建议一种有效的方法来查找满足以下条件的堆中的最后位置：
1）通过指针而非通过数组
2）我们可以在哪里插入或删除节点
我可以在O（n）时间复杂度中找到它，但建议采用O（logn）或O（1）时间复杂度的方法。
答案 0 :(得分：2)
我在这里假设您的意思是二进制堆。
如果您知道堆中有多少个节点，则可以通过将计数转换为二进制，然后遵循从高到低的位路径，在O（log n）时间内找到最后一个节点。也就是说，如果该位为0则采用左侧节点，如果该位为1则采用右侧节点。
例如，如果堆中有三个节点，则计数的二进制表示为11.根始终是第一个节点，只剩下1。然后，您使用右分支获取最后一个节点。 / p>
假设堆中有5个节点：
(model
(define-fun z () (_ FloatingPoint 11 53)
(_ NaN 11 53))
(define-fun y () (_ FloatingPoint 11 53)
(fp #b0 #b00000000000 #x0000000004000))
(define-fun x () (_ FloatingPoint 11 53)
(_ +zero 11 53))
)
在二进制文件中，那就是101.所以你要扎根。下一个数字是0，所以你采取左分支。下一个数字是1，所以你选择正确的分支，留在节点5。
如果你想要下一个可用的插槽，你可以在计数中添加1并执行相同的操作。所以6将是110.你取根，然后是右分支，3的左子是你添加新节点的地方。
你可以对任何d-ary heap做同样的事情，除了转换为基数d而不是转换为二进制。因此，如果您的堆节点每个最多有三个子节点，那么您将计数转换为基数3，并使用与上面相同的逻辑。
另一种方法是维护对堆中最后一个节点的引用，每次修改堆时都要更新它。或者，如果您想知道下一个节点的放置位置，则保留对没有两个子节点的第一个节点的引用。那是O（1），但每次插入或删除时都需要记账。
答案 1 :(得分：1)
我正在回答我自己的问题，在插入堆（通过指针堆）时没有必要跟踪下一个指针，即使没有必要跟踪父，我附加运行java代码的堆，所有可能的方法都包含在其中，getMin（）= O（1），insert（）= O（logn），extractMin = O（logn），decreasePriorityOfHead = O（logn），我已经为通用代码实现了它，所以它会有助于理解通用概念。
class MinHeap<E extends Comparable<E>> {
private DoublyNode<E> root;
private int size = 0;
public DoublyNode<E> getRoot() {
return root;
}
public void setRoot(DoublyNode<E> root) {
this.root = root;
}
public int getSize() {
return size;
}
public void setSize(int size) {
this.size = size;
}
public MinHeap() {
}
public MinHeap(E data) {
this.root = new DoublyNode<E>(data);
this.size++;
}
private class NodeLevel<E extends Comparable<E>> {
private int level;
private DoublyNode<E> node;
public int getLevel() {
return level;
}
public void setLevel(int level) {
this.level = level;
}
public DoublyNode<E> getNode() {
return node;
}
public void setNode(DoublyNode<E> node) {
this.node = node;
}
public NodeLevel(DoublyNode<E> node, int level) {
this.node = node;
this.level = level;
}
}
public void insert(E data) {
if (this.size == 0) {
this.root = new DoublyNode<E>(data);
this.size++;
return;
}
DoublyNode<E> tempRoot = this.root;
Integer insertingElementPosition = this.size + 1;
char[] insertingElementArray = Integer.toBinaryString(
insertingElementPosition).toCharArray();
DoublyNode<E> newNode = new DoublyNode<E>(data);
int i;
for (i = 1; i < insertingElementArray.length - 1; i++) {
if (newNode.getData().compareTo(tempRoot.getData()) < 0) {
this.swap(newNode, tempRoot);
}
char c = insertingElementArray[i];
if (c == '0') {
tempRoot = tempRoot.getLeft();
} else {
tempRoot = tempRoot.getRight();
}
}
// newNode.setParent(tempRoot);
if (newNode.getData().compareTo(tempRoot.getData()) < 0) {
this.swap(newNode, tempRoot);
}
if (insertingElementArray[i] == '0') {
tempRoot.setLeft(newNode);
} else {
tempRoot.setRight(newNode);
}
this.size++;
}
public void swap(DoublyNode<E> node1, DoublyNode<E> node2) {
E temp = node1.getData();
node1.setData(node2.getData());
node2.setData(temp);
}
public E getMin() {
if (this.size == 0) {
return null;
}
return this.root.getData();
}
public void heapifyDownWord(DoublyNode<E> temp) {
if (temp == null) {
return;
}
DoublyNode<E> smallerChild = this.getSmallerChild(temp);
if (smallerChild == null) {
return;
}
if (smallerChild.getData().compareTo(temp.getData()) < 0) {
this.swap(temp, smallerChild);
this.heapifyDownWord(smallerChild);
}
}
public DoublyNode<E> getSmallerChild(DoublyNode<E> temp) {
if (temp.getLeft() != null && temp.getRight() != null) {
return (temp.getLeft().getData()
.compareTo(temp.getRight().getData()) < 0) ? temp.getLeft()
: temp.getRight();
} else if (temp.getLeft() != null) {
return temp.getLeft();
} else {
return temp.getRight();
}
}
public E extractMin() {
if (this.root == null) {
return null;
}
E temp = this.root.getData();
if (this.root.getLeft() == null && this.root.getRight() == null) {
this.root = null;
this.size--;
return temp;
}
DoublyNode<E> parentOfLastData = this.getParentOfLastData();
if (parentOfLastData.getRight() != null) {
this.root.setData(parentOfLastData.getRight().getData());
parentOfLastData.setRight(null);
} else {
this.root.setData(parentOfLastData.getLeft().getData());
parentOfLastData.setLeft(null);
}
this.heapifyDownWord(this.root);
return temp;
}
public DoublyNode<E> getParentOfLastData() {
