数据结构-有序链表的合并

1：已知两个链表head1和head2各自有序，请把它们合并成一个链表，依然有序。使用非递归方法以及递归方法。

2：首先介绍非递归方法。局部引用方法：这种方法避免使用虚拟节点(dummy node)，而是使用一个指向指针的指针，struct node** lastPtrRef，这个指针指向结果链表的最后一个节点。在这个方法中，所有由虚拟节点完成的工作都有lastPtrRef完成。代码如下：

// ConsoleApplication15.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <malloc.h>
#include <iostream>
#include <assert.h>
using namespace std;

typedef struct node//定义链表结构体
{
    int data;//节点内容
    node *next;//指向结构体的指针，下一个节点
}node;

node *create()//创建单链表
{
    int i = 0;//链表中数据的个数
    node *head, *p, *q;//这些的本质是节点的地址
    int x = 0;
    head = NULL;
    q = NULL;//初始化q，q代表末节点
    p = NULL;
    while (1)
    {
        printf("please input the data:");
        scanf_s("%d", &x);
        if (x == 0)
            break;//data为0时创建结束
        p = (node *)malloc(sizeof(node));//用于每次输入链表的数据
        p->data = x;
        if (++i == 1)//链表头的指针指向下一个节点
        {
            head = p;
            q = p;
        }
        else
        {
            q->next = p;//连接到链表尾端
            q = p;
        }
        q->next = NULL;/*尾结点的后继指针为NULL(空)*/
    }
    return head;
}

int length(node *head)
{
    int len = 0;
    node *p;
    p = head->next;
    while (p != NULL)
    {
        len++;
        p = p->next;
    }
    return len;
}

void print(node *head)
{
    node *p;
    p = head;
    while (p)/*直到结点q为NULL结束循环*/
    {
        printf("%d ", p->data);/*输出结点中的值*/
        p = p->next;/*指向下一个结点*/
    }
}

node *search_node(node *head, int pos)//查找单链表pos位置的节点，返回节点的指针。pos从0开始，0返回head节点
{
    node *p = head->next;
    if (pos < 0)//pos位置不正确
    {
        printf("incorrect position to search node!");//pose位置不正确
        return NULL;
    }
    if (pos == 0)
    {
        return head;
    }
    if (pos == NULL)
    {
        printf("Link is empty!");//链表为空
        return NULL;
    }
    while (--pos)
    {
        if ((p = p->next) == NULL)
        {
            printf("incorrect position to search node!");//超出链表返回
            break;
        }
    }
    return p;
}

node *insert_node(node *head, int pos, int data)//单链表的插入
{
    node *item = NULL;
    node *p;
    item = (node *)malloc(sizeof(node));
    item->data = data;
    if (pos == 0)//插在head后面
    {
        head->next = item;//head后面是item
        return head;
    }
    p = search_node(head, pos);//获得pos的节点指针
    if (p != NULL)
    {
        item->next = p->next;//item指向原pos节点的后一个节点
        p->next = item;//把item插入到pos的后面
    }
    return head;
}

node *delete_node(node *head, int pos)//删除节点
{
    node *item = NULL;
    node *p = head->next;
    if (p = NULL)
    {
        printf("link is empty!");
        return NULL;
    }
    p = search_node(head, pos - 1);//获得位置pos节点的指针
    if (p != NULL&&p->next != NULL)
    {
        item = p->next;
        p->next = item->next;
        delete item;
    }
    return head;
}

node *reverse(node *head)//链表的逆置
{
    node *next;
    node *prev = NULL;
    while (head != NULL)
    {
        next = head->next;
        head->next = prev;
        prev = head;
        head = next;
    }
    return prev;
}

node *search(node *head)//寻找单链表的中间元素
{
    int i = 0;
    int j = 0;
    node *current = NULL;
    node *middle = NULL;
    current = middle = head->next;
    while (current != NULL)
    {
        if (i / 2 > j)
        {
            j++;
            middle = middle->next;
        }
        i++;
        current = current->next;
    }
    return middle;
}

