算法导论 O(n)时间内反转单链表

算法导论 O(n)时间内反转单链表

1. 算法导论原题

Give a O(n) time nonrecursive procedure that reverses a singly linked list of n elements. The procedure should use no more than constant storage beyond that needed for thelist itself.
译：实现一个时间复杂度为O(n)的非递归过程反转一个有n个元素的单链表。这个过程应该使用常量的储存空间（除了链表本身）。

2. 如何在O(n)时间内反转单链表？

由于是单链表，想要在O(n)时间内反转单链表，就不可能遍历整个链表到后面的结点来跟前面结点交换数据。因此我们能做的，就是改变链表每一个结点的指针指向为前一个结点。我们需要用三个结点的储存空间：上一个结点、当前结点、下一个结点。首先将当前结点的下一个结点保存（因为下一步要改变当前结点的下一个结点），然后将当前结点指向上一个结点，再将当前结点保存到上一个结点，最后将当前结点移动到刚刚保存的下一个结点。题目没有说是用循环单链表，但是循环单链表和普通单链表它们的存储空间和O(n)时间内反转实现原理是一样的，所以我这里直接用循环单链表就行了。

3. 主要代码实现（C++）

template<typename ElemType>bool CircularSinglyLink<ElemType>::Reverse(){    Node<ElemType>* pPrevNode = m_pHeadNode;    Node<ElemType>* pCurrentNode = m_pHeadNode->GetNext();     while(pCurrentNode != m_pHeadNode)    {        Node<ElemType>* nextNode = pCurrentNode->GetNext();        pCurrentNode->SetNext(pPrevNode);        pPrevNode = pCurrentNode;        pCurrentNode = nextNode;    }    m_pHeadNode->SetNext(pPrevNode);    return true;}

