利用樹求解算術表達式的值

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#include <stdio.h>
#include <string.h>
#include <malloc.h>
//#include "btree.h"
#define MaxSize 100
#include<stdlib.h>
typedef struct Node
{
?? ?char data;
?? ?struct Node *lchild;
?? ?struct Node *rchild;
}BTNode,*BTree;
//用s[i]到s[j]之間的字符串，構造二叉樹的表示形式
BTNode *CreateTree(char s[],int i,int j)
{
?? ?BTNode *p;
?? ?int k,plus=0,posi;
?? ?if (i==j) //i和j相同，意味著只有一個字符，構造的是一個葉子節點
?? ?{
?? ??? ?p=(BTNode *)malloc(sizeof(BTNode)); //分配存儲空間
?? ??? ?p->data=s[i]; //值為s[i]
?? ??? ?p->lchild=NULL;
?? ??? ?p->rchild=NULL;
?? ??? ?return p;
?? ?}
?? ?//以下為i!=j的情況
?? ?for (k=i; k<=j; k++)
?? ??? ?if (s[k]=='+' || s[k]=='-')
?? ??? ?{
?? ??? ??? ?plus++;
?? ??? ??? ?posi=k; //最后一個+或-的位置
?? ??? ?}
?? ??? ?if (plus==0) //沒有+或-的情況(因為若有+、-，前面必會執行plus++)
?? ??? ??? ?for (k=i; k<=j; k++)
?? ??? ??? ??? ?if (s[k]=='*' || s[k]=='/')
?? ??? ??? ??? ?{
?? ??? ??? ??? ??? ?plus++;
?? ??? ??? ??? ??? ?posi=k;
?? ??? ??? ??? ?}
?? ??? ??? ??? ?//以上的處理考慮了優先將+、-放到二叉樹較高的層次上
?? ??? ??? ??? ?//由于將來計算時，運用的是后序遍歷的思路
?? ??? ??? ??? ?//處于較低層的乘除會優先運算
?? ??? ??? ??? ?//從而體現了“先乘除后加減”的運算法則
?? ??? ??? ??? ?//創建一個分支節點，用檢測到的運算符作為節點值
?? ??? ??? ??? ?if (plus!=0)
?? ??? ??? ??? ?{
?? ??? ??? ??? ??? ?p=(BTNode *)malloc(sizeof(BTNode));
?? ??? ??? ??? ??? ?p->data=s[posi]; //節點值是s[posi]
?? ??? ??? ??? ??? ?p->lchild=CreateTree(s,i,posi-1); //左子樹由s[i]至s[posi-1]構成
?? ??? ??? ??? ??? ?p->rchild=CreateTree(s,posi+1,j); //右子樹由s[poso+1]到s[j]構成
?? ??? ??? ??? ??? ?return p;
?? ??? ??? ??? ?}
?? ??? ??? ??? ?else //若沒有任何運算符，返回NULL
?? ??? ??? ??? ??? ?return NULL;
}

int find_split(char express[], int start, int end)
{
?? ?int tag = -1;

?? ?if (express[start] == '(' && express[end] == ')')
?? ?{
?? ??? ?++start;
?? ??? ?--end;
?? ?}

?? ?int is_in_braket = 0;
?? ?int more_grade = 0;
?? ?for (int i = start; i <= end; i++)
?? ?{
?? ??? ?if (express[i] == '(')
?? ??? ??? ?++is_in_braket;
?? ??? ?else if (express[i] == ')')
?? ??? ??? ?--is_in_braket;

?? ??? ?if ((express[i] == '+' || express[i] == '-')
?? ??? ??? ?&& is_in_braket == 0)
?? ??? ?{
?? ??? ??? ?more_grade = 1;
?? ??? ??? ?tag = i; //無break, 找最后一個符合條件的運算符, 取頂級的+和-
?? ??? ?}
?? ??? ?else if ((express[i] == '*' || express[i] == '/')
?? ??? ??? ?&& more_grade == 0
?? ??? ??? ?&& is_in_braket == 0)
?? ??? ?{
?? ??? ??? ?tag = i; //無break, 找最后一個符合條件的運算符
?? ??? ?}
?? ?}
?? ?return tag;
}

BTree Creat_Btree( char *express, int start, int end)
{
?? ?BTree pTree = NULL;

