学习笔记-数据结构与算法之线性表

于 2021-04-29 21:21:11 发布
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分类专栏： 数据结构与算法 编程
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本文链接：https://blog.youkuaiyun.com/TI__boyue/article/details/116261002
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本文详细讲解了顺序结构（线性表）和链式结构（包括插入、删除、翻转方法）的实现，涉及C++代码示例，涵盖创建、验证、基本操作和高级技巧如链表翻转的多种算法。

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目录

框架图

在这里插入图片描述

线性表

顺序结构

#include<iostream>
using namespace std;

#define maxsize 100
typedef int elemtype;

#define ok 1
#define error 0
typedef int status;

typedef struct List{
	elemtype data[maxsize];
	int length;
}list;

void create_list(list* sqlist);
void out_elem(list sqlist);
status get_elem(list sqlist,int i,elemtype *e);
status insert(list& sqlist,int i,elemtype e);
status delete1(list& sqlist,int i,elemtype *e);

int main(){
	
	list sqlist;
	// 创建
	create_list(&sqlist);
	// 输出验证
	out_elem(sqlist);
	cout<<endl;
	
	cout<<"获取第i个元素"<<endl;
	elemtype e;
	cout<<get_elem(sqlist,2,&e)<<endl;
	cout<<e<<endl;
	
	cout<<"插入元素"<<endl;
	cout<<insert(sqlist,3,9)<<endl;
	// 输出验证
	out_elem(sqlist);
	cout<<endl;
	cout<<"删除元素"<<endl;
	cout<<delete1(sqlist,4,&e)<<endl;
	// 输出验证
	out_elem(sqlist);
	cout<<endl;
	
	return 0;
}

创建线性表

void create_list(list* sqlist){
	elemtype temp[] = {1,2,3,4,5};
	int length = sizeof(temp)/sizeof(temp[0]);
	for(int i=0;i<length;i++){
		sqlist->data[i] = temp[i];
	}
	sqlist->length = length;
}

输出验证

void out_elem(list sqlist){
	for(int i=0;i<sqlist.length;i++){
		cout<<sqlist.data[i]<<' ';
	}
}

获取第i个元素

status get_elem(list sqlist,int i,elemtype *e){
	if(sqlist.length == 0 || i<1 || i>sqlist.length)
		return error;
	*e = sqlist.data[i-1];
	return ok;
}

插入元素到特定位置

status insert(list& sqlist,int i,elemtype e){
	
	if(sqlist.length == maxsize){
		cout<<"空间已满"<<endl;
		return error;
	}
	if(i<1 ||i>sqlist.length+1){
		cout<<"i不在范围"<<endl;
		return error;
	}
	
	int k = sqlist.length;
	if(i!=k+1){ //不在表尾
		while(i<=k){
			sqlist.data[k]=sqlist.data[k-1];
			k--;
		}
	}
	sqlist.data[k] = e;
	sqlist.length++;
	return ok;
}

删除特定位置元素

status delete1(list& sqlist,int i,elemtype *e){
	
	if(sqlist.length == 0 || i<1 || i>sqlist.length)
		return error;
	*e = sqlist.data[i-1];
	
	if(i!=sqlist.length){
		while(sqlist.length > i){
			sqlist.data[i-1] = sqlist.data[i];
			i++;
		}
	}
	sqlist.length --;
	return ok;
}

整体代码

#include<iostream>
using namespace std;

#define maxsize 100
typedef int elemtype;