if (this.size == 0) {
return null;
}
DoublyNode<E> tempRoot = this.root;
Integer insertingElementPosition = this.size;
char[] insertingElementArray = Integer.toBinaryString(
insertingElementPosition).toCharArray();
int i;
for (i = 1; i < insertingElementArray.length - 1; i++) {
char c = insertingElementArray[i];
if (c == '0') {
tempRoot = tempRoot.getLeft();
} else {
tempRoot = tempRoot.getRight();
}
}
return tempRoot;
}
public DoublyNode<E> getParentOfLastEmptyPosition() {
if (this.size == 0) {
return null;
}
DoublyNode<E> tempRoot = this.root;
Integer insertingElementPosition = this.size + 1;
char[] insertingElementArray = Integer.toBinaryString(
insertingElementPosition).toCharArray();
System.out.println(insertingElementArray.toString());
int i;
for (i = 1; i < insertingElementArray.length - 1; i++) {
char c = insertingElementArray[i];
if (c == '0') {
tempRoot = tempRoot.getLeft();
} else {
tempRoot = tempRoot.getRight();
}
}
return tempRoot;
}
public void print() {
if (this.root == null) {
System.out.println("Heap via pointer is empty!");
return;
}
System.out.println("\n Heap via pointer is:- ");
Queue<NodeLevel<E>> dataQueue = new Queue<NodeLevel<E>>();
Queue<Space> spaceQueue = new Queue<Space>();
dataQueue.enQueue(new NodeLevel<E>(this.root, 1));
int heightOfTree = this.getHeightOfHeap();
Double powerHeghtBST = Math.pow(heightOfTree, 2);
spaceQueue.enQueue(new Space(powerHeghtBST.intValue(), false));
while (!dataQueue.isEmpty()) {
Space space = spaceQueue.deQueue();
NodeLevel<E> nodeLevel = dataQueue.deQueue();
while (space.isNullSpace()) {
space.printNullSpace();
spaceQueue.enQueue(space);
space = spaceQueue.deQueue();
}
space.printFrontSpace();
System.out.print(nodeLevel.getNode().getData().printingData());
space.printBackSpace();
if (nodeLevel.getNode().getLeft() != null) {
dataQueue.enQueue(new NodeLevel<E>(nodeLevel.getNode()
.getLeft(), nodeLevel.getLevel() + 1));
spaceQueue.enQueue(new Space(space.getSpaceSize() / 2, false));
} else {
spaceQueue.enQueue(new Space(space.getSpaceSize() / 2, true));
}
if (nodeLevel.getNode().getRight() != null) {
dataQueue.enQueue(new NodeLevel<E>(nodeLevel.getNode()
.getRight(), nodeLevel.getLevel() + 1));
spaceQueue.enQueue(new Space(space.getSpaceSize() / 2, false));
} else {
spaceQueue.enQueue(new Space(space.getSpaceSize() / 2, true));
}
if (!dataQueue.isEmpty()
&& nodeLevel.getLevel() + 1 == dataQueue.getFrontData()
.getLevel()) {
System.out.println("\n");
}
}
}
public int getHeightOfHeap() {
if (this.size == 0) {
return 0;
}
Double height = Math.log(this.size) / Math.log(2) + 1;
return height.intValue();
}
public void changePriorityOfHeapTop(E data) {
if (this.root == null) {
return;
}
this.root.setData(data);
this.heapifyDownWord(this.root);
}
}
interface Comparable<T> extends java.lang.Comparable<T> {
/**
* this methos returns a string of that data which to be shown during
* printing tree
*
* @return
*/
public String printingData();
}
public class PracticeMainClass {
public static void main(String[] args) {
MinHeap<Student> minHeap1 = new MinHeap<Student>();
minHeap1.insert(new Student(50, "a"));
minHeap1.insert(new Student(20, "a"));
minHeap1.insert(new Student(60, "a"));
minHeap1.insert(new Student(30, "a"));
minHeap1.insert(new Student(40, "a"));
minHeap1.insert(new Student(70, "a"));
minHeap1.insert(new Student(10, "a"));
minHeap1.insert(new Student(55, "a"));
minHeap1.insert(new Student(35, "a"));
minHeap1.insert(new Student(45, "a"));
minHeap1.print();
minHeap1.getMin();
minHeap1.print();
System.out
.println("\nminimum is:- " + minHeap1.getMin().printingData());
minHeap1.print();
System.out.println("\nminimum is:- "
+ minHeap1.extractMin().printingData());
minHeap1.print();
minHeap1.changePriorityOfHeapTop(new Student(75, "a"));
minHeap1.print();
}
}
class DoublyNode<E extends Comparable<E>> {
private E data;
private DoublyNode<E> left;
private DoublyNode<E> right;
// private DoublyNode<E> parent;
public DoublyNode() {
}
public DoublyNode(E data) {
this.data = data;
}
public E getData() {
return data;
}
public void setData(E data) {
this.data = data;
}
