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0.1#xff09;本文旨在总结出表达式树的构建步骤#xff0c; 其中还涉及到中缀转后缀表达式#xff0c;以及如何计算 表达式树中的值#xff1b; 0.2#xff09;本文源代码均为原创#xff1b; 0.3#xff09; 其实#xff0c; 实现一个简单的计算器本文旨在总结出表达式树的构建步骤 其中还涉及到中缀转后缀表达式以及如何计算 表达式树中的值 0.2本文源代码均为原创 0.3 其实 实现一个简单的计算器 也即求出中缀表达式的值我们也可以用栈来实现 参见 http://blog.csdn.net/pacosonswjtu/article/details/49225529 此处给出 表达式树的实现 仅在于加深对表达式树的理解及它的应用 【1】表达式树的相关概念
1.1定义表达式树的树叶是 操作数operand比如常量或变量而其他节点是操作符 operator 1.2对上图中的表达式进行遍历先序中序后序
先序遍历 a * b c * * d e f g中序遍历 a b * c d * c f * g 这里要加上括号 这也是我们为什么要采用 后缀或逆波兰记法 来表示 用户输入的运算表达式 以计算结果 一句话方便可靠后序遍历 a b c * d e * f g * Attention这里我们没有给出源代码因为这个先序后序 or 中序 的源代码和二叉树遍历的源代码相差无几这里只是了解下 表达式树的概念并了解下用 树的遍历计算 表达式的值
【2】如何构造一颗表达式树表达式树的定义很关键对于写我们的递归程序而言
我们给出一种算法将后缀表达式转变为 表达式树
step1用户输入中缀表达式 我们首先将其转为后缀表达式step2我们将后缀表达式转为 表达式树的形式step3我们来计算该表达式树的计算结果是多少
2.1 ) download source code: https://github.com/pacosonTang/dataStructure-algorithmAnalysis/tree/master/chapter4/p71_compute_expr_tree 2.2 ) source code at a glance:
2.2.1expr_tree.c source code :
#include stack.h
#include binary_tree.hextern void infir_to_postfix();
extern int computeResult(int operand1, int operand2, int operator_);
extern ElementType compute_postfix();
extern Stack operand;
extern int isOperator(char ch);
extern int computeResult(int operand1, int operand2, int operator_);// building an expr tree for storing postfix expr
BinaryTree postfixToExprTree()
{ int value; BinaryTree* treeArray; int size;int index;ElementType *p;int i ;size getTopOfStack(operand) 1; //get the top of stack, and add 1 to compute size of the stacktreeArray (BinaryTree*)malloc(size * sizeof(BinaryTree)); // alloc memory for treeArrayindex 0; // set the index of treeArray 0 p getArray(operand);i 0;while(i getTopOfStack(operand)){value *(pi);if(value ) // if the value equals , continue continue;treeArray[index] createBinaryTree(value);// for every element need to build tree nodeif(isOperator(value)) // if the value belongs to operator, { index--; insertNode(treeArray[index-1], treeArray[index], 0); insertNode(treeArray[index-2], treeArray[index], 1);treeArray[index-2] treeArray[index];index --;} // (treeArrayindex) createBinaryTree(value);// if the value belongs to operand, push the element into the treeArray}return *treeArray;
}// preorder the tree
void printPreorder(int depth, BinaryTree root)
{ int i;if(root) { for(i 0; i depth; i)printf( ); printf(%c\n, root-value);printPreorder(depth 1, root-left); printPreorder(depth 1, root-right); // Attention: theres difference between traversing binary tree and common tree }else {for(i 0; i depth; i)printf( ); printf(NULL\n);}
}// postordering expression tree with operantors and operands to compute the result of these nodes
int postorder_compute_postfix_expr_tree(BinaryTree root)
{ int temp1;int temp2;if(isOperator(root-value)) { temp1 postorder_compute_postfix_expr_tree(root-left); temp2 postorder_compute_postfix_expr_tree(root-right); // Attention: theres difference between traversing binary tree and common tree return computeResult(temp1, temp2, root-value);}else return root-value - 48;
}int main()
{ BinaryTree bt;// 1.convert infix into postfix exprprintf(\n convert infix into postfix expr \n);infir_to_postfix(); // after this func is called over, we get the postfix of the expr// 2.convert postfix into the expression tree bt postfixToExprTree();printPreorder(1, bt); //3.compute postfix expr stored in the expression treeprintf(the final result is : %2d \n, postorder_compute_postfix_expr_tree(bt));return 0;
}
2.2.2binary_tree.c source code :
#include binary_tree.h// create a BinaryTree with root node
BinaryTree createBinaryTree(TreeElementType value)
{ BinaryTree t;t (BinaryTree)malloc(sizeof(struct BinaryTree));if(!t) {Error(out of space, from func createBinaryTree); return NULL;} t-left NULL;t-right NULL; t-value value;return t;
}// make the BinaryTree empty
BinaryTree makeTreeEmpty(BinaryTree t)
{if(t){makeTreeEmpty(t-left);makeTreeEmpty(t-right); free(t);} return NULL;
}//insert a Tree node with value e into left child or right child of the parent
BinaryTree insert(TreeElementType e, BinaryTree parent, int isLeft)