#define ok 1
#define error 0
typedef int status;

typedef struct List{
	elemtype data[maxsize];
	int length;
}list;

void create_list(list* sqlist);
void out_elem(list sqlist);
status get_elem(list sqlist,int i,elemtype *e);
status insert(list& sqlist,int i,elemtype e);
status delete1(list& sqlist,int i,elemtype *e);// delete 是一个c++的函数 定义时需作出改变

int main(){
	
	list sqlist;
	// 创建
	create_list(&sqlist);
	// 输出验证
	out_elem(sqlist);
	cout<<endl;
	
	cout<<"获取第i个元素"<<endl;
	elemtype e;
	cout<<get_elem(sqlist,2,&e)<<endl;
	cout<<e<<endl;
	
	cout<<"插入元素"<<endl;
	cout<<insert(sqlist,3,9)<<endl;
	// 输出验证
	out_elem(sqlist);
	cout<<endl;
	cout<<"删除元素"<<endl;
	cout<<delete1(sqlist,4,&e)<<endl;
	// 输出验证
	out_elem(sqlist);
	cout<<endl;
	
	return 0;
}
/* 创建线性表*/
void create_list(list* sqlist){
	elemtype temp[] = {1,2,3,4,5};
	int length = sizeof(temp)/sizeof(temp[0]);
	for(int i=0;i<length;i++){
		sqlist->data[i] = temp[i];
	}
	sqlist->length = length;
}
// 输出验证
void out_elem(list sqlist){
	for(int i=0;i<sqlist.length;i++){
		cout<<sqlist.data[i]<<' ';
	}
}
/* 获取第i个元素 */
status get_elem(list sqlist,int i,elemtype *e){
	if(sqlist.length == 0 || i<1 || i>sqlist.length)
		return error;
	*e = sqlist.data[i-1];
	return ok;
}
/*插入元素到特定位置*/
status insert(list& sqlist,int i,elemtype e){
	
	if(sqlist.length == maxsize){
		cout<<"空间已满"<<endl;
		return error;
	}
	if(i<1 ||i>sqlist.length+1){
		cout<<"i不在范围"<<endl;
		return error;
	}
	
	int k = sqlist.length;
	if(i!=k+1){ //不在表尾
		while(i<=k){
			sqlist.data[k]=sqlist.data[k-1];
			k--;
		}
	}
	sqlist.data[k] = e;
	sqlist.length++;
	return ok;
}

/*删除特定位置元素*/
// delete 是一个c++的函数 定义时需作出改变
status delete1(list& sqlist,int i,elemtype *e){
	
	if(sqlist.length == 0 || i<1 || i>sqlist.length)
		return error;
	*e = sqlist.data[i-1];
	
	if(i!=sqlist.length){
		while(sqlist.length > i){
			sqlist.data[i-1] = sqlist.data[i];
			i++;
		}
	}
	sqlist.length --;
	return ok;
}

链式结构

#include<iostream>
using namespace std;

typedef int elemtype;

typedef struct node {
	elemtype data;
	struct node *next;
} node, *link_node;

typedef int status;
#define ok 1
#define error 0

void create_node_list(link_node head);
void out_elem(node head_node);
status get_elem(link_node head, int i, elemtype *e);
status insert_node(link_node head, int i, elemtype e);
status delete_node(link_node head, int i, elemtype *e);
status delete_list(link_node head);

int main() {

	node head_node;
	cout << "创建链表" << endl;
	create_node_list(&head_node);
	out_elem(head_node);
	cout << "获取第i个元素" << endl;
	elemtype e;
	cout << get_elem(&head_node, 10, &e) << endl;
	cout << e << endl;
	cout << "插入元素" << endl;
	cout << insert_node(&head_node, 5, 12) << endl;
	out_elem(head_node);
	cout << "删除元素" << endl;
	cout << delete_node(&head_node, 5, &e) << endl;
	cout << e << endl;
	out_elem(head_node);
	cout<<"删除整表"<<endl;
	delete_list(&head_node);
	out_elem(head_node);
	return 0;
}

创建链表

void create_node_list(link_node head) {
	link_node p, q;

	elemtype array[] = { 1,2,3,4,5,6,7,8,9,10 };
	int length = sizeof(array) / sizeof(array[0]);
	q = head;
	head->data = length;
	head->next = NULL;

	for (int i = 0; i < length; i++) {
		p = new node;
		p->data = array[i];
		p->next = NULL; // 尾插法
		q->next = p;
		q = p;
	}
}

