数据结构与算法-第12章二叉树和其他树-004求二叉树的最多结点数及对应的层数

 1 package chapter12Tree;
 2 
 3 import dataStructures.ArrayQueue;
 4 
 5 //We perform a level-order traversal. To differentiate among nodes at different levels,
 6 //we use a unique pointer which serves as an end of level marker. 
 7 //This pointer is added to the level order queue following the last node at each level. 
 8 //As nodes are removed from the queue, a counter is incremented until the end of level 
 9 //marker is removed. This strategy enables us to determine the number of nodes 
10 //in a level. The code is given below.
11 public class BinaryTreeMaxLevel
12 {
13    /** @return level with max umber of nodes */
14    public static int maxLevel(BinaryTreeNode t)
15    {
16       if (t == null)
17          // tree is empty
18          return 0;
19 
20       // maxLevel is current level with max nodes
21       // maxNodes is number of nodes on level maxLevel
22       int maxLevel = 0;
23       int maxNodes = 0;
24       
25       // create a unique pointer to use an end of level marker in queue
26       BinaryTreeNode endOfLevel = new BinaryTreeNode();
27    
28       // put t and endOfLevel marker on queue q
29       ArrayQueue q = new ArrayQueue();
30       q.put(t);
31       q.put(endOfLevel);
32 
33       // do a level order traversal
34       int currentLevel = 1;    // level of nodes being examined
35       int numOfNodes = 0;      // number of nodes seen of currentLevel
36       while (true) 
37       {
38          BinaryTreeNode p = (BinaryTreeNode) q.remove();
39          if (p == endOfLevel)
40          {
41             // see if currentLevel has more nodes than MaxLevel
42             if (numOfNodes > maxNodes)
43             {// found a level with more nodes
44                maxNodes = numOfNodes;
45                 maxLevel = currentLevel;
46             }
47             else
48                if (numOfNodes == 0)
49                   // empty level, no more nodes
50                   return maxLevel;
51 
52             // set currentLevel and numOfNodes to start new level
53             currentLevel++;
54             numOfNodes = 0;
55 
56             q.put(endOfLevel);
57          }
58          else
59          {// continuation of current level
60             numOfNodes++;
61 
62             // put p‘s children on queue
63             if (p.leftChild != null) 
64                q.put(p.leftChild);
65             if (p.rightChild != null)
66                q.put(p.rightChild);
67          }
68       }
69     }
70 }

  1 /** a queue class that uses a one-dimensional array */
  2 
  3 package dataStructures;
  4 
  5 public class ArrayQueue implements Queue
  6 {
  7    // data members
  8    int front;          // one counterclockwise from first element
  9    int rear;           // position of rear element of queue
 10    Object [] queue;    // element array
 11 
 12    // constructors
 13    /** create a queue with the given initial capacity */
 14    public ArrayQueue(int initialCapacity)
 15    {
 16       if (initialCapacity < 1)
 17          throw new IllegalArgumentException
 18                ("initialCapacity must be >= 1");
 19       queue = new Object [initialCapacity + 1];
 20       // default front = rear = 0
 21    }
 22 
 23    /** create a queue with initial capacity 10 */
 24    public ArrayQueue()
 25    {// use default capacity of 10
 26       this(10);
 27    }
 28 
 29    // methods
 30    /** @return true iff queue is empty */
 31    public boolean isEmpty()
 32       {return front == rear;}
 33 
 34 
 35    /** @return front element of queue
 36      * @return null if queue is empty */
 37    public Object getFrontElement()
 38    {
 39       if (isEmpty())
 40          return null;
 41       else
 42          return queue[(front + 1) % queue.length];
 43    }
 44 
 45    /** @return rear element of queue
 46      * @return null if the queue is empty */
 47    public Object getRearElement()
 48    {
 49       if (isEmpty())
 50          return null;
 51       else
 52          return queue[rear];
 53    }
 54 
 55    /** insert theElement at the rear of the queue */
 56    public void put(Object theElement)
 57    {
 58       // increase array length if necessary
 59       if ((rear + 1) % queue.length == front)
 60       {// double array size
 61          // allocate a new array
 62          Object [] newQueue = new Object [2 * queue.length];
 63 
 64          // copy elements into new array
 65          int start = (front + 1) % queue.length;
 66          if (start < 2)
 67             // no wrap around
 68             System.arraycopy(queue, start, newQueue, 0,
 69                              queue.length - 1);
 70          else
 71          {  // queue wraps around
 72             System.arraycopy(queue, start, newQueue, 0,
 73                              queue.length - start);
 74             System.arraycopy(queue, 0, newQueue,
 75                              queue.length - start, rear + 1);
 76          }
 77 
 78          // switch to newQueue and set front and rear
 79          front = newQueue.length - 1;
 80          rear = queue.length - 2;   // queue size is queue.length - 1
 81          queue = newQueue;
 82       }
 83 
 84       // put theElement at the rear of the queue
 85       rear = (rear + 1) % queue.length;
 86       queue[rear] = theElement;
 87    }
 88 
 89    /** remove an element from the front of the queue
 90      * @return removed element
 91      * @return null if the queue is empty */
 92    public Object remove()
 93    {
 94       if (isEmpty())
 95          return null;
 96       front = (front + 1) % queue.length;
 97       Object frontElement = queue[front];
 98       queue[front] = null;   // enable garbage collection
 99       return frontElement;
100    }
101    
102    /** test program */
103    public static void main(String [] args)
104    {  
105       int x;
106       ArrayQueue q = new ArrayQueue(3);
107       // add a few elements
108       q.put(new Integer(1));
109       q.put(new Integer(2));
110       q.put(new Integer(3));
111       q.put(new Integer(4));
112 
113       // remove and add to test wraparound array doubling
114       q.remove();
115       q.remove();
116       q.put(new Integer(5));
117       q.put(new Integer(6));
118       q.put(new Integer(7));
119       q.put(new Integer(8));
120       q.put(new Integer(9));
121       q.put(new Integer(10));
122       q.put(new Integer(11));
123       q.put(new Integer(12));
124 
125       // delete all elements
126       while (!q.isEmpty())
127       {
128          System.out.println("Rear element is " + q.getRearElement());
129          System.out.println("Front element is " + q.getFrontElement());
130          System.out.println("Removed the element " + q.remove());
131       }
132    }  
133 }