{ BinaryTree node;if(!parent){Error(for parent BinaryTree node is empty , you cannot insert one into the parent node, from func insert); return NULL;}node (BinaryTree)malloc(sizeof(struct BinaryTree));if(!node) {Error(out of space, from func insert); return NULL;}node-value e;node-right NULL;node-left NULL;// building the node with value e overif(isLeft) { // the tree node inserting into left child of the parent if(parent-left) {Error(for parent has already had a left child , you cannot insert one into the left child, from func insert); return NULL; }parent-left node;}else { // the tree node inserting into right child of the parent if(parent-right) {Error(for parent has already had a right child , you cannot insert one into the right child, from func insert); return NULL; }parent-right node;} return node;
}//insert a Tree node into left child or right child of the parent
BinaryTree insertNode(BinaryTree node, BinaryTree parent, int isLeft)
{ if(!parent){Error(for parent BinaryTree node is empty , you cannot insert one into the parent node, from func insert); return NULL;}if(!node) {Error(for the node inserted is NULL , so you cannot insert a NULL node, from func insert); return NULL;} if(isLeft) // the tree node inserting into left child of the parent parent-left node; else // the tree node inserting into right child of the parent parent-right node; return node;
}// find the BinaryTree root node with value equaling to e
BinaryTree find(TreeElementType e, BinaryTree root)
{BinaryTree temp;if(root NULL)return NULL;if(root-value e)return root;temp find(e, root-left); if(temp) return temp;elsereturn find(e, root-right);
}// analog print directories and files name in the BinaryTree, which involves postorder traversal.
void printPostorder(int depth, BinaryTree root)
{ int i;if(root) { printPostorder(depth 1, root-left); printPostorder(depth 1, root-right); // Attention: theres difference between traversing binary tree and common treefor(i 0; i depth; i)printf( ); printf(%c\n, root-value); }else {for(i 0; i depth; i)printf( ); printf(NULL\n);}
}
2.2.3stack.h source code :
#include stdio.h
#include malloc.h#define ElementType int
#define EmptyStack -1
#define Error(str) printf(%s,str)
#define FatalError(str) printf(%s,str)
#define minStackSize 5struct Stack;
typedef struct Stack *Stack;int isFull(Stack s);
int isEmpty(Stack s);
Stack createStack(int);
void disposeStack(Stack s);
void makeEmpty(Stack s);
void push(ElementType e, Stack s);
ElementType top(Stack s);
void pop(Stack s);
ElementType top(Stack s);
int getTopOfStack(Stack s);
ElementType *getArray(Stack s);void printStack(Stack s);
void printStack_postfix(Stack s);struct Stack {int capacity;int topOfStack;ElementType *array;
} ;
2.2.4binary_tree.h source code :
#include stdio.h
#include malloc.h#define TreeElementType char
#define Error(str) printf(%s,str) struct BinaryTree;
typedef struct BinaryTree *BinaryTree;BinaryTree createBinaryTree(TreeElementType); // this func is different from that in p70_preorder_binary_tree.c
BinaryTree makeTreeEmpty(BinaryTree);
BinaryTree insert(TreeElementType, BinaryTree, int);
BinaryTree insertNode(BinaryTree, BinaryTree, int);
BinaryTree find(TreeElementType, BinaryTree);
void printPostorder(int depth, BinaryTree root);// we adopt child-sibling notation
struct BinaryTree
{TreeElementType value;BinaryTree left;BinaryTree right;
};
2.2.5stack.c source code :
#include stack.hint getTopOfStack(Stack s)
{return s-topOfStack;
}//return stacks array
ElementType *getArray(Stack s)
{return s-array;
}//judge whether the stack is empty or not
int isFull(Stack s)
{return s-capacity - 1 s-topOfStack ? 1 : 0;
}//judge whether the stack is empty or not
int isEmpty(Stack s)
{return s-topOfStack -1;
}//create stack with the head node
Stack createStack(int size)
{Stack s;s (Stack)malloc(sizeof(struct Stack));if(size minStackSize) {Error(stack size is too small, and creating stack with defualt size 5); size minStackSize;}if(s NULL) {FatalError(out of space when allocting memory for stack s);return NULL;}s-array (ElementType *)malloc(size * sizeof(ElementType)); if(s-array NULL) {FatalError(out of space when allocting memory for stacks array );return NULL;}s-topOfStack -1;s-capacity size; return s;
}//dispose stack
void disposeStack(Stack s)
{free(s-array);free(s);
}//pop all elements in the stack
void makeEmpty(Stack s)
{if(s-topOfStack -1)Error(must create the stack first);while(!isEmpty(s))pop(s);
}//push the node with value e into the stack s
//attend that first moving ptr ,then executing push operation
void push(ElementType e, Stack s)
{ElementType *temp s-array;if(isFull(s))Error(the Stack is full, push failure! ); else{s-topOfStack ;s-array[s-topOfStack] e; }
}// pop the node or element on the top of stack
//attend that first executing pop operation,then moving ptr
void pop(Stack s)
{if(isEmpty(s))Error(empty stack);else s-topOfStack --;
}// return the value of the top node in the stack