输出验证

void out_elem(node head_node) {
	link_node p = head_node.next;
	while (p) {
		cout << p->data << ' ';
		p = p->next;
	}
	cout << endl;
}

获取第i个元素

status get_elem(link_node head, int i, elemtype *e) {
	if (head->data == 0 || i<1 || i>head->data)
		return error;
	int count = 1;
	link_node p = head->next;
	while (p && count < i) {
		p = p->next;
		count++;
	}
	*e = p->data;
	return ok;
}

插入元素

status insert_node(link_node head, int i, elemtype e) {
	if (i<1 || i>head->data + 1) return error;

	link_node q, p = head;
	int count = 1;
	while (p && count < i) {
		p = p->next;
		count++;
	}

	q = new node;
	q->data = e;
	q->next = p->next;
	p->next = q;

	head->data++;
	return ok;
}

删除元素

status delete_node(link_node head, int i, elemtype *e) {
	if (head->data ==0 || i<1 || i>head->data)
		return error;

	int count = 1;
	link_node q, p = head;
	while (p && count < i) {
		p = p->next;
		count++;
	}

	q = p->next;
	*e = q->data;
	p->next = q->next;
	delete q;

	head->data--;
	return ok;
}

删除整表

status delete_list(link_node head){
	link_node q,p=head->next;
	while(p){
		q=p;
		p=q->next;
		delete q;
		head->data--;
	}
	head->next=NULL;
	return ok;
}

完整代码

#include<iostream>
using namespace std;

typedef int elemtype;
typedef struct node {
	elemtype data;
	struct node *next;
} node, *link_node;

typedef int status;
#define ok 1
#define error 0

void create_node_list(link_node head);
void out_elem(node head_node);
status get_elem(link_node head, int i, elemtype *e);
status insert_node(link_node head, int i, elemtype e);
status delete_node(link_node head, int i, elemtype *e);
status delete_list(link_node head);

int main() {

	node head_node;
	cout << "创建链表" << endl;
	create_node_list(&head_node);
	out_elem(head_node);
	cout << "获取第i个元素" << endl;
	elemtype e;
	cout << get_elem(&head_node, 10, &e) << endl;
	cout << e << endl;
	cout << "插入元素" << endl;
	cout << insert_node(&head_node, 5, 12) << endl;
	out_elem(head_node);
	cout << "删除元素" << endl;
	cout << delete_node(&head_node, 5, &e) << endl;
	cout << e << endl;
	out_elem(head_node);
	cout<<"删除整表"<<endl;
	delete_list(&head_node);
	out_elem(head_node);
	return 0;

}
// 创建链表
void create_node_list(link_node head) {
	link_node p, q;

	elemtype array[] = { 1,2,3,4,5,6,7,8,9,10 };
	int length = sizeof(array) / sizeof(array[0]);
	q = head;
	head->data = length;
	head->next = NULL;

	for (int i = 0; i < length; i++) {
		p = new node;
		p->data = array[i];
		p->next = NULL; // 尾插法
		q->next = p;
		q = p;
	}
}
// 输出验证
void out_elem(node head_node) {
	link_node p = head_node.next;
	while (p) {
		cout << p->data << ' ';
		p = p->next;
	}
	cout << endl;
}
// 获取第i个元素
status get_elem(link_node head, int i, elemtype *e) {
	if (head->data == 0 || i<1 || i>head->data)
		return error;
	int count = 1;
	link_node p = head->next;
	while (p && count < i) {
		p = p->next;
		count++;
	}
	*e = p->data;
	return ok;
}
// 插入元素
status insert_node(link_node head, int i, elemtype e) {
	if (i<1 || i>head->data + 1) return error;

	link_node q, p = head;
	int count = 1;
	while (p && count < i) {
		p = p->next;
		count++;
	}

	q = new node;
	q->data = e;
	q->next = p->next;
	p->next = q;

	head->data++;
	return ok;
}
// 删除元素
status delete_node(link_node head, int i, elemtype *e) {
	if (head->data ==0 || i<1 || i>head->data)
		return error;

	int count = 1;
	link_node q, p = head;
	while (p && count < i) {
		p = p->next;
		count++;
	}

	q = p->next;
	*e = q->data;
	p->next = q->next;
	delete q;

	head->data--;
	return ok;
}
// 删除整表
status delete_list(link_node head){
	link_node q,p=head->next;
	while(p){
		q=p;
		p=q->next;
		delete q;
		head->data--;
	}
	head->next=NULL;
	return ok;
}