4. 完整代码实现（C++）

//CircularSinglyLink.h#pragma once#include <assert.h>#include <stdio.h>template<typename ElemType>class Node{public:    Node(Node<ElemType>* pNext = NULL, ElemType* pData = NULL);    ElemType const& GetData() const;    void SetData(ElemType val) ;    Node<ElemType>* const& GetNext() const;    void SetNext(Node<ElemType>* val);private:    ElemType* m_pData;    Node<ElemType>* m_pNext;};template<typename ElemType>class CircularSinglyLink{public:    CircularSinglyLink();    unsigned int const& GetLength() const;    bool Insert(ElemType elem, unsigned int pos);    bool InsertByPosNode(ElemType elem, Node<ElemType>* posNode, Node<ElemType>** RetInsetNode = NULL);    bool Delete(unsigned int pos, ElemType* elem);    bool Search(unsigned int pos, ElemType* elem) const;    bool Visit(ElemType* elem, const unsigned int& pos) const;    bool Empty();    Node<ElemType>* HavaHeadNode();    bool Reverse();private:    Node<ElemType>* m_pHeadNode;    unsigned int m_length;};//————————————————————————————————//Node类的实现template<typename ElemType>Node<ElemType>::Node(Node<ElemType>* pNext /*= NULL*/, ElemType* pData /*= NULL*/)    :m_pNext(pNext),m_pData(pData){}template<typename ElemType>void Node<ElemType>::SetNext(Node<ElemType>* val){    m_pNext = val;}template<typename ElemType>Node<ElemType>* const& Node<ElemType>::GetNext() const{    return m_pNext;}template<typename ElemType>void Node<ElemType>::SetData(ElemType val){    m_pData = val;}template<typename ElemType>ElemType const& Node<ElemType>::GetData() const{    return *m_pData;}//————————————————————————————————//CircularSinglyLink类实现template<typename ElemType>CircularSinglyLink<ElemType>::CircularSinglyLink()    :m_pHeadNode(new Node<ElemType>()),m_length(0){    m_pHeadNode->SetNext(m_pHeadNode);}template<typename ElemType>bool CircularSinglyLink<ElemType>::InsertByPosNode(ElemType elem, Node<ElemType>* posNode, Node<ElemType>** RetInsetNode /*= NULL*/){    Node<ElemType>* insertNode = new Node<ElemType>(posNode->GetNext(),new ElemType(elem));    posNode->SetNext(insertNode);    ++m_length;    *RetInsetNode = insertNode;    return true;}template<typename ElemType>bool CircularSinglyLink<ElemType>::Insert(ElemType elem, unsigned int pos){    if (pos > GetLength() || pos < 0)    {        assert(false && "Error: SinglyLink's insert pos is out of range!\n");        return false;    }    for(Node<ElemType>* pCurrentNode = m_pHeadNode; pCurrentNode != NULL; pCurrentNode = pCurrentNode->GetNext())    {        if (pos-- == 0)        {            Node<ElemType>* insertNode = new Node<ElemType>(pCurrentNode->GetNext(),new ElemType(elem));            pCurrentNode->SetNext(insertNode);            ++m_length;            return true;        }    }    assert(false && "Error: SinglyLink Insert failed for unknow reason!");    return false;}template<typename ElemType>bool CircularSinglyLink<ElemType>::Delete(unsigned int pos, ElemType* elem){    if (pos >= GetLength() || pos < 0)    {        assert(false && "Error: SinglyLink's delete pos is out of range!\n");    }    for(Node<ElemType>* pCurrentNode = m_pHeadNode; pCurrentNode != NULL; pCurrentNode = pCurrentNode->GetNext())    {        if (pos-- == 0)        {            Node<ElemType>* deleteNode = pCurrentNode->GetNext();            pCurrentNode->SetNext(deleteNode->GetNext());            *elem = deleteNode->GetData();            delete deleteNode;            --m_length;            return true;        }    }    assert(false && "Error: SinglyLink pos delete failed for unknow reason!");    return false;}template<typename ElemType>unsigned int const& CircularSinglyLink<ElemType>::GetLength() const{    return m_length;}template<typename ElemType>bool CircularSinglyLink<ElemType>::Search(unsigned int pos, ElemType* elem) const{    if (pos >= GetLength() || pos < 0)    {        assert(false && "Error: SinglyLink's search pos is out of range!\n");    }    for(Node<ElemType>* pCurrentNode = m_pHeadNode; pCurrentNode != NULL; pCurrentNode = pCurrentNode->GetNext())    {        if (pos-- == 0 && (pCurrentNode->GetNext() != NULL) )        {            *elem = pCurrentNode->GetNext()->GetData();            return true;        }    }    return false;}template<typename ElemType>bool CircularSinglyLink<ElemType>::Visit(ElemType* elem, const unsigned int& pos) const{    if (pos >= GetLength() || pos < 0)    {        return false;    }    return Search(pos,elem);}template<typename ElemType>bool CircularSinglyLink<ElemType>::Empty(){    return !m_length;}template<typename ElemType>Node<ElemType>* CircularSinglyLink<ElemType>::HavaHeadNode(){    return m_pHeadNode;}template<typename ElemType>bool CircularSinglyLink<ElemType>::Reverse(){    Node<ElemType>* pPrevNode = m_pHeadNode;    Node<ElemType>* pCurrentNode = m_pHeadNode->GetNext();     while(pCurrentNode != m_pHeadNode)    {        Node<ElemType>* nextNode = pCurrentNode->GetNext();        pCurrentNode->SetNext(pPrevNode);        pPrevNode = pCurrentNode;        pCurrentNode = nextNode;    }    m_pHeadNode->SetNext(pPrevNode);    return true;}

//Util.h#pragma oncenamespace Util{    template<typename T>    void PrintMemory(const T& dateStruct, unsigned int size)    {        cout << "PrintMemory: ";        for (int i = 0; i != size; i++)        {            ElemType tempElem;            if (!dateStruct.Visit(&tempElem,i))            {                printf("\n");                return;            }            printf("%d ",tempElem);        }        printf("\n");    }}

//main.cpp#include "Util.h"#include "CircularSinglyLink.h"#include <iostream>using namespace std;typedef int ElemType;int main(){    CircularSinglyLink<int> testCircularSinglyLink;    for (int i = 0; i != 5; i++)    {        testCircularSinglyLink.Insert(i+1,i);    }    cout << "testCircularSinglyLink:\n";    Util::PrintMemory(testCircularSinglyLink,testCircularSinglyLink.GetLength());    cout << "\nReverse testCircularSinglyLink...\n";    testCircularSinglyLink.Reverse();    cout << "\ntestCircularSinglyLink:\n";    Util::PrintMemory(testCircularSinglyLink,testCircularSinglyLink.GetLength());    return 0;}

5. 程序运行结果

testCircularSinglyLink:
PrintMemory: 1 2 3 4 5

Reverse testCircularSinglyLink…

testCircularSinglyLink:
PrintMemory: 5 4 3 2 1