数据结构研究如何使用存储区解决问题
算法研究解决常见问题的方法
数字之间的关系可以从两个完全不同的角度
进行描述
逻辑关系（逻辑结构）描述数字之间和计算机
无关的关系
物理关系（物理结构）描述存放数字的存储区
之间的关系
逻辑结构分为如下几种
1.集合结构：所有数字可以看作一个整体
2.线性结构：可以用一条有顺序的线把所有
数字连起来
3.树状结构：所有数据都是从一个数据开始
向一个方向扩展出来的，任何数据
可以扩展出多个其他数据
4.网状结构：任何两个数字之间可以有直接的
联系，所有数字之间的联系没有统一
方向
物理结构有以下两种
1.顺序结构：所有存储区在内存里连续排列
数组和动态分配内存都是顺序结构的例子
顺序结构中每个存储区有一个编号，
可以根据编号直接找到对应的存储区
根据编号找到存储区的方法叫随机访问，
顺序结构支持随机访问能力
顺序结构中存储区个数很难调整，这
有可能造成内存的浪费
顺序结构不适合进行插入或删除操作
/* 顺序结构演示 */ #include <stdio.h> void remove_num(int *p_num, int size, int num) { int num1 = 0; for (num1 = 0;num1 <= size - 1;num1++) { if (num < *(p_num + num1)) { *(p_num + num1 - 1) = *(p_num + num1); } else if (num1 && *(p_num + num1) < *(p_num + num1 - 1)) { *(p_num + num1 - 1) = *(p_num + num1); break; } } } void insert(int *p_num, int size, int num) { int tmp = num, num1 = 0, tmp1 = 0; for (num1 = 0;num1 <= size - 1;num1++) { if (tmp < *(p_num + num1)) { tmp1 = tmp; tmp = *(p_num + num1); *(p_num + num1) = tmp1; } else if (num1 && *(p_num + num1) < *(p_num + num1 - 1)) { tmp1 = tmp; tmp = *(p_num + num1); *(p_num + num1) = tmp1; break; } } } int main() { int arr[20] = {2, 6, 12, 14, 17, 21, 23, 31, 35, 37}; int num = 0; insert(arr, 20, 27); for (num = 0;num <= 19;num++) { printf("%d ", arr[num]); } printf(" "); remove_num(arr, 20, 14); for (num = 0;num <= 19;num++) { printf("%d ", arr[num]); } printf(" "); return 0; }
2.链式物理结构：由多个无关的存储区构成，
任何两个存储区之间可以用指针连接
链式物理结构中每个存储区叫做一个
结点
单向线性链式物理结构中任何两个结点
之间都有前后关系（每个结点里只
需要包含一个指针）
单向线性链式物理结构中最后一个结点
里的指针必须是空指针
链式物理结构不直接支持随机访问能力
可以在所有结点前增加一个无效头结点，
在所有结点后增加一个无效尾结点，这样
可以简化程序的编写
/* 链式物理结构演示 */ #include <stdio.h> typedef struct node { int num; struct node *p_next; } node; int main() { node node1 = {1}, node2 = {5}, node3 = {12}, head = {0}, tail = {0}, node4 = {7}; int cnt = 0; node *p_node = NULL; node1.p_next = &node2; node2.p_next = &node3; head.p_next = &node1; node3.p_next = &tail; for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail) { printf("%d ", p_mid->num); } } printf(" "); for (p_node = &head;p_node != &tail;p_node= p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail && cnt == 2) { printf("数字是%d ", p_mid->num); } cnt++; } for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid == &tail || p_mid->num > node4.num) { p_first->p_next = &node4; node4.p_next = p_mid; break; } } for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail) { printf("%d ", p_mid->num); } } printf(" "); for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail && p_mid->num == 5) { p_first->p_next = p_last; break; } } for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail) { printf("%d ", p_mid->num); } } printf(" "); return 0; }
链式物理结构中每个有效结点都应该是动态
分配的
链式物理结构中能容纳的数字数量可以灵活
变化
数据结构由一组存储区和一组相关的函数构成
这些函数提供了对存储区的使用方法
程序中的其他语句只能通过这组函数使用这些
存储区
/* 动态分配链式物理结构演示 */ #include <stdio.h> #include <stdlib.h> typedef struct node { int num; struct node *p_next; } node; int main() { int num = 0; node head = {0}, tail = {0}, *p_tmp = NULL, *p_node = NULL; head.p_next = &tail; while (1) { printf("请输入一个数字："); scanf("%d", &num); if (num < 0) { break; } p_tmp = (node *)malloc(sizeof(node)); if (!p_tmp) { continue; } p_tmp->num = num; p_tmp->p_next = NULL; for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid == &tail) { p_first->p_next = p_tmp; p_tmp->p_next = p_mid; break; } } } printf("请输入要删除的数字："); scanf("%d", &num); for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail && p_mid->num == num) { p_first->p_next = p_last; free(p_mid); p_mid = NULL; break; } } for (p_node = &head;p_node != &tail;p_node = p_node->p_next) { node *p_first = p_node; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; if (p_mid != &tail) { printf("%d ", p_mid->num); } } printf(" "); while (head.p_next != &tail) { node *p_first = &head; node *p_mid = p_first->p_next; node *p_last = p_mid->p_next; p_first->p_next = p_last; free(p_mid); p_mid = NULL; } return 0; }