链表翻转

迭代反转法

// 翻转 -- 迭代反转法 -- 从首部开始
void turn_iteration_list(link_node head){
	//是否最多只有一个元素
	if(head->next == NULL || head->next->next == NULL) return;
	
	link_node p,q,s;
	q=NULL;
	p=head->next;
	s=p->next;
	while(1){
		p->next =q;
		if(s == NULL) break;
		q=p;
		p=s;s=p->next;
	}
	head->next = p;
}

递归翻转法

link_node turn_recursive_list(link_node first){
	// 递归出口
	if(first == NULL || first->next == NULL) return first;
	
	link_node new_head =  turn_recursive_list(first->next); 
	
	first->next->next = first;
	first->next = NULL;
	
	return new_head; // 持续返回新头部指针，恒定
}

头插法翻转

void turn_insert_head_list(link_node head){
	if(head->next == NULL || head->next->next == NULL) return;
	
	link_node end = head;
	while(end->next){
		end = end->next;
	}
	link_node p,q;
	p=head->next;
	while(p!=end){
		q=p->next;
		p->next = end->next;
		end->next = p;
		p = q;
	}
	head->next = end;
}

就地逆置法翻转

void turn_local_list(link_node head){
	if(head->next == NULL || head->next->next == NULL) return;
	
	link_node p,q;
	q=head->next;
	p=q->next;
	
	while(p){
		q->next = p->next;
		p->next = head->next;
		head->next = p;
		p=q->next;
	}
}

完整代码

#include<iostream>
using namespace std;

typedef int elemtype;
typedef struct node{
	elemtype data;
	struct node *next;
}node,*link_node;

void create_node_list(link_node head) {
	link_node p, q;

	elemtype array[] = {1,2,3,4,5,6,7,8,9,10};
	int length = sizeof(array) / sizeof(array[0]);
	q = head;
	head->data = length;
	head->next = NULL;

	for (int i = 0; i < length; i++) {
		p = new node;
		p->data = array[i];
		p->next = NULL; // 尾插法
		q->next = p;
		q = p;
	}
}
void out_elem(node head_node) {
	link_node p = head_node.next;
	while (p) {
		cout << p->data << ' ';
		p = p->next;
	}
	cout << endl;
}
void turn_iteration_list(link_node head);
link_node turn_recursive_list(link_node first);
void turn_insert_head_list(link_node head);
void turn_local_list(link_node head);
int main(){
	node head_node;
	create_node_list(&head_node);
	out_elem(head_node);
	cout<<"迭代翻转法："<<endl;
	turn_iteration_list(&head_node);
	out_elem(head_node);
	cout<<"迭代翻转法"<<endl;
	head_node.next = turn_recursive_list(head_node.next);
	out_elem(head_node);
	cout<<"头插法翻转"<<endl;
	turn_insert_head_list(&head_node);
	out_elem(head_node);
	cout<<"就地翻转"<<endl;
	turn_local_list(&head_node);
	out_elem(head_node);
	return 0;
}
// 翻转 -- 迭代反转法 -- 从首部开始
void turn_iteration_list(link_node head){
	//是否最多只有一个元素
	if(head->next == NULL || head->next->next == NULL) return;
	
	link_node p,q,s;
	q=NULL;
	p=head->next;
	s=p->next;
	while(1){
		p->next =q;
		if(s == NULL) break;
		q=p;
		p=s;s=p->next;
	}
	head->next = p;
}
// 递归翻转法 -- 从尾部开始
link_node turn_recursive_list(link_node first){
	// 递归出口
	if(first == NULL || first->next == NULL) return first;
	
