8 +27,8 @@ in-degree:O(V+E)
 2. 遍历旧表的每个顶点a的Adj[a]。  
 3. 每遍历到一个顶点b，往Adj[b]的尾部插入a，如果a!=b且a不在Adj[b]里出现过。  
 
-### 22.1-5 The **square** of a directed graph G=(V,E) is the graph G2 =(V,E2) such that (u,w) in E2 if and only if for some v in V, both(u,v) in E and(v,w) in E.That is,G2 contains an edge between u and w whenever G contains a path with exactly two edges between u and w. Describe efficient algorithms for computing G2 from G for both the adjacency-list and adjacency-matrix representations of G. Analyze the running times of your algorithms.  
-
+### 22.1-5 有向图G = (V, E)的**平方图**是图G2 = (V, E2)，该图满足下列条件：(u, w)属于E2当且仅当v属于V，有(u, v)属于E，且(v, w)属于E。亦即，如果图G中顶点u和w之间存在着一条恰包含两条边的路径时，则G2必包含该边(u, w)。针对图G邻接表和邻接矩阵两种表示，分别写出根据G产生G2的有效算法，并分析所给出算法的运行时间。  
+见[代码](https://github.com/zhuxiuwei/CLRS/blob/master/src/chap22_ElementaryGraphAlgo/Prac22_1_5_SquareGraph.java)  
 
 
 

src/chap22_ElementaryGraphAlgo/Prac22_1_5_SquareGraph.java

@@ -0,0 +1,61 @@
+package chap22_ElementaryGraphAlgo;
+
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+
+/**
+ * 161018
+ * @author xiuzhu
+ * 22.1-5 有向图G = (V, E)的**平方图**是图G2 = (V, E2)，该图满足下列条件：(u, w)属于E2当且仅当v属于V，有(u, v)属于E，且(v, w)属于E。
+ * 亦即，如果图G中顶点u和w之间存在着一条恰包含两条边的路径时，则G2必包含该边(u, w)。针对图G邻接表和邻接矩阵两种表示，分别写出根据G产生G2的有效算法，并分析所给出算法的运行时间。  
+ */
+public class Prac22_1_5_SquareGraph {
+
+	/**
+	 * @param g 有向图G的邻接矩阵表示. O(V^3)
+	 * @return 平方图G2的邻接矩阵表示
+	 */
+	public int[][] transform(int[][] g){
+		if(g == null)
+			return null;
+
+		int[][] g2 = new int[g.length][g.length];
+		for (int i = 0; i < g.length; i++) {
+			for (int j = 0; j < g.length; j++) {
+				if(g[j][i] == 1){
+					for (int k = 0; k < g.length; k++) {
+						if(g[i][k] == 1)
+							g2[j][k] = 1;
+					}
+				}
+			}
+		}
+		return g2;
+	}
+
+	/**
+	 * @param g 有向图G的邻接表表示
+	 * @return 平方图G2的邻接表表示
+	 */
+	public Map<Integer, List<Integer>> transform(Map<Integer, List<Integer>> g){
+		if(g == null)
+			return null;
+
+		Map<Integer, List<Integer>> g2 = new HashMap<Integer, List<Integer>>();
+
+		for (Integer k: g.keySet()) {
+			List<Integer> neighbors = g.get(k);
+
+		}
+		return g2;
+	}
+
+	public static void main(String[] args) {
+		Prac22_1_5_SquareGraph p = new Prac22_1_5_SquareGraph();
+		System.out.println(Arrays.deepToString(p.transform(new int[][]{{0,1,1},{0,0,1},{0,0,0}})));
+		System.out.println(Arrays.deepToString(p.transform(new int[][]{{0,1,1},{0,0,1},{1,0,0}})));
+	}
+
+}