【数据结构】中缀表达式转后缀表达式（带括号）用栈实现

中缀表达式：9+(3-1)*3+10/2

转化为后缀表达式：931-3*+102/+

规则：

从左到右遍历中缀表达式的每个数字和符号，若是数字就输出，即成为表达式的一部分；若是符号，则判断其与栈顶符号的优先级，是右括号或是优先级不高于栈顶符号则栈顶元素依次出栈并输出，并将当前符号进栈，直到最终输出后缀表达式为止。

代码是用最简单的逻辑写的，没有绕任何弯子，绝对可以看懂。我是新手，勿喷望指正。

代码 c++：VS2013 + WIN7

#include <iostream>using namespace std;#define ok 0#define error -1typedef int Elemtype;typedef int status;//函数返回的状态，如ok  errortypedef struct StackNode{Elemtype data;struct StackNode *next;}StackNode, *StackNodeP;typedef struct LinkStack{StackNodeP top;int count;}LinkStack;LinkStack* LinkStack_Create();//链栈的创建status LinkStack_Clear(LinkStack* stack);//链栈的清空int LinkStack_Isempty(LinkStack* stack);//链栈是否为空status LinkStack_Push(LinkStack* stack, Elemtype e);//链栈的入栈Elemtype LinkStack_Pop(LinkStack* stack);//链栈的出栈int LinkStack_Length(LinkStack* stack);//链栈的长度Elemtype LinkStack_Top(LinkStack* stack);//链栈的头部元素status change(char* buf,char* afterbuf){int i=0;LinkStack* LS = LinkStack_Create();/*设定+   1-   2*   3/   4 */while (*buf){if ((*buf >= '0') && (*buf <= '9')){while ((*buf >= '0') && (*buf <= '9')){afterbuf[i] = *buf;buf++;i++;}afterbuf[i++] = ',';}if (*buf == '+'){if (LinkStack_Isempty(LS))//如果链栈为空，则直接将‘+’入栈LinkStack_Push(LS, 1);else if ( LinkStack_Top(LS)> 2)//如果链栈的头结点上为‘*’‘/’，则栈中所有都弹出{while (!LinkStack_Isempty(LS))//直到将栈中的所有都弹出{if (LinkStack_Top(LS) == -1)//如果为'（'则停止循环{break;}else{switch (LinkStack_Top(LS)){case 1:afterbuf[i++] = '+'; afterbuf[i++] = ','; break;case 2:afterbuf[i++] = '-'; afterbuf[i++] = ','; break;case 3:afterbuf[i++] = '*'; afterbuf[i++] = ','; break;case 4:afterbuf[i++] = '/'; afterbuf[i++] = ','; break;}}LinkStack_Pop(LS);}LinkStack_Push(LS, 1);}else//如果链栈中也是‘+’‘-’则直接入栈LinkStack_Push(LS, 1);buf++;}if (*buf == '-'){if (LinkStack_Isempty(LS))//如果链栈为空，则直接将‘+’入栈LinkStack_Push(LS, 2);else if (LinkStack_Top(LS)> 2)//如果链栈的头结点上为‘*’‘/’，则栈中所有都弹出{while (!LinkStack_Isempty(LS))//直到将栈中的所有都弹出{if (LinkStack_Top(LS) == -1)//如果为'（'则停止循环{break;}else{switch (LinkStack_Top(LS)){case 1:afterbuf[i++] = '+'; afterbuf[i++] = ','; break;case 2:afterbuf[i++] = '-'; afterbuf[i++] = ','; break;case 3:afterbuf[i++] = '*'; afterbuf[i++] = ','; break;case 4:afterbuf[i++] = '/'; afterbuf[i++] = ','; break;}}LinkStack_Pop(LS);}LinkStack_Push(LS, 2);}else//如果链栈中也是‘+’‘-’则直接入栈LinkStack_Push(LS, 2);buf++;}if (*buf == '*')//如果为'*'直接入栈{LinkStack_Push(LS, 3);buf++;}if (*buf == '/')//如果为'/'直接入栈{LinkStack_Push(LS, 4);buf++;}if (*buf == '(')//如果为左括号则直接进栈{LinkStack_Push(LS, -1);buf++;}if (*buf == ')')//如果为右括号则出栈直到左括号{while (LinkStack_Top(LS) != -1){switch (LinkStack_Top(LS)){case 1:afterbuf[i++] = '+'; afterbuf[i++] = ','; break;case 2:afterbuf[i++] = '-'; afterbuf[i++] = ','; break;case 3:afterbuf[i++] = '*'; afterbuf[i++] = ','; break;case 4:afterbuf[i++] = '/'; afterbuf[i++] = ','; break;}LinkStack_Pop(LS);}LinkStack_Pop(LS);//最后把左括号给弹出来buf++;}}while (!LinkStack_Isempty(LS)){switch (LinkStack_Top(LS)){case 1:afterbuf[i++] = '+'; afterbuf[i++] = ','; break;case 2:afterbuf[i++] = '-'; afterbuf[i++] = ','; break;case 3:afterbuf[i++] = '*'; afterbuf[i++] = ','; break;case 4:afterbuf[i++] = '/'; afterbuf[i++] = ','; break;}LinkStack_Pop(LS);}return NULL;}int main(void){char* buf = (char*)malloc(sizeof(char));char afterbuf[1024] = {0};cin >> buf;change(buf,afterbuf);//中缀表达式转后缀表达式cout << afterbuf<<endl;system("pause");}//链栈的创建LinkStack* LinkStack_Create(){LinkStack* temp = NULL;temp = (LinkStack*)malloc(sizeof(LinkStack));if (temp == NULL)cout << "LinkStack_create 出错"<< endl;temp->count = 0;temp->top= NULL;return temp;}//链栈的清空status LinkStack_Clear(LinkStack* stack){if (stack == NULL)return ok;stack->top->next = NULL;stack->count = 0;return ok;}//链栈是否为空int LinkStack_Isempty(LinkStack* stack){if (stack == NULL)return error;return stack->top == NULL ? 1 : 0;}//链栈的长度int LinkStack_Length(LinkStack* stack){if (stack == NULL)return error;return stack->count;}//链栈的入栈status LinkStack_Push(LinkStack* stack, Elemtype e){if (stack == NULL)return error;LinkStack* temp = NULL;temp = (LinkStack*)stack;StackNodeP SNP = (StackNodeP)malloc(sizeof(StackNode));SNP->data = e;SNP->next = temp->top;temp->top = SNP;temp->count++;return ok;}//链栈的出栈Elemtype LinkStack_Pop(LinkStack* stack){if (stack == NULL)return error;LinkStack* temp = NULL;temp = (LinkStack*)stack;Elemtype node = temp->top->data;//这是将要删除的元素缓存下来StackNodeP p = temp->top;//将栈顶结点赋值给ptemp->top = temp->top->next;//栈顶指针下移一位，指向后一个结点free(p);//释放结点temp->count--;return node;}//链栈的头部元素Elemtype LinkStack_Top(LinkStack* stack){if (stack == NULL)return error;return stack->top->data;}

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