?? ?if (start == end)
?? ?{
?? ??? ?pTree = (BTree)malloc(sizeof(BTNode));
?? ??? ?pTree->data = express[start];
?? ??? ?pTree->lchild = NULL;
?? ??? ?pTree->rchild = NULL;
?? ?}
?? ?else
?? ?{ ? //遞歸調用, 各自創建左右的表達式的對應二叉樹
?? ??? ?int tag = find_split(express, start, end);
?? ??? ?if (tag < 0)
?? ??? ?{
?? ??? ??? ?printf("1.invalid express, exit.\n");
?? ??? ??? ?exit(-1);
?? ??? ?}
?? ??? ?else
?? ??? ?{
?? ??? ??? ?pTree = (BTree)malloc(sizeof(BTNode));
?? ??? ??? ?pTree->data = express[tag];
?? ??? ?}
?? ??? ?if (express[start] == '(' && express[end] == ')')
?? ??? ?{
?? ??? ??? ?++start;
?? ??? ??? ?--end;
?? ??? ?}
?? ??? ?pTree->lchild = Creat_Btree(express, start, tag - 1);
?? ??? ?pTree->rchild = Creat_Btree(express, tag + 1, end);
?? ?}
?? ?return pTree;
}
double post_traverser_calc(BTree pTree)
{
?? ?if (pTree == NULL)
?? ??? ?return -1;
?? ?else if ('0' <= pTree->data &&pTree->data <= '9')
?? ??? ?return pTree->data - '0';
?? ?else if(pTree->data=='+')
?? ??? ?return post_traverser_calc(pTree->lchild) + post_traverser_calc(pTree->rchild);
?? ?else if(pTree->data=='-')
?? ??? ?return post_traverser_calc(pTree->lchild) - post_traverser_calc(pTree->rchild);
?? ?else if(pTree->data=='*')
?? ??? ?return post_traverser_calc(pTree->lchild) * post_traverser_calc(pTree->rchild);
?? ?else if(pTree->data=='/')
?? ??? ?return post_traverser_calc(pTree->lchild) / post_traverser_calc(pTree->rchild);
}

double CalcuValue(BTNode *b)
{
?? ?double v1,v2;
?? ?if (b==NULL)
?? ??? ?return 0;
?? ?if (b->lchild==NULL && b->rchild==NULL) //葉子節點，應該是一個數字字符（本項目未考慮非法表達式）
?? ??? ?return b->data-'0'; //葉子節點直接返回節點值，結點中保存的數字用的是字符形式，所以要-'0'
?? ?v1=CalcuValue(b->lchild); //先計算左子樹
?? ?v2=CalcuValue(b->rchild); //再計算右子樹
?? ?switch(b->data) //將左、右子樹運算的結果再進行運算，運用的是后序遍歷的思路
?? ?{
?? ?case '+':
?? ??? ?return v1+v2;
?? ?case '-':
?? ??? ?return v1-v2;
?? ?case '*':
?? ??? ?return v1*v2;
?? ?case '/':
?? ??? ?if (v2!=0)
?? ??? ??? ?return v1/v2;
?? ??? ?else
?? ??? ??? ?abort();
?? ?}
}
void TreePrint(BTree T,int level)?
/*按樹狀打印的二叉樹*/?
{ ??
? ? int i;
? ? if(T==NULL)?? ??? ??? ??? ??? ?/*如果指針為空，返回上一層*/?
? ? ? ? return;
? ? TreePrint(T->rchild,level+1);/*打印右子樹，并將層次加1*/?
? ? for(i=0;i<level;i++)?? ??? ??? ?/*按照遞歸的層次打印空格*/?
? ? ? ? printf(" ? ");
? ? printf("%c\n",T->data);?? ??? ?/*輸出根結點*/?
? ? TreePrint(T->lchild,level+1);/*打印左子樹，并將層次加1*/?
}
void DestroyBTree(BTree *T)
/*銷毀二叉樹操作*/
{
?? ?if(*T) ?? ??? ??? ??? ??? ??? ??? ?/*如果是非空二叉樹*/
?? ?{
?? ??? ?if((*T)->lchild)
?? ??? ??? ?DestroyBTree(&((*T)->lchild));
?? ??? ?if((*T)->rchild)
?? ??? ??? ?DestroyBTree(&((*T)->rchild));
?? ??? ?free(*T);
?? ??? ?*T=NULL;
?? ?}
}
int main()
{
?? ?BTNode *b;
?? ?char s[MaxSize]="1+2*3-4/5";
?? ?printf("算術表達式%s\n",s);
?? ?/*
?? ?b=CreateTree(s,0,strlen(s)-1);

?? ?printf("對應二叉樹:\n");
?? ?TreePrint(b,0);
?? ?printf("\n表達式的值:%g\n",CalcuValue(b));
?? ?DestroyBTree(&b);
?? ?*/

?? ?double result=0;
?? ?BTree express_tree = Creat_Btree(s, 0, strlen(s)-1);
?? ?result=post_traverser_calc(express_tree);
?? ?printf("后綴表達式：");
?? ?post_traverser_calc(express_tree);
?? ?printf("\n");
?? ?printf("表達式結果為：%.2f\n", result);

?? ?return 0;
}

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