栈的使用之 表达式求值,如 1+1*(2-3 ) *(1- 3)

 表达式求值, 包括了中序表达式,后序表达式求值,

 

实现了中序转后序mid2post  ,中序转前序,算法基本相同

代码用将一个字符串式的中序表达式分解成 一个个的字符串, 保存在链表List 中

 

其中使用了List 链表,Stack 堆栈(自已进行了实现)  stack.h  list.h

 

 

#include<stdio.h> #include<stdlib.h> #include<string.h> #include<stack.h> #include<list.h> #define MAX 100 int operatorsLength=6; char operators[]={'+','-','*','/','(',')'}; //返回操作符的优先级 ,这个没用到 int priority(char oper){ if (oper=='+'||oper=='-'){ return 1; }else if (oper=='*'||oper=='/'){ return 2; }else if (oper==')'){ return 3; }else if (oper=='('){ return 0; } return 0; } int isOperatorByChar(char unit){ int i ; for(i=0;i<operatorsLength;i++){ char c1 =operators[i]; if (c1==unit){ return 1; } } return 0; } int isOperator(char* unit){ int i ; int len=strlen(unit); if (len==1){ for(i=0;i<operatorsLength;i++){ char c1 =operators[i]; if (c1==unit[0]){ return 1; } } } return 0; } /*获得下一个表达示单元,根把操作符切割 str 表达示 index 表达示的索引,表示从何处对表达示进行处理 return 下一个单元,同时调整index 的值,便 于下一个单元的切割 */ char* getNextExpUnit(char* str,int* index){ int i; int len= strlen(str); char *nextToken=(char*) malloc(len*sizeof(char)); int nextIndex=0; for(i=*index;i<len;i++){ char c =str[i]; *index=i+1; if (c==' '||c=='/t'){ continue; } if (isOperatorByChar(c)){ if (nextIndex!=0){ *index=i; nextToken[nextIndex]='/0'; return nextToken; }else{ nextToken[0]=c; nextToken[1]='/0'; return nextToken; } }else{ nextToken[nextIndex]=c; nextIndex++; } } return nextToken; } List getExpTokens(char* exp){ List tokens= list_create(); int index=0,*pi=&index; int len=strlen(exp); while(*pi<len){ list_add(tokens,getNextExpUnit(exp,pi)); } return tokens; } /* 计算 num1 + num2 */ void cal(double *num1,double *num2,char oper){ if (oper=='+') *num1=*num1+*num2; if (oper=='-') *num1=*num1-*num2; if (oper=='*') *num1=*num1*(*num2); if (oper=='/') *num1=*num1 / *num2; } //中序表达示求值, double* cal_mid_Fun(List mid){ //存操作符的栈 Stack opers= createStack(); //存操作数的栈 Stack nums= createStack(); int i ; for(i=0;i<list_sizeOf(mid);i++){//表示还没有遍历完表示达 char *cp=list_get_at(mid,i); if (isOperator(cp)){//如果是操作符 char oper=cp[0]; if (oper==')'){ char *oper2; do { double *d2=(double*)pop(nums); double *d1=(double*)pop(nums); char *oper1=(char*)pop(opers); oper2=(char*)peek(opers);//peek出堆栈里的顶层操作符,以便判断是不是( ,是的话就结束,否则继续进行运算 cal(d1,d2,oper1[0]); push(nums,d1); } while(oper2[0]!='(');//直到取出的下一个操作符是( ,结束运算 pop(opers);//pop 左括号 }else if (oper=='('){//如果是 * 或/ 或( push(opers,cp); }else { //如果是+-*/ int cur_priority=priority(oper); if (!isEmpty(opers)){//如果操作符栈非空, char *proOper= (char*)peek(opers); int pro_priority=priority(proOper[0]); if (pro_priority>=cur_priority){//如果优先级相等或者栈里的优先级高 ,先做栈里的运算,再将当前操作符入栈,注意到最后,所有东西入栈后,运算顺序从栈底开始, double *d2=(double*)pop(nums); double *d1=(double*)pop(nums); cal(d1,d2,proOper[0]); push(nums,d1); char *oper3=(char*)pop(opers); } } push(opers,cp); } } else{ double *dp=(double*)malloc(sizeof(double)); *dp=strtod(cp,NULL); push(nums,dp); } } while (!isEmpty(opers)){ double *d2=(double*)pop(nums); double *d1=(double*)pop(nums); char *oper3=(char*)pop(opers); cal(d1,d2,oper3[0]); push(nums,d1); } double *d= (double*)pop(nums); free(opers); free(nums); return d; } //中 //前序表达式求值+/abc 读取方式 ,从右向左,遇数入栈,遇符取栈中两数计算 // (a/b)+c double* cal_pro_Fun(List pro_tokens){ list_inverse(pro_tokens);//倒序pro_tokens ,便于从右向左读取 int i ; Stack nums= createStack(); for(i=0;i<list_sizeOf(pro_tokens);i++){ char *token=list_get_at(pro_tokens,i); if (isOperator(token)){ double *num1=(double*)pop(nums); double *num2=(double*)pop(nums); cal(num1,num2,token[0]); push(nums,num1); }else{ double *num=(double*)malloc(sizeof(double)); *num=strtod(token,NULL); push(nums,num); } } double* result=(double*)pop(nums); freeStack(nums); return result; //List tokens= getExpTokens(exp); } double* cal_post_Fun(List post_tokens){ int i ; Stack nums= createStack(); for(i=0;i<list_sizeOf(post_tokens);i++){ char *token=list_get_at(post_tokens,i); if (isOperator(token)){ double *num2=(double*)pop(nums); double *num1=(double*)pop(nums); cal(num1,num2,token[0]); push(nums,num1); }else{ double *num=(double*)malloc(sizeof(double)); *num=strtod(token,NULL); push(nums,num); } //free(token); } double* result=(double*)pop(nums); freeStack(nums); return result; //List tokens= getExpTokens(exp); } //1 + 2 * ( 2 + 2 - 6 ) //1 2 2 2 + 6 - * + //中序表达式转后序表达式 List mid2post(List mid){ Stack opers= createStack(); List post=list_create(); int i =0; for(i=0;i<list_sizeOf(mid);i++){//表示还没有遍历完表示达 char *cp=list_get_at(mid,i); if (isOperator(cp)){//如果是操作符 char oper=cp[0]; if (oper==')'){ char *oper2=(char*)pop(opers); do { list_add(post,oper2); oper2=(char*)pop(opers); } while(oper2[0]!='('); }else if (oper=='('){//如果是 * 或/ 或( push(opers,cp); }else { //如果是+-* / int cur_priority=priority(oper); if (!isEmpty(opers)){//如果操作符栈非空, char *proOper= (char*)peek(opers); int pro_priority=priority(proOper[0]); if (pro_priority>=cur_priority){ list_add(post,proOper); pop(opers); } } push(opers,cp); } } else{ list_add(post,cp); } } while(!isEmpty(opers)){ char* oper=pop(opers); list_add(post,oper); } freeStack(opers); return post; } int main(){ int i ; char* exp="1+2*(2+2-6)"; puts(exp); List mid=getExpTokens(exp); for(i=0;i<list_sizeOf(mid);i++){ printf("%s ",(char*)list_get_at(mid,i)); } double *d=cal_mid_Fun(mid); printf("/nresult=%f/n ",*d); List post=mid2post(getExpTokens(exp)); for(i=0;i<list_sizeOf(post);i++){ printf("%s ",(char*)list_get_at(post,i)); } //d=cal_post_Fun(post); printf("/nresult=%f/n ",*d); list_free(mid); list_free(post); } 

