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Algorithm/Graph/Tree/表达式树/后缀分治.cpp

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+#include <iostream>
+#include <string>
+using namespace std;
+
+template <class T> 
+struct Node{
+	T element;
+	Node<T>* left;
+	Node<T>* right;
+	
+	Node() : element(-1), left(nullptr), right(nullptr) {}
+	Node(T x) : element(x), left(nullptr), right(nullptr) {}
+};
+
+template <class T>
+struct Tree{
+	Node<T>* root;
+	
+	Tree() : root(nullptr) {}
+	Tree(Node<T>* x) : root(x) {}
+	void inOrder(Node<T>* x){
+		if(!x) return;
+		inOrder(x->left);
+		cout << x->element << " ";
+		inOrder(x->right);
+	}
+	void preOrder(Node<T>* x){
+		if(!x) return;
+		cout << x->element << " ";
+		preOrder(x->left);
+		preOrder(x->right);
+	}
+	void postOrder(Node<T>* x){
+		if(!x) return;
+		postOrder(x->left);
+		postOrder(x->right);
+		cout << x->element << " ";
+	}
+};
+
+bool checky(char s){
+	if(s == '+' || s == '-' || s == '*' || s == '/') return true;
+	return false; 
+}
+
+int checkb(char s){
+	if(s == '(') return 1;
+	if(s == ')') return -1;
+	return 0;
+}
+
+//[x, y)
+template <class T> 
+Node<T>* build(const string& s, const int& x, const int& y){
+    if ((y - x) == 1) return new Node<T>(s[x]);
+
+    // ȥ<><C8A5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+    if (s[x] == '(' && s[y-1] == ')') {
+        int cnt = 0; bool ok = true;
+        for (int i = x; i < y; i++) {
+            if (s[i] == '(') cnt++;
+            if (s[i] == ')') cnt--;
+            if (cnt == 0 && i < y-1) { ok = false; break; }
+        }
+        if (ok) return build<T>(s, x+1, y-1);
+    }
+
+    // <20><><EFBFBD><EFBFBD>ɨ<EFBFBD>裺<EFBFBD><E8A3BA> +-<2D><><EFBFBD><EFBFBD> */
+    for (int pass = 0; pass < 2; pass++) {
+        int js = 0;
+        for (int i = y-1; i >= x; i--) {
+            js += checkb(s[i]);
+            if (checky(s[i]) && js == 0) {
+                if ((pass == 0 && (s[i] == '+' || s[i] == '-')) ||
+                    (pass == 1 && (s[i] == '*' || s[i] == '/'))) {
+                    Node<T>* tmp = new Node<T>(s[i]);
+                    tmp->right = build<T>(s, i+1, y);
+                    tmp->left  = build<T>(s, x, i);
+                    return tmp;
+                }
+            }
+        }
+    }
+
+    return nullptr;
+}
+
+int main(){
+	string a;
+	cin >> a;
+	Node<char>* root = build<char>(a, 0, a.size());
+	Tree<char> t(root); 
+	t.preOrder(root);
+	cout << endl; 
+	t.inOrder(root);
+	cout << endl; 
+	t.postOrder(root);
+	cout << endl; 
+	return 0;
+}