# CSC301: Week 7: Undirected Graphs (4.1)

 Contents [0/9]

 Homework [1/9] Tree print prefix [2/9] Prefix-order is depth-first [3/9] Prefix order with loop [4/9] Level-order is breadth-first [5/9] General trees [6/9] Natural style is cautious [7/9] Over graphs [8/9] Iterative DFS contrasted with BFS [9/9]

 Homework [1/9]

Read through section 4.2 of the text.

For homework, complete the following, using only Graph and GraphGenerator from algs41. You may copy code from other classes in algs41, but you should not use the classes themselves.

In particular, you may not use BreadthFirstPaths although you may copy code from there.

The eccentricity of a vertex v is the length of the shortest path from that vertex to the furthest vertex from v. The diameter of a graph is the maximum eccentricity of any vertex. The radius of a graph is the smallest eccentricity of any vertex. A center is a vertex whose eccentricity is the radius. Implement the following API. (See the starter code on D2L.)

```public class MyGraphProperties {
// constructor (exception if G not connected)
MyGraphProperties(Graph G) {
}

// eccentricity of v
int eccentricity(int v) {  }

// diameter of G
int diameter() {  }

// a center of G --- any one will do
int center() {  }
}
```

 Tree print prefix [2/9]

 ``` // recursive version public void printPre () { printPre (root); StdOut.println (); } private static void printPre (Node x) { if (x == null) return; StdOut.print (x.key + " "); printPre (x.left); printPre (x.right); }``` ``` // iterative version public void printPre () { Stack s = new Stack<> (); s.push (root); while (!s.isEmpty ()) { Node x = s.pop (); if (x == null) continue; StdOut.print (x.key + " "); s.push (x.right); s.push (x.left); } StdOut.println (); }```

 Prefix-order is depth-first [3/9]

 ``` // prefix traversal of tree public void printPre () { printPre (root); StdOut.println (); } private static void printPre (Node x) { if (x == null) return; StdOut.print (x.key + " "); printPre (x.left); printPre (x.right); }``` ``` // depth first traversal of graph // mark when visiting public void printPre () { printPre (root, new HashSet()); StdOut.println (); } private static void printPre (Node x, HashSet marked) { if (x == null || marked.contains (x)) return; marked.add (x); StdOut.print (x.key + " "); printPre (x.left, marked); printPre (x.right, marked); }```

 Prefix order with loop [4/9]

 ``` // prefix order traversal of a tree public void printPrefix () { Stack s = new Stack<> (); s.push (root); while (!s.isEmpty ()) { Node x = s.pop (); if (x == null) continue; StdOut.print (x.key + " "); s.push (x.right); s.push (x.left); } StdOut.println (); }``` ``` // depth first traversal of a graph // mark when enqueuing public void printPrefix () { Stack s = new Stack<> (); HashSet marked = new HashSet<> (); s.push (root); marked.add (root); while (!s.isEmpty ()) { Node x = s.pop (); if (x == null || marked.contains (x)) continue; StdOut.print (x.key + " "); s.push (x.right); marked.add (x.right) s.push (x.left); marked.add (x.left) } StdOut.println (); }```

 ``` // level order traversal of a tree public void printLevel () { Queue q = new Queue<> (); q.enqueue (root); while (!q.isEmpty ()) { Node x = q.dequeue (); if (x == null) continue; StdOut.print (x.key + " "); q.enqueue (x.left); q.enqueue (x.right); } StdOut.println (); }``` ``` // breadth first traversal of a graph // mark when enqueuing public void printLevel () { Queue q = new Queue<> (); HashSet marked = new HashSet<> (); q.enqueue (root); marked.add (root); while (!q.isEmpty ()) { Node x = q.dequeue (); if (x == null || marked.contains (x)) continue; StdOut.print (x.key + " "); q.enqueue (x.left); marked.add (x.left) q.enqueue (x.right); marked.add (x.right) } StdOut.println (); }```

 General trees [6/9]

To get closer to the code for graphs, consider general trees, such as the following.

