1 #include<stdio.h>  2 #include "stdlib.h"  3 #include<iostream>  4 #include<stack>  5 #include<queue>  6 using namespace std;  7   8 //节点定义  9 typedef struct biNode{ 10     char val; 11     biNode* left; 12     biNode* right; 13 }biNode; 14  15 //创建一棵树 16 void createBