表达式求值
github仓库：https://github.com/EanoJiang/Data-structures-and-algorithms
栈——表达式求值
枚举
typedef enum{
枚举元素;
}枚举名;
后缀表达式运算逻辑
遇到数字入栈，遇到符号出栈运算，运算结果入栈，\0结束
#include <stdio.h>
#include <stdlib.h>
typedef int ElemType;
#define MAXSIZE 100
typedef struct Stack{
int top;
ElemType *data;
}Stack;
// 初始化栈
Stack* initStack(){
Stack *s = (Stack*)malloc(sizeof(Stack));
s->data = (ElemType*)malloc(MAXSIZE * sizeof(ElemType));
s->top = -1;
return s;
}
int isEmpty(Stack* s){
return s->top == -1;
}
//入栈
int push(Stack *s, ElemType e){
if(s->top == MAXSIZE-1){
printf("栈满\n");
return 0;
}
s->top++;
//从栈顶入栈
s->data[s->top] = e;
return 1;
}
//出栈
ElemType pop(Stack *s,ElemType *e){
if(s->top == -1){
printf("栈空\n");
return 0;
}
*e = s->data[s->top];
s->top--;
return *e;
}
//查看栈顶元素
ElemType getTop(Stack *s,ElemType *e){
if(s->top == -1){
printf("栈空\n");
return 0;
}
*e = s->data[s->top];
return *e;
}
typedef enum {
LEFT_PARE,RIGHT_PARE,
ADD,SUB,MUL,DIV,MOD,
EOS,NUM
}contentType;
char expr[] = "82/2+56*-";
contentType getToken(char *symbol,int *index){
//存储当前字符
*symbol = expr[*index];
//这句不能写成*index++：指针*index的地址自增
*index = *index + 1;//指针*index的值自增
switch(*symbol){
case '(':
return LEFT_PARE;
case ')':
return RIGHT_PARE;
case '+':
return ADD;
case '-':
return SUB;
case '*':
return MUL;
case '/':
return DIV;
case '%':
return MOD;
case '\0':
return EOS;
default:
if(*symbol >= '0' && *symbol <= '9'){
return NUM;
}
else{
printf("非法字符\n");
return -1;
}
}
}
//计算后缀表达式
int eval(Stack *s){
char symbol;
int op1,op2;
int index = 0;
ElemType result;
contentType token;
token = getToken(&symbol,&index);
//结束条件\0
while(token!= EOS){
//遇到数字
if(token == NUM){
//将数字(字符相应ASCII码-'0')压入栈中
push(s,symbol - '0');
}
//遇到操作符
else{
//出栈，把被操作数存到op2和op1中
pop(s,&op2);
pop(s,&op1);
//计算结果入栈
switch(token){
case ADD:
push(s,op1 + op2);
break;
case SUB:
push(s,op1 - op2);
break;
case MUL:
push(s,op1 * op2);
break;
case DIV:
push(s,op1 / op2);
break;
case MOD:
push(s,op1 % op2);
break;
default:
printf("非法字符\n");
return 0;
}
}
//更新token
token = getToken(&symbol,&index);
}
//循环结束条件\0后，栈中只有一个元素，出栈并打印
pop(s,&result);
printf("结果为：%d\n",result);
return 1;
}
int main(){
Stack *s = initStack();
eval(s);
return 0;
}
中缀表达式转后缀表达式
#include <stdio.h>
#include <stdlib.h>
typedef int ElemType;
#define MAXSIZE 100
typedef struct Stack{
int top;
ElemType *data;
}Stack;
// 初始化栈
Stack* initStack(){
Stack *s = (Stack*)malloc(sizeof(Stack));
s->data = (ElemType*)malloc(MAXSIZE * sizeof(ElemType));
s->top = -1;
return s;
}
int isEmpty(Stack* s){
return s->top == -1;
}
//入栈
int push(Stack *s, ElemType e){
if(s->top == MAXSIZE-1){
printf("栈满\n");
return 0;
}
s->top++;
//从栈顶入栈
s->data[s->top] = e;
return 1;
}
//出栈
ElemType pop(Stack *s,ElemType *e){
if(s->top == -1){
printf("栈空\n");
return 0;
}
*e = s->data[s->top];
s->top--;
return *e;
}
//查看栈顶元素
ElemType getTop(Stack *s,ElemType *e){
if(s->top == -1){
printf("栈空\n");
return 0;
}
*e = s->data[s->top];
return *e;
}
typedef enum {
LEFT_PARE,RIGHT_PARE,
ADD,SUB,MUL,DIV,MOD,
EOS,NUM
}contentType;
char expr[] = "x/(i-j)*y";
contentType getToken(char *symbol,int *index){
//当前字符存到指针symbol中
*symbol = expr[*index];
//这句不能写成*index++：指针*index的地址自增
*index = *index + 1;//指针*index的值自增
switch(*symbol){
case '(':
return LEFT_PARE;
case ')':
return RIGHT_PARE;
case '+':
return ADD;
case '-':
return SUB;
case '*':
return MUL;
case '/':
return DIV;
case '%':
return MOD;
case '\0':
return EOS;
default:
return NUM;
}
}
//计算后缀表达式
int eval(Stack *s){
char symbol;
int op1,op2;
int index = 0;
ElemType result;
contentType token;
token = getToken(&symbol,&index);
//结束条件\0
while(token!= EOS){
//遇到数字
if(token == NUM){
//将数字(字符相应ASCII码-'0')压入栈中
push(s,symbol - '0');
}
//遇到操作符
else{
//出栈，把被操作数存到op2和op1中
pop(s,&op2);
pop(s,&op1);
//计算结果入栈
switch(token){
case ADD:
push(s,op1 + op2);
break;
case SUB:
push(s,op1 - op2);
break;
case MUL:
push(s,op1 * op2);
break;
case DIV:
push(s,op1 / op2);
break;
case MOD:
push(s,op1 % op2);
break;
default:
printf("非法字符\n");
return 0;
}
}
//更新token
token = getToken(&symbol,&index);
}
//循环结束条件\0后，栈中只有一个元素，出栈并打印
pop(s,&result);
printf("结果为：%d\n",result);
return 1;
}
//打印token
int print_token(contentType token)
{
switch(token)
{
case ADD:
printf("+");
break;
case SUB:
printf("-");
break;
case MUL:
printf("*");
break;
case DIV:
printf("/");
break;
case MOD:
printf("%%");
break;
default:
return 0;
}
return 1;
}
//中缀转后缀表达式,打印
void postfix(Stack *s){
//运算符优先级
//LEFT_PARE,RIGHT_PARE,ADD,SUB,MUL,DIV,MOD,EOS
int in_stack[] = {0,19,12,12,13,13,13,0};//栈内运算符(左括号在栈里面的时候优先级是0)
int out_stack[] = {20, 19, 12, 12, 13, 13, 13, 0};//栈外运算符
contentType token;
int index = 0;
//栈顶先放一个\0，作为优先级最低的token
s->top = 0;
s->data[0] = EOS;
char symbol;
ElemType e;
token = getToken(&symbol,&index);
//结束条件\0，就不再获取新的token了
while(token!= EOS){
//遇到数字
if(token == NUM)
{
printf("%c",symbol);
}
//遇到右括号
else if(token == RIGHT_PARE){
//出栈并打印，结束条件：遇到左括号
while(s->data[s->top] != LEFT_PARE){
pop(s,&e);
print_token(e);
}
//出栈左括号
pop(s,&e);
}
//遇到其他操作符
else{
//优先级越小越优先
//优先级：当前元素(优先)<=栈顶元素，出栈并打印
while(out_stack[token] <= in_stack[s->data[s->top]]){
pop(s,&e);
print_token(e);
}
//优先级：当前元素>栈顶元素(优先)，入栈
push(s,token);
}
//更新token
token = getToken(&symbol,&index);
}
//出栈剩余的元素
pop(s, &e);
//打印剩余的元素
token = e;
while(token != EOS)
{
print_token(token);
pop(s, &e);
token = e;
}
printf("\n");
}
int main(){
Stack *s = initStack();
printf("中缀表达式：%s\n",expr);
postfix(s);
return 0;
}
浙公网安备 33010602011771号