 

 

stack.h

typedef void *Void; struct StackNode{ Void ele ; struct StackNode *next; }; typedef struct StackNode NodeClass; typedef NodeClass *Node; struct StackStruct{ Node n; int top; }; typedef struct StackStruct StackClass; typedef StackClass *Stack; Stack createStack(); int isEmpty(Stack s); int sizeS(Stack s); Stack push (Stack s ,Void ele); Void pop(Stack s ); Void peek(Stack s ); void freeStack(Stack s);

 

list.h

typedef void* Void; struct ListStructNode{ Void ele; struct ListStructNode *next; }; typedef struct ListStructNode ListNodeClass; typedef ListNodeClass *ListNode; struct ListStruct{ int size; ListNode nodes; }; typedef struct ListStruct ListClass; typedef ListClass *List; List list_create(); void list_merge_at(List headList ,int index ,List tailList); void list_append(List headList, List tailList); void list_delete_at(List list ,int index); void list_delete_last(List list ); void list_inverse (List list ); void list_add_at (List list ,Void ele,int index ); void list_add (List list ,Void ele ); void list_modify_at (List list ,Void ele ,int index ); int list_sizeOf(List list); Void list_get_at(List list,int index); Void list_get_last(List list); void list_free(List list);

 

stack的实现#include<stdio.h> #include<stdlib.h> #include<stack.h> /* 这一次的修改更具用通过性， 因为这里定义了一个 typedef void *Void 所以下面出现Void 的时个相当于void* 类型的， 而void* 类型的指针可以转换为任意类型， 所以 无论是结构体，还是普通的int float 类型的指针，都可以往里放 */ Stack createStack(){ Stack s ; s =(Stack)malloc(sizeof(StackClass)); s->top=-1; return s; } int isEmpty(Stack s){ return s->top ==-1; } int sizeS(Stack s){ return (s->top)+1; } Node getNode(Node n,int index ){ if (n==NULL||index==-1){ return NULL; } int i; Node tmp=n; for(i=0;i<index;i++){ tmp=tmp->next; } return tmp; } Node getLastNodeButOne(Stack s ){ int top=s->top; if (top<1){//保证s 至少有两个节点,lastButOne 才会有值 return NULL; } return getNode(s->n,top-1); } Node getLastNode(Stack s ){ return getNode(s->n,s->top); } Stack push (Stack s ,Void ele){ if (s->n==NULL){ Node root =malloc(sizeof(NodeClass)); s->n=root; root->ele=ele; root->next=NULL; s->top++; return s; } Node lastNode=getLastNode(s); Node newNode= (Node)malloc(sizeof(NodeClass)); newNode->ele=ele; newNode->next=NULL; lastNode->next=newNode; s->top++; return s; } Void peek(Stack s ){ if (s->top==-1){ return NULL; } Node lastNode=getLastNode(s); return lastNode->ele ; } Void pop(Stack s ){ if (s->top==-1){ s->n=NULL; return NULL; }else if (s->top==0){ Void ele= s->n->ele; free(s->n); s->n=NULL; s->top--; return ele; } Node n = s->n; Node lastNodeButOne=getLastNodeButOne(s); Node last=lastNodeButOne->next; lastNodeButOne->next=NULL; s->top--; Void ele=last->ele; free(last); return ele ; } void freeStack(Stack s){ while(!isEmpty(s)){ Void ele= pop(s); free(ele); } free(s); } /* int main(){ Stack s =createStack(); int i =231; int *p; p=&i; push(s,p); int j=23; p=&j; push(s,p); p=peek(s); printf("%d/n",*p); p=pop(s); printf("%d,%d/n",*p,sizeS(s)); p=pop(s); printf("%d,%d/n",*p,sizeS(s)); } */ 

 

