第1章 绪论
1.3 抽象数据类型的表示与实现
将一些常用的头文件包含到一个头文件中,以后就只用调用这个头文件了:
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//c1.h(程序名)
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#include <string.h>
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#include <ctype.h>
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#include <malloc.h> //malloc()等
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#include <limits.h> //INT_MAX等
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#include <stdio.h> //EOF(=^Z或F6),NULL
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#include <stdlib.h> //atoi()
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#include <io.h>
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#include <math.h>
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#include <process.h>
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#include <iostream.h>
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//函数结果状态代码
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#define TRUE 1
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#define FALSE 0
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#define OK 1
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#define ERROR 0
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#define INFEASIBLE -1
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typedef int Status; //Status是函数的类型,其值是函数结果状态代码,如OK等
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typedef int Boolean; //Boolean是布尔类型
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采用动态分配的顺序存储结构
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//c1-1.h 采用动态分配的顺序存储结构
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typedef ElemType *Triplet; //由InitTriplet分配3个元素存储空间
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//Triplet类型是ElemType类型的指针,存放ElemType类型的地址
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有关抽象数据类型Triplet和ElemType的8个基本操作函数。
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// bo1-1.cpp 抽象数据类型Triplet和ElemType(由c1-1.h定义)的基本操作(8个)
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Status InitTriplet(Triplet &T,ElemType v1,ElemType v2,ElemType v3)
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{ // 操作结果:构造三元组T,依次置T的3个元素的初值为v1,v2和v3
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if(!(T=(ElemType *)malloc(3*sizeof(ElemType))))
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exit(OVERFLOW);
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T[0]=v1,T[1]=v2,T[2]=v3;
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return OK;
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}
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Status DestroyTriplet(Triplet &T)
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{ // 操作结果:三元组T被销毁
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free(T);
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T=NULL;
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return OK;
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}
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Status Get(Triplet T,int i,ElemType &e)
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{ // 初始条件:三元组T已存在,1≤i≤3。操作结果:用e返回T的第i元的值
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if(i<1||i>3)
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return ERROR;
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e=T[i-1];
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return OK;
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}
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Status Put(Triplet T,int i,ElemType e)
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{ // 初始条件:三元组T已存在,1≤i≤3。操作结果:改变T的第i元的值为e
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if(i<1||i>3)
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return ERROR;
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T[i-1]=e;
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return OK;
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}
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Status IsAscending(Triplet T)
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{ // 初始条件:三元组T已存在。操作结果:如果T的3个元素按升序排列,返回1,否则返回0
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return(T[0]<=T[1]&&T[1]<=T[2]);
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}
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Status IsDescending(Triplet T)
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{ // 初始条件:三元组T已存在。操作结果:如果T的3个元素按降序排列,返回1,否则返回0
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return(T[0]>=T[1]&&T[1]>=T[2]);
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}
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Status Max(Triplet T,ElemType &e)
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{ // 初始条件:三元组T已存在。操作结果:用e返回指向T的最大元素的值
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e=T[0]>=T[1]?T[0]>=T[2]?T[0]:T[2]:T[1]>=T[2]?T[1]:T[2];
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return OK;
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}
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Status Min(Triplet T,ElemType &e)
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{ // 初始条件:三元组T已存在。操作结果:用e返回指向T的最小元素的值
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e=T[0]<=T[1]?T[0]<=T[2]?T[0]:T[2]:T[1]<=T[2]?T[1]:T[2];
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return OK;
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}
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检查基本操作的主函数
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// main1-1.cpp 检验基本操作bo1-1.cpp的主函数
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#include"c1.h" // 要将程序中所有#include命令所包含的文件拷贝到当前目录下
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// 以下2行可根据需要选用一个(且只能选用一个),而不需改变基本操作bo1-1.cpp
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typedef int ElemType; // 定义抽象数据类型ElemType在本程序中为整型
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//typedef double ElemType; // 定义抽象数据类型ElemType在本程序中为双精度型
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#include"c1_1.h" // 在此命令之前要定义ElemType的类型
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//#include"bo1_1.cpp" // 在此命令之前要包括c1-1.h文件(因为其中定义了Triplet)
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#include"bo1_1.h"
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void main()
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{
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Triplet T;
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ElemType m;
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Status i;
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i=InitTriplet(T,5,7,9); // 初始化三元组T,其3个元素依次为5,7,9
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//i=InitTriplet(T,5.0,7.1,9.3); // 当ElemType为双精度型时,可取代上句