node *InsertSort(void)//单链表的正向排序
{
    int data = 0;
    struct node *head = NULL, *New, *Cur, *Pre=NULL;
    while (1)
    {
        printf("please input the data
");
        scanf_s("%d", &data);
        if (data == 0)
        {
            break;
        }
        New = (struct node*)malloc(sizeof(struct node));
        New->data = data;
        New->next = NULL;
        if (head == NULL)//第一次循环时对头节点赋值
        {
            head = New;
            continue;
        }
        if (New->data <= head->data)
        {//head之前插入节点
            New->next = head;
            head = New;
            continue;
        }
        Cur = head;
        while (New->data > Cur->data && Cur->next != NULL)//找到需要插入的位置
        {
            Pre = Cur;
            Cur = Cur->next;
        }
        if (Cur->data >= New->data)//位置在中间
        {
            Pre->next = New;
            New->next = Cur;
        }
        else//位置在末尾
            Cur->next = New;//把New节点插到Cur之后
    }
    return head;
}

bool IsLoop(node *head, node **start)//判断链表是否存在环形链表，start为回环开始节点的地址
{
    node *p1 = head, *p2 = head;
    if (head == NULL || head->next == NULL)//head为NULL或者链表为空时返回false
    {
        return false;
    }
    do
    {
        p1 = p1->next;//p1走一步
        p2 = p2->next->next;//p2走两步
    } while (p2 && p2->next && p1 != p2);
    if (p1 == p2)
    {
        *start = p1;//p1为回环开始节点
        return true;
    }
    else
    {
        return false;
    }
}


void MoveNode(struct node** destRef, struct node** sourceRef)//用于局部引用方法合并有序链表
{
    /* the front source node */
    struct node* newNode = *sourceRef;
    assert(newNode != NULL);

    /*Advance the source pointer */
    *sourceRef = newNode->next;

    /* Link th eold dest off the new node */
    newNode->next = *destRef;

    /*Move dest to point to the new node */
    *destRef = newNode;
}

struct node* SortedMerge(struct node* a, struct node* b)//局部引用方法合并有序链表
{
    struct node* result = NULL;

    /*point to the last result pointer */
    struct node** lastPtrRef = &result;

    while (1)
    {
        if (a == NULL)
        {
            *lastPtrRef = b;
            break;
        }
        else if (b == NULL)
        {
            *lastPtrRef = a;
            break;
        }
        if (a->data <= b->data)
        {
            MoveNode(lastPtrRef, &a);
        }
        else
        {
            MoveNode(lastPtrRef, &b);
        }
        /*tricky:advance to point to the next ".next" field */
        lastPtrRef = &((*lastPtrRef)->next);
    }
    return (result);
}
int main()
{
    node *head1 = create();//创建单链表1
    node *head2 = create();//创建单链表2
    node *head = SortedMerge(head1, head2);
    print(head);
    return 0;
}

运行结果：

3：递归方法如下：

// ConsoleApplication15.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <malloc.h>
#include <iostream>
using namespace std;

typedef struct node//定义链表结构体
{
    int data;//节点内容
    node *next;//指向结构体的指针，下一个节点
}node;

node *create()//创建单链表
{
    int i = 0;//链表中数据的个数
    node *head, *p, *q;//这些的本质是节点的地址
    int x = 0;
    head = NULL;
    q = NULL;//初始化q，q代表末节点
    p = NULL;
    while (1)
    {
        printf("please input the data:");
        scanf_s("%d", &x);
        if (x == 0)
            break;//data为0时创建结束
        p = (node *)malloc(sizeof(node));//用于每次输入链表的数据
        p->data = x;
        if (++i == 1)//链表头的指针指向下一个节点
        {
            head = p;
            q = p;
        }
        else
        {
            q->next = p;//连接到链表尾端
            q = p;
        }
        q->next = NULL;/*尾结点的后继指针为NULL(空)*/
    }
    return head;
}

int length(node *head)
{
    int len = 0;
    node *p;
    p = head->next;
    while (p != NULL)
    {
        len++;
        p = p->next;
    }
    return len;
}

void print(node *head)
{
    node *p;
    p = head;
    while (p)/*直到结点q为NULL结束循环*/
    {
        printf("%d ", p->data);/*输出结点中的值*/
        p = p->next;/*指向下一个结点*/
    }
}