 file:XTree.java [source] [doc-public] [doc-private]
 ``` 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 ``` ```package algs32; import java.util.Scanner; import algs13.Queue; import stdlib.*; public class XTree { private Node root; private XTree (Node root) { this.root = root; } private static class Node { public final int val; public final Queue children; // children must not be null public Node (int val) { this.val = val; this.children = new Queue<>(); } } // tree input has the form "num ( ... )" // where num is an integer and ... is another tree input // example: "0 ( 1 ( 11 12 13 ) 2 ( 21 22 ( 221 222 223 ) ) 3 ( ) 4 )" // empty parens "( )" are optional. public static XTree parse (String in) { Scanner sc = new Scanner (in); Node root = parseHelper (sc); return new XTree (root); } private static Node parseHelper (Scanner sc) { int val = sc.nextInt (); Node result = new Node (val); if (sc.hasNext ("\\(")) { sc.next (); // gobble "(" while (sc.hasNextInt ()) { Node child = parseHelper (sc); result.children.enqueue (child); } sc.next ("\\)"); //gobble ")" } return result; } // prefix with parenthesis public String toString() { StringBuilder sb = new StringBuilder(); if (root != null) toString (sb, root); return sb.toString (); } private static void toString (StringBuilder sb, Node n) { sb.append (n.val); sb.append (" "); if (!n.children.isEmpty ()) { sb.append ("( "); for (Node child : n.children) toString (sb, child); sb.append (") "); } } public void toGraphviz(String filename) { GraphvizBuilder gb = new GraphvizBuilder (); if (root != null) toGraphviz (gb, null, root); gb.toFileUndirected (filename, "ordering=\"out\""); } private static void toGraphviz (GraphvizBuilder gb, Node parent, Node n) { gb.addLabeledNode (n, Integer.toString (n.val)); if (parent != null) gb.addEdge (parent, n); for (Node child : n.children) toGraphviz (gb, n, child); } // prefix order traversal public void printPre () { if (root != null) printPre (root); StdOut.println (); } private static void printPre (Node n) { StdOut.print (n.val + " "); for (Node child : n.children) { printPre (child); } } // level order traversal public void printLevel () { Queue queue = new Queue<>(); if (root != null) queue.enqueue(root); while (!queue.isEmpty()) { Node n = queue.dequeue(); StdOut.print (n.val + " "); for (Node child : n.children) { queue.enqueue(child); } } StdOut.println (); } public static void main(String[] args) { XTree xtree = XTree.parse ("0 ( 1 ( 11 12 ( 121 ( 1211 1212 ) 122 123 124 125 ) 13 ) 2 ( 21 22 ( 221 222 223 ) ) 3 )"); StdOut.println (xtree); xtree.printPre (); xtree.printLevel (); xtree.toGraphviz ("xtree.png"); } } ```

 Natural style is cautious [7/9]

 ``` // prefix order traversal public void printPre () { if (root != null) printPre (root); StdOut.println (); } private static void printPre (Node n) { StdOut.print (n.val + " "); for (Node child : n.children) { printPre (child); } }``` ``` // level order traversal public void printLevel () { Queue queue = new Queue<>(); if (root != null) queue.enqueue(root); while (!queue.isEmpty()) { Node n = queue.dequeue(); StdOut.print (n.val + " "); for (Node child : n.children) { queue.enqueue(child); } } StdOut.println (); }```

Since there are a variable number of children, it makes sense to disallow null children.

Only the root can be null.

Cautious stye is natural here, since we do not need to check nullity except at the root.

 Over graphs [8/9]

 ``` // TREE code // prefix order traversal public void printPre () { if (root != null) printPre (root); StdOut.println (); } private static void printPre (Node n) { StdOut.print (n.val + " "); for (Node child : n.children) { printPre (child, marked); } } // level order traversal public void printLevel () { Queue queue = new Queue<>(); if (root != null) queue.enqueue(root); while (!queue.isEmpty()) { Node n = queue.dequeue(); StdOut.print (n.val + " "); for (Node child : n.children) { queue.enqueue(child); } } StdOut.println (); } }``` ``` // GRAPH code // preorder traversal public void printPre () { if (root != null) printPre (root, new HashSet ()); StdOut.println (); } private static void printPre (Node n, HashSet marked) { StdOut.print (n.val + " "); marked.add (n); for (Node child : n.children) { if (!marked.contains (child)) printPre (child, marked); } } // level order traversal public void printLevel () { Queue queue = new Queue<> (); HashSet marked = new HashSet<> (); if (root != null) { queue.enqueue(root); marked.add (root); } while (!queue.isEmpty()) { Node n = queue.dequeue(); StdOut.print (n.val + " "); for (Node child : n.children) { if (!marked.contains (child)) { queue.enqueue(child); marked.add (n); } } } StdOut.println (); }```

 Iterative DFS contrasted with BFS [9/9]

 ```// DFS -- mark when pushing public void printPre () { Stack stack = new Stack<> (); HashSet marked = new HashSet<> (); if (root != null) { stack.push (root); marked.add (root); } while (!stack.isEmpty()) { Node n = stack.pop (); StdOut.print (n.val + " "); for (Node child : n.children) { if (!marked.contains (child)) { stack.push (child); marked.add (n); } } } StdOut.println (); }``` ``` // BFS -- mark when enqueuing public void printLevel () { Queue queue = new Queue<> (); HashSet marked = new HashSet<> (); if (root != null) { queue.enqueue (root); marked.add (root); } while (!queue.isEmpty()) { Node n = queue.dequeue(); StdOut.print (n.val + " "); for (Node child : n.children) { if (!marked.contains (child)) { queue.enqueue (child); marked.add (n); } } } StdOut.println (); }```

Revised: 2008/03/17 13:01