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printf("调用初始化函数后,i=%d(1:成功) T的3个值为:",i);
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cout<<T[0]<<' '<<T[1]<<' '<<T[2]<<endl;
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// 为避免ElemType的类型变化的影响,用cout取代printf()。注意结尾要加endl
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i=Get(T,2,m); // 将三元组T的第2个值赋给m
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if(i==OK) // 调用Get()成功
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cout<<"T的第2个值为:"<<m<<endl;
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i=Put(T,2,6); // 将三元组T的第2个值改为6
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if(i==OK) // 调用Put()成功
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cout<<"将T的第2个值改为6后,T的3个值为:"<<T[0]<<' '<<T[1]<<' '<<T[2]<<endl;
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i=IsAscending(T); // 此类函数实参与ElemType的类型无关,当ElemType的类型变化时,实参不需改变
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printf("调用测试升序的函数后,i=%d(0:否 1:是)\n",i);
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i=IsDescending(T);
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printf("调用测试降序的函数后,i=%d(0:否 1:是)\n",i);
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if((i=Max(T,m))==OK) // 先赋值再比较
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cout<<"T中的最大值为:"<<m<<endl;
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if((i=Min(T,m))==OK)
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cout<<"T中的最小值为:"<<m<<endl;
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DestroyTriplet(T); // 函数也可以不带回返回值
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cout<<"销毁T后,T="<<T<<"(NULL)"<<endl;
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}
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程序运行结果:
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变量的引用类型和非引用类型的区别
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// algo1-3.cpp 变量的引用类型和非引用类型的区别
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#include<stdio.h>
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void fa(int a) // 在函数中改变a,将不会带回主调函数(主调函数中的a仍是原值)
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{
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a++;
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printf("在函数fa中:a=%d\n",a);
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}
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void fb(int &a) // 由于a为引用类型,在函数中改变a,其值将带回主调函数
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{
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a++;
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printf("在函数fb中:a=%d\n",a);
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}
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void main()
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{
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int n=1;
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printf("在主程中,调用函数fa之前:n=%d\n",n);
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fa(n);
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printf("在主程中,调用函数fa之后,调用函数fb之前:n=%d\n",n);
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fb(n);
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printf("在主程中,调用函数fb之后:n=%d\n",n);
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}
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程序运行结果:
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1.4 算法和算法分析
同样是计算:1-1/x+1/x*x-1/x*x*x+...,algo1_1.cpp的语句频度表达式为:(1+n)*n/2,它的时间复杂度T(n)=O(n*n);而algo1_2.cpp的语句频度表达式是n,时间复杂度T(n)=O(n)。
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// algo1-1.cpp 计算1-1/x+1/x*x…
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#include<stdio.h>
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#include<sys/timeb.h>
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void main()
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{
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timeb t1,t2;
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long t;
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double x,sum=1,sum1;
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int i,j,n;
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printf("请输入x n:");
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scanf("%lf%d",&x,&n);
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ftime(&t1); // 求得当前时间
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for(i=1;i<=n;i++)
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{
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sum1=1;
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for(j=1;j<=i;j++)
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sum1=sum1*(-1.0/x);
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sum+=sum1;
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}
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ftime(&t2); // 求得当前时间
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t=(t2.time-t1.time)*1000+(t2.millitm-t1.millitm); // 计算时间差
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printf("sum=%lf 用时%ld毫秒\n",sum,t);
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}
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// algo1-2.cpp 计算1-1/x+1/x*x…的更快捷的算法
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#include<stdio.h>
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#include<sys/timeb.h>
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void main()
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{
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timeb t1,t2;
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long t;
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double x,sum1=1,sum=1;
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int i,n;
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printf("请输入x n: ");
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scanf("%lf%d",&x,&n);
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ftime(&t1); // 求得当前时间
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for(i=1;i<=n;i++)
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{
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sum1*=-1.0/x;
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sum+=sum1;
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}
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ftime(&t2); // 求得当前时间
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t=(t2.time-t1.time)*1000+(t2.millitm-t1.millitm); // 计算时间差
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printf("sum=%lf 用时%ld毫秒\n",sum,t);
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}
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程序运行结果:(左边的时间与计算机的配置有关)
![chap01re03.gif](/images/cnblogs_com/ctoroad/DataStructures/chap01/chap01re03.gif)
![chap01re04.gif](/images/cnblogs_com/ctoroad/DataStructures/chap01/chap01re04.gif)