写得时候思路还是很清晰的，所以没花费多久便基本实现了，不过过程还是遇到一些bug。
版本1：
#include <iostream>
#include <algorithm>
#include <stack>
#include <string>
using namespace std;
class tree {
public:
char val;
tree * leftchild;
tree * rightchild;
};
class ExpressionTree {
public:
void build_expression(tree * & root, string str);
void proorder_print(tree * root);
void inorder_print(tree * root);
void postorder_print(tree * root);
void show(tree * root);
void destory(tree * & root);
};
void ExpressionTree::build_expression(tree * & root, string str)
{
stack<tree *> treestack;
for (auto c : str)
{
tree*node = new tree;
node->val = c;
node->leftchild = nullptr;
node->rightchild = nullptr;
if (c >= ‘0‘ && c <= ‘9‘ || c >= ‘a‘ && c <= ‘z‘)
treestack.push(node);
else if (c == ‘+‘ || c == ‘-‘ || c == ‘*‘ || c == ‘/‘)
{
if (!treestack.empty())
{
node->rightchild = treestack.top();
treestack.pop();
}
if (!treestack.empty())
{
node->leftchild = treestack.top();
treestack.pop();
}
treestack.push(node);
}
else
{
cout << "表达式有误!" << endl;
exit(1);
}
}
root = treestack.top();
while (!treestack.empty())
treestack.pop();
}
void ExpressionTree::proorder_print(tree * root)
{
if (root != nullptr)
{
cout << root->val;
proorder_print(root->leftchild);
proorder_print(root->rightchild);
}
}
void ExpressionTree::inorder_print(tree * root)
{
if (root != nullptr)
{
cout << ‘(‘;
inorder_print(root->leftchild);
cout << root->val;
inorder_print(root->rightchild);
cout << ‘)‘;
}
}
void ExpressionTree::postorder_print(tree * root)
{
if (root != nullptr)
{
postorder_print(root->leftchild);
postorder_print(root->rightchild);
cout << root->val;
}
}
void ExpressionTree::show(tree * root)
{
cout << "前缀表达式:" << endl;
proorder_print(root);
cout << endl;
cout << "中缀表达式:" << endl;
inorder_print(root);
cout << endl;
cout << "后缀表达式:" << endl;
postorder_print(root);
cout << endl;
}
void ExpressionTree::destory(tree * & root)
{
if (root != nullptr)
{
destory(root->leftchild);
destory(root->rightchild);
delete root;
}
}
int main()
{
string str = "23+456+**";
ExpressionTree res;
tree * root;
res.build_expression(root, str);
res.show(root);
res.destory(root);
getchar();
return 0;
}
版本2：
#include <iostream>
#include <algorithm>
#include <stack>
#include <string>
using namespace std;
class tree {
public:
char val;
tree * leftchild;
tree * rightchild;
};
class ExpressionTree {
public:
tree * root;
ExpressionTree()
{
this->root = new tree;
}
~ExpressionTree()
{
destory(this->root);
}
void insert(char c, stack<tree *> & treestack);
void build_expression(string str);
void proorder_print(tree * root);
void inorder_print(tree * root);
void postorder_print(tree * root);
void show();
void destory(tree * root);
};
void ExpressionTree::insert(char c, stack<tree *> & treestack)
{
tree*node = new tree;
node->val = c;
node->leftchild = nullptr;
node->rightchild = nullptr;
if (c >= ‘0‘ && c <= ‘9‘)
treestack.push(node);
else if (c == ‘+‘ || c == ‘-‘ || c == ‘*‘ || c == ‘/‘)
{
try {
node->rightchild = treestack.top();
treestack.pop();
node->leftchild = treestack.top();
treestack.pop();
}
catch (overflow_error) {
cout << "表达式有误!";
exit(1);
}
treestack.push(node);
}
else
{
cout << "表达式有误!" << endl;
exit(1);
}
}
void ExpressionTree::build_expression(string str)
{
stack<tree *> treestack;
for (auto s : str)
insert(s, treestack);
this->root = treestack.top();
while (!treestack.empty())
treestack.pop();
}
void ExpressionTree::proorder_print(tree * root)
{
if (root != nullptr)
{
cout << root->val;
proorder_print(root->leftchild);
proorder_print(root->rightchild);
}
}
void ExpressionTree::inorder_print(tree * root)
{
if (root != nullptr)
{
cout << ‘(‘;
inorder_print(root->leftchild);
cout << root->val;
inorder_print(root->rightchild);
cout << ‘)‘;
}
}
void ExpressionTree::postorder_print(tree * root)
{
if (root != nullptr)
{
postorder_print(root->leftchild);
postorder_print(root->rightchild);
cout << root->val;
}
}
void ExpressionTree::show()
{
cout << "前缀表达式:" << endl;
proorder_print(this->root);
cout << endl;
cout << "中缀表达式:" << endl;
inorder_print(this->root);
cout << endl;
cout << "后缀表达式:" << endl;
postorder_print(this->root);
cout << endl;
}
void ExpressionTree::destory(tree * root)
{
if (root != nullptr)
{
destory(root->leftchild);
destory(root->rightchild);
delete root;
}
}
int main()
{
string str = "23+456+**";
ExpressionTree res;
res.build_expression(str);
res.show();
getchar();
return 0;
}
基本思路：建立树的方式类似由下而上建立堆的办法，所以时间复杂度为O(n)，这样算法就会变得很简单，只用考虑处理栈中的节点即可。好像也没什么好说的了。