ElementType top(Stack s)
{if(!isEmpty(s)) return s-array[s-topOfStack];Error(the stack is empty from func top\n);return -1;
}//print value of element in the stack s
void printStack(Stack s)
{int i;if(isEmpty(s)){Error(empty stack);return ;}for(i0; i s-topOfStack; i) printf(%4d, s-array[i]);printf(\n);
}//print value of element in the stack s with postfix
void printStack_postfix(Stack s)
{int i;if(isEmpty(s)){Error(empty stack);return ;}printf(stack elements list: );for(i0; i s-topOfStack; i) printf(%c, s-array[i]);printf(\n);
}
2.2.6compute_postfix.c source code :
#include stack.h#define Size 100// refer to p50.c and put it into the same project
extern struct Stack;
typedef struct Stack *Stack;extern Stack operand; // operand is an extern variable defined in infixToPostfix
extern int isOperator(char ch);
extern void infir_to_postfix();
int computeResult(int operand1, int operand2, int operator_);int computeResult(int operand1, int operand2, int operator_)
{switch(operator_){case : return operand1 operand2;case *: return operand1 * operand2;default: return 0; break;}
}// compute final result of responding postfix
ElementType compute_postfix()
{Stack output;int i;ElementType *p;int value;int operand1;int operand2;output createStack(Size); // create stack with length Sizei 0;p getArray(operand); // get operand-arraywhile(i getTopOfStack(operand)){value *(pi);if(value )continue;if(isOperator(value)){operand1 top(output);pop(output);operand2 top(output);pop(output);value computeResult(operand1, operand2, value);push(value, output);continue;}push(value - 48, output);}return getArray(output)[0];
}
2.2.7infixToPostfix.c source code :
#include stack.h#define Size 100// refer to p50.c and put it into the same project
extern struct Stack;
typedef struct Stack *Stack;
Stack operand; // declaration of Stack operand
int isOperator(char ch);
void infir_to_postfix();//compare operators priority between ch1 and ch2, return -1, 0 or 1
int priorityBigger(char ch1, char ch2)
{int size 8;char operator_[]{ (, ), , , -, , *, /};int index1, index2;int i;if(ch1 - ch2 0)return 0;for(i 0; i size; i)if(operator_[i] ch1)index1 i; else if(operator_[i] ch2)index2 i; index1 - index2;if(index1 1 || index1 -1) return 0;else if(index1 1)return 1;else if(index1 -1)return -1;
}//judge whether the ch is operator or not ,also 1 or 0
int isOperator(char ch)
{int size;char operator_[]{(, , -, *, /, )};int i;size 6;for(i 0; i size; i)if(ch operator_[i])break;return i size ? 0 : 1;
}//convert a part of str with length len into responding element value
ElementType strToElement(int *str, int len)
{int i;int value;i value 0;while(i len){value *(stri) - 48;if(i len)break;value * 10;}return value;
}// convert infix expr into postfix expr
//for operand and operator cannot be in the same type ,we treat them as char and split them with space
void infixToPostfix(Stack s1, Stack s2,char *expr)
{char ch; int i;char top_t; int flag; i 0; flag 0; while((ch *(expri)) ! \0) { if(ch )){// if ch equals ), pop elements in stack s2 between ( and ) into stack s1while((top_t top(s2)) ! ( ) { push(top_t, s1);push( , s1);pop(s2);} pop(s2); // pop ( in stack s2 continue;}if(isOperator(ch)) // isOperator is true { if(ch () {push(ch, s2); // push ( into operator stack s2flag 1;continue;} while((top_t top(s2)) ! -1 priorityBigger(top_t, ch) 0 flag 0) { pop(s2); push(top_t, s1);push( , s1); } push(ch, s2); // push operator into operator stack s2 flag 0;}else {push(ch, s1); push( , s1); // we treat them as char and split them with space}}// pop element in s2 and push it into s1while(!isEmpty(s2)) { push(top(s2), s1);push( , s1);pop(s2);}
}// read expr from console till \n and we just only focus on and *;
// postfix expression like 6 5 2 3 8 * 3 *
char *read()
{char *temp;int len; char ch;temp (char*)malloc(Size * sizeof(char));len 0; while((ch getchar()) ! \n) { if(ch )continue;temp[len] ch; }temp[len] \0;return temp;
} // there are 2 stacks, thats operand and operator;
//works list
//1.read expr, 2.convert the expr from infix to postfix, 3./*
int main()
{ Stack operand;Stack operator_;operand createStack(Size);operator_ createStack(Size);// convert infix into postfix exprinfixToPostfix(operand, operator_, read()); printStack_postfix(operand);// compute postfix exprreturn 0;
}
*/void infir_to_postfix()
{ Stack operator_;//create stack operand and operator_operand createStack(Size);operator_ createStack(Size);// convert infix into postfix exprinfixToPostfix(operand, operator_, read()); printStack_postfix(operand);
}