	link_node new_head =  turn_recursive_list(first->next); 
	
	first->next->next = first;
	first->next = NULL;
	
	return new_head; // 持续返回新头部指针，恒定
}
// 头插法翻转
void turn_insert_head_list(link_node head){
	if(head->next == NULL || head->next->next == NULL) return;
	
	link_node end = head;
	while(end->next){
		end = end->next;
	}
	link_node p,q;
	p=head->next;
	while(p!=end){
		q=p->next;
		p->next = end->next;
		end->next = p;
		p = q;
	}
	head->next = end;
}
// 就地逆置法翻转
void turn_local_list(link_node head){
	if(head->next == NULL || head->next->next == NULL) return;
	
	link_node p,q;
	q=head->next;
	p=q->next;
	
	while(p){
		q->next = p->next;
		p->next = head->next;
		head->next = p;
		p=q->next;
	}
}

合并链表

#include<iostream>
using namespace std;

typedef int elemtype;
typedef struct node{
	elemtype data;
	struct node *next;
}node,*link_node;

void create_node_list(link_node head,elemtype array[],int length);
void out_elem(node head_node);
void combine_node_list(link_node head_combin,node head_node1,node head_node2);
void combin_node_list_no(link_node head1,link_node head2);
int main(){
	
	node head_node1,head_node2,head_node_combine;
	elemtype array1[]={0,1,3,5,7,9};
	elemtype array2[]={1,2,4,6,8,10,11,12};
	cout<<"head_node1"<<endl;
	create_node_list(&head_node1,array1,sizeof(array1)/sizeof(array1[0]));
	out_elem(head_node1);
	cout<<"head_node2"<<endl;
	create_node_list(&head_node2,array2,sizeof(array2)/sizeof(array2[0]));
	out_elem(head_node2);
	cout<<"合并后新建链表"<<' ';
	combine_node_list(&head_node_combine,head_node1,head_node2);
	cout<<"长度:"<<head_node_combine.data<<endl;
	out_elem(head_node_combine);
	cout<<"原空间-以head_node1为主";
	combin_node_list_no(&head_node1,&head_node2);
	cout<<" 长度:"<<head_node1.data<<endl;
	out_elem(head_node1);
	return 0;
}
void create_node_list(link_node head,elemtype array[],int length){
	
	head->data=length;
	head->next=NULL;
	
	link_node q,p;
	p=head;
	
	for(int i=0;i<length;i++){
		q = new node;
		q->data = array[i];
		q->next = NULL;
		p->next = q;
		p=q;
	}
}
void out_elem(node head_node){
	if(head_node.next == NULL) return;
	link_node p=head_node.next;
	while(p){
		cout<<p->data<<" ";
		p=p->next;
	}
	cout<<endl;
}
void combine_node_list(link_node head_combin,node head_node1,node head_node2){
	link_node p,q,s,m;
	elemtype temp;
	head_combin->next=NULL;
	head_combin->data=0;
	
	p=head_combin;
	q=head_node1.next;
	s=head_node2.next;
	
	while(q&&s){
		if(q->data<=s->data){
			temp=q->data;
			q=q->next;
		}else {
			temp = s->data;
			s=s->next;
		}
		m = new node;
		m->data = temp;
		m->next = NULL;
		p->next=m;
		p=m;
	}
	if(q){
		p->next=q;
	}
	if(s){
		p->next=s;
	}
	head_combin->data = head_node1.data+head_node2.data;
}

void combin_node_list_no(link_node head1,link_node head2){
	link_node p,q,s;
	s=head1;
	p=head1->next;q=head2->next;
	while( p && q){
		if(p->data<=q->data){
			s->next = p;
			s=p;
			p=p->next;
		}else {
			s->next = q;
			s=q;
			q=q->next;
		}
	}
	if(p) s->next = p;
	if(q) s->next = q;
	head1->data=head1->data+head2->data;
}

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