List 的实现#include<stdio.h> #include<stdlib.h> #include<list.h> /**get last node */ ListNode getLastListNode(ListNode head){ if (head==NULL){ return NULL; } if (head->next==NULL){ return head; } ListNode n=head; while (n->next!=NULL){ n=n->next; } return n; } ListNode getListNode(ListNode head,int index){ if(index<0||head==NULL){ return NULL; } ListNode n=head; int i=0; while (n!=NULL){ if (i==index){ return n; } n=n->next; i++; } return NULL; } int sizeOfListNode(ListNode listNode){ if (listNode==NULL){ return 0; } ListNode n =listNode; int i =0; while (n!=NULL){ i++; n=n->next; } return i; } ListNode createNewNode(Void ele){ ListNode newNode=(ListNode)malloc(sizeof(ListNodeClass)); if (newNode==NULL) return ; newNode->next=NULL; newNode->ele=ele; return newNode; } ListNode mergeListNodeAt(ListNode head ,int index ,ListNode tail){ if (head==NULL) return tail ; ListNode nLast=getLastListNode(tail); if (index==-1){ nLast->next=head; return tail; } ListNode indexListNode = getListNode(head,index); if (indexListNode==NULL){ //index 越界, ListNode headLastNode=getLastListNode(head); headLastNode->next=tail; return head; } ListNode nextListNode=indexListNode->next; indexListNode->next=tail; nLast->next=nextListNode; return head; } /* add the list n to head at heat.index position , when index=-1 means append head to n */ List list_create(){ List list=(List)malloc(sizeof(ListClass)); if (list!=NULL){ list->size=0; list->nodes=NULL; } return list; } void list_merge_at(List headList ,int index ,List tailList){ if(tailList==NULL||headList==NULL) return; ListNode head=headList->nodes; ListNode n=tailList->nodes; ListNode nLast=getLastListNode(n); if (index==-1){ nLast->next=head; headList->size+=tailList->size; headList->nodes=n; return ; } ListNode indexListNode = getListNode(head,index); if (indexListNode==NULL){ //为NULL 有两种情况,一种是head==NULL, 另一种是index 越界, if (head==NULL){//如果head 是NULL, 则返回n ,相当于head 原本的长度为0, headList->size=tailList->size; headList->nodes=n; return ; }else{//另一种是index 越界, 则直接将n添加到head 末尾 ListNode headLastNode=getLastListNode(head); headList->size+=tailList->size; headLastNode->next=n; return ; } } ListNode nextListNode=indexListNode->next; indexListNode->next=n; nLast->next=nextListNode; headList->size+=tailList->size; return; } void list_append(List headList, List tailList){ if (headList==NULL) headList=tailList; list_merge_at(headList,headList->size-1,tailList); } void list_delete_at(List list ,int index){ ListNode head=list->nodes; if(index<0||list==NULL||list->size==0){ return ; } if(index==0){ ListNode next=head->next; head->next=NULL; free(head->ele); free(head); list->nodes=next; list->size--; return ; } ListNode pro= getListNode(head,index-1); if(pro==NULL){//如果index 越界,则不删除任何元素 return ; } ListNode n= pro->next; if (n!=NULL){ pro->next=n->next; n->next=NULL; free(n->ele); free(n); list->size--; } } void list_delete_last(List list ){ list_delete_at(list,list->size-1); } void list_inverse (List list ){ ListNode p =list->nodes; ListNode pro=NULL ,next; if (p!=NULL){ next= p->next; } while (p!=NULL){ p->next= pro; pro=p; p=next; if (next!=NULL){ next= next->next; } } list->nodes=pro; } void list_add_at (List list ,Void ele,int index ){ ListNode node=list->nodes; ListNode newNode= createNewNode(ele); list->nodes= mergeListNodeAt(list->nodes ,index,newNode); list->size++; } void list_add (List list ,Void ele ){ list_add_at(list,ele,list->size-1); } void list_modify_at (List list ,Void ele ,int index ){ ListNode listNode=list->nodes; if (listNode==NULL||index<0){ return ; } ListNode indexNode=getListNode(listNode,index); if (indexNode!=NULL){ free(indexNode->ele); indexNode->ele=ele; return ; } return ; } Void list_get_at(List list,int index){ ListNode head=list->nodes; ListNode node=getListNode(head,index); if (node==NULL) return NULL; return node->ele; } Void list_get_last(List list){ ListNode lastNode= getLastListNode(list->nodes); if (lastNode==NULL){ return NULL; } return lastNode->ele; } int list_sizeOf(List list){ return list->size; } void list_free(List list){ ListNode n,head=list->nodes; while (head!=NULL){ n=head; head=head->next; n->next=NULL; free(n->ele); free(n); } free(list); } /* int main(){ List list=list_create(); printf("size=%d/n",list_sizeOf(list)); int i ; for(i=0;i<10;i++){ int *j =(int*)malloc(sizeof(int)) ; *j=i; list_add(list,j); } for(i=0;i<list_sizeOf(list);i++){ int *j=list_get_at(list,i); printf("j=%d/n",*j); } printf("size=%d/n",list_sizeOf(list)); list_delete_at(list,0); list_delete_at(list,3); list_delete_last(list); for(i=0;i<list_sizeOf(list);i++){ int *j=list_get_at(list,i); printf("j=%d/n",*j); } printf("size=%d/n",list_sizeOf(list)); list_free(list); list=NULL; list=list_create(); List list2=list_create(); for(i=0;i<10;i++){ int *j =(int*)malloc(sizeof(int)) ; *j=i; list_add(list,j); list_add(list2,j); } //list_merge_at(list,9,list2); list_append(list,list2); for(i=0;i<list_sizeOf(list);i++){ int *j=list_get_at(list,i); printf("j=%d/n",*j); } printf("size=%d/n",list_sizeOf(list)); list_inverse(list); for(i=0;i<list_sizeOf(list);i++){ int *j=list_get_at(list,i); printf("j=%d/n",*j); } int *q= list_get_last(list); printf("%d/n",*q); q= list_get_at(list,2); printf("%d/n",*q); } */