Problem：
实现二叉树的先序、中序、后序遍历，包括递归方式和非递归方式
Solution：
切记递归规则：
先遍历根节点，然后是左孩子，右孩子，
根据不同的打印位置来确定中序、前序、后续遍历。
Code:
1 #pragma once 2 #include <iostream> 3 #include <vector> 4 #include <queue> 5 #include <stack> 6 #include <string> 7 #include <sstream> 8 9 10 using namespace std; 11 12 13 struct Node 14 { 15 int val; 16 Node* lchild; 17 Node* rchild; 18 Node(int a = -1) :val(a), lchild(NULL), rchild(NULL) {} 19 }; 20 21 void Create1(Node*& root, vector<int>num, int i)//前序构造树 22 { 23 if (num[i] < 0) 24 root = NULL; 25 else if (i < num.size()) 26 { 27 root = new Node(num[i]); 28 Create1(root->lchild, num, i + 1); 29 Create1(root->rchild, num, i + 1); 30 } 31 } 32 33 void Create2(Node*& root, vector<int>num)//层序构造树 34 { 35 queue<Node*>q; 36 root = new Node(num[0]); 37 q.push(root); 38 int i = 1; 39 while (i < num.size() && !q.empty()) 40 { 41 Node* p = q.front(); 42 q.pop(); 43 if (!p)//空节点p 44 break; 45 if(num[i]>0) 46 p->lchild = new Node (num[i++]); 47 if(num[i]>0) 48 p->rchild = new Node (num[i++]); 49 q.push(p->lchild); 50 q.push(p->rchild); 51 } 52 } 53 54 void PreTravel(Node* root)//前序遍历 55 { 56 if (!root) 57 return; 58 cout << root->val << " "; 59 PreTravel(root->lchild); 60 PreTravel(root->rchild); 61 } 62 63 void NotPreTravel(Node* root)//非递归前序遍历 64 { 65 stack<Node*>s; 66 if (root) 67 { 68 s.push(root); 69 while (!s.empty()) 70 { 71 root = s.top(); 72 cout << root->val << " "; 73 s.pop(); 74 if (root->rchild) 75 s.push(root->rchild); 76 if (root->lchild) 77 s.push(root->lchild); 78 } 79 } 80 } 81 82 void MidTravel(Node* root)//中序遍历 83 { 84 if (!root) 85 return; 86 87 MidTravel(root->lchild); 88 cout << root->val << " "; 89 MidTravel(root->rchild); 90 } 91 92 void NotMidTravel(Node* root)//非递归中序遍历 93 { 94 stack<Node*>s; 95 if (root) 96 { 97 while (!s.empty() || root) 98 { 99 if (root) 100 { 101 s.push(root); 102 root = root->lchild; 103 } 104 else 105 { 106 root = s.top(); 107 s.pop(); 108 cout << root->val << " "; 109 root = root->rchild; 110 } 111 } 112 } 113 } 114 115 116 117 void LastTravel(Node* root)//后序遍历 118 { 119 if (!root) 120 return; 121 LastTravel(root->lchild); 122 LastTravel(root->rchild); 123 cout << root->val << " "; 124 } 125 126 void NotLastTravel(Node* root)//非递归后序遍历 127 { 128 stack<Node*>s1; 129 stack<Node*>s2; 130 if (root) 131 { 132 s1.push(root); 133 while (!s1.empty()) 134 { 135 root = s1.top(); 136 s1.pop(); 137 s2.push(root); 138 if (root->lchild) 139 s1.push(root->lchild); 140 if(root->rchild) 141 s1.push(root->rchild); 142 } 143 while (!s2.empty()) 144 { 145 root = s2.top(); 146 s2.pop(); 147 cout << root->val << " "; 148 } 149 } 150 } 151 152 void NotLastTravel2(Node* root)//非递归后序遍历,使用一个栈 153 { 154 stack<Node*>s; 155 if (root) 156 { 157 s.push(root); 158 Node* p; 159 while (!s.empty()) 160 { 161 p = s.top(); 162 if (p->lchild && root != p->lchild && root != p->rchild) 163 s.push(p->lchild); 164 else if (p->rchild && root != p->rchild ) 165 s.push(p->rchild); 166 else 167 { 168 cout << p->val << " "; 169 s.pop(); 170 root = p; 171 } 172 } 173 174 } 175 } 176 177 178 179 180 string getSpace(int num) 181 { 182 string space = " "; 183 for (int i = 0; i < num; ++i) 184 space.append(" "); 185 return space; 186 } 187 188 void PrintShape(Node* root, int h, string c, int len) 189 { 190 if (root) 191 { 192 PrintShape(root->rchild, h + 1, "v", len); 193 string val; 194 stringstream ss; 195 ss << root->val; 196 ss >> val; 197 val = c + val + c; 198 int lenM = val.length(); 199 int lenL = (len - lenM) / 2; 200 int lenR = len - lenM - lenL; 201 val = getSpace(lenL) + val + getSpace(lenR); 202 cout << getSpace(h*len) + val << endl; 203 PrintShape(root->lchild, h + 1, "^", len); 204 } 205 206 } 207 208 //直观地打印一颗树，即打印一横向的树，每个节点的左上角节点为其父节点 209 void PrintTree(Node* root) 210 { 211 cout << "The shape of tree is: " << endl; 212 cout << "===============================================" << endl; 213 PrintShape(root, 0, "H", 17); 214 cout << "===============================================" << endl; 215 } 216 217 218 219 void Test() 220 { 221 //我们使用多种方法来构造一颗树： 222 // 1 223 // 2 3 224 // 4 5 6 7 225 // 8 9 10 11 12 N N NULL 226 // 使用层序遍历来打印树 227 228 Node* root1 = NULL; 229 vector<int>num1 = { 1,2,4,8,9,5,10,11,3,6,12,-1,7,-1,-1 }; 230 Create1(root1, num1, 0);//前序构造树 231 232 Node* root2 = NULL; 233 vector<int>num2 = { 1,2,3,4,5,6,7,8,9,10,11,12,-1,-1,-1}; 234 Create2(root2, num2);//层序构造树 235 236 237 cout << endl << "==============前序遍历============" << endl; 238 PreTravel(root2);//前序遍历 239 240 cout << endl << "===============中序遍历=============" << endl; 241 MidTravel(root2);//中序遍历 242 243 cout << endl << "===============后序遍历============" << endl; 244 LastTravel(root2);//后序遍历 245 246 cout << endl << "===============非递归前序遍历============" << endl; 247 NotPreTravel(root2);//非递归前序遍历 248 249 cout << endl << "===============非递归中序遍历============" << endl; 250 NotMidTravel(root2);//非递归中序遍历 251 252 cout << endl << "===============非递归后序遍历============" << endl; 253 NotLastTravel2(root2);//非递归后序遍历 254 255 cout << endl << "===============打印树============" << endl; 256 PrintTree(root2); 257 258 int a = 1; 259 260 261 262 }