node *search_node(node *head, int pos)//查找单链表pos位置的节点，返回节点的指针。pos从0开始，0返回head节点
{
    node *p = head->next;
    if (pos < 0)//pos位置不正确
    {
        printf("incorrect position to search node!");//pose位置不正确
        return NULL;
    }
    if (pos == 0)
    {
        return head;
    }
    if (pos == NULL)
    {
        printf("Link is empty!");//链表为空
        return NULL;
    }
    while (--pos)
    {
        if ((p = p->next) == NULL)
        {
            printf("incorrect position to search node!");//超出链表返回
            break;
        }
    }
    return p;
}

node *insert_node(node *head, int pos, int data)//单链表的插入
{
    node *item = NULL;
    node *p;
    item = (node *)malloc(sizeof(node));
    item->data = data;
    if (pos == 0)//插在head后面
    {
        head->next = item;//head后面是item
        return head;
    }
    p = search_node(head, pos);//获得pos的节点指针
    if (p != NULL)
    {
        item->next = p->next;//item指向原pos节点的后一个节点
        p->next = item;//把item插入到pos的后面
    }
    return head;
}

node *delete_node(node *head, int pos)//删除节点
{
    node *item = NULL;
    node *p = head->next;
    if (p = NULL)
    {
        printf("link is empty!");
        return NULL;
    }
    p = search_node(head, pos - 1);//获得位置pos节点的指针
    if (p != NULL&&p->next != NULL)
    {
        item = p->next;
        p->next = item->next;
        delete item;
    }
    return head;
}

node *reverse(node *head)//链表的逆置
{
    node *next;
    node *prev = NULL;
    while (head != NULL)
    {
        next = head->next;
        head->next = prev;
        prev = head;
        head = next;
    }
    return prev;
}

node *search(node *head)//寻找单链表的中间元素
{
    int i = 0;
    int j = 0;
    node *current = NULL;
    node *middle = NULL;
    current = middle = head->next;
    while (current != NULL)
    {
        if (i / 2 > j)
        {
            j++;
            middle = middle->next;
        }
        i++;
        current = current->next;
    }
    return middle;
}

node *InsertSort(void)//单链表的正向排序
{
    int data = 0;
    struct node *head = NULL, *New, *Cur, *Pre=NULL;
    while (1)
    {
        printf("please input the data
");
        scanf_s("%d", &data);
        if (data == 0)
        {
            break;
        }
        New = (struct node*)malloc(sizeof(struct node));
        New->data = data;
        New->next = NULL;
        if (head == NULL)//第一次循环时对头节点赋值
        {
            head = New;
            continue;
        }
        if (New->data <= head->data)
        {//head之前插入节点
            New->next = head;
            head = New;
            continue;
        }
        Cur = head;
        while (New->data > Cur->data && Cur->next != NULL)//找到需要插入的位置
        {
            Pre = Cur;
            Cur = Cur->next;
        }
        if (Cur->data >= New->data)//位置在中间
        {
            Pre->next = New;
            New->next = Cur;
        }
        else//位置在末尾
            Cur->next = New;//把New节点插到Cur之后
    }
    return head;
}

bool IsLoop(node *head, node **start)//判断链表是否存在环形链表，start为回环开始节点的地址
{
    node *p1 = head, *p2 = head;
    if (head == NULL || head->next == NULL)//head为NULL或者链表为空时返回false
    {
        return false;
    }
    do
    {
        p1 = p1->next;//p1走一步
        p2 = p2->next->next;//p2走两步
    } while (p2 && p2->next && p1 != p2);
    if (p1 == p2)
    {
        *start = p1;//p1为回环开始节点
        return true;
    }
    else
    {
        return false;
    }
}



struct node* SortedMerge(struct node* a, struct node* b)//将两个链表合并，递归法
{
    struct node* result = NULL;

    /*Base cases*/
    if (a == NULL)
        return (b);
    else if (b == NULL)
        return (a);

    /*Pick either a or b, and recur */
    if (a->data <= b->data)
    {
        result = a;
        result->next = SortedMerge(a->next, b);
    }
    else
    {
        result = b;
        result->next = SortedMerge(a, b->next);
    }
    return (result);
}
int main()
{
    node *head1 = create();//创建单链表1
    node *head2 = create();//创建单链表2
    node *head = SortedMerge(head1, head2);
    print(head);


    

    return 0;
}

运行结果：