public DoublyNode<E> getLeft() {
return left;
}
public void setLeft(DoublyNode<E> left) {
this.left = left;
}
public DoublyNode<E> getRight() {
return right;
}
public void setRight(DoublyNode<E> right) {
this.right = right;
}
// public DoublyNode<E> getParent() {
// return parent;
// }
// public void setParent(DoublyNode<E> parent) {
// this.parent = parent;
// }
}
class Space {
private boolean isNullSpace = false;
private String frontSpace;
private String backSpace;
private String nullSpace;
private int spaceSize;
public boolean isNullSpace() {
return isNullSpace;
}
public void setNullSpace(boolean isNullSpace) {
this.isNullSpace = isNullSpace;
}
public int getSpaceSize() {
return spaceSize;
}
public void setSpaceSize(int spaceSize) {
this.spaceSize = spaceSize;
}
public Space(int spaceSize, boolean isNullSpace) {
this.isNullSpace = isNullSpace;
this.spaceSize = spaceSize;
if (spaceSize == 0) {
this.frontSpace = "";
this.backSpace = "";
this.nullSpace = " ";
} else if (spaceSize == 1) {
this.frontSpace = " ";
this.backSpace = "";
this.nullSpace = " ";
} else if (spaceSize == 2) {
this.frontSpace = " ";
this.backSpace = "";
this.nullSpace = " ";
} else {
this.frontSpace = String.format("%" + (spaceSize) + "s", " ");
this.backSpace = String.format("%" + (spaceSize - 2) + "s", " ");
this.nullSpace = String.format("%" + 2 * (spaceSize) + "s", " ");
}
}
public void printFrontSpace() {
System.out.print(this.frontSpace);
}
public void printBackSpace() {
System.out.print(this.backSpace);
}
public void printNullSpace() {
System.out.print(this.nullSpace);
}
}
class Queue<E> {
private Node<E> front;
private Node<E> rear;
private int queueSize = 0;
public Queue() {
}
public Queue(E data) {
this.front = new Node(data);
this.rear = this.front;
}
public void enQueue(E data) {
if (this.rear == null) {
this.rear = new Node(data);
this.front = this.rear;
} else {
Node newNode = new Node(data);
this.rear.setNext(newNode);
this.rear = newNode;
}
this.queueSize++;
}
public E deQueue() {
E returnValue;
if (this.front == null) {
return null;
} else if (this.front == this.rear) {
returnValue = this.front.getData();
this.front = null;
this.rear = null;
} else {
returnValue = this.front.getData();
this.front = this.front.getNext();
}
this.queueSize--;
return returnValue;
}
public void print() {
Node temp = this.front;
System.out.print("\n Queue is:- ");
if (temp == null) {
System.out.println(" Empty! ");
}
while (temp != null) {
System.out.print(temp.getData() + ",");
temp = temp.getNext();
}
}
public int getQueueSize() {
return queueSize;
}
public E getFrontData() {
if (this.front == null) {
System.out.println("queue is empty!");
return null;
}
return this.front.getData();
}
public E getRearData() {
if (this.rear == null) {
System.out.println("queue is empty!");
return null;
}
return this.rear.getData();
}
public boolean isEmpty() {
return this.front == null;
}
}
class Node<E> {
private E data;
private Node next;
public Node(E data) {
this.data = data;
}
public E getData() {
return data;
}
public void setData(E data) {
this.data = data;
}
public Node getNext() {
return next;
}
public void setNext(Node next) {
this.next = next;
}
}
class Student implements Comparable<Student> {
private int id;
private String name;
@Override
public int compareTo(Student student) {
if (this.id == student.id) {
return 0;
} else if (this.id < student.id) {
return -1;
} else {
return 1;
}
}
public Student(int id, String name) {
this.id = id;
this.name = name;
}
public int getId() {
return id;
}
public void setId(int id) {
this.id = id;
}
public String getName() {
return name;
}
public void setName(String name) {
this.name = name;
}
@Override
public String printingData() {
// String printingData = "{ id: "+this.id+" name: "+this.name+" }";
String printingData = String.valueOf(this.id);
return printingData;
}
}
此代码的输出为： -
Heap via pointer is:-
10
30 20
35 40 70 60
55 50 45
Heap via pointer is:-
10
30 20
35 40 70 60
55 50 45
minimum is:- 10
Heap via pointer is:-
10
30 20
35 40 70 60
55 50 45
minimum is:- 10
Heap via pointer is:-
20
30 45
35 40 70 60
55 50
Heap via pointer is:-
30
35 45
50 40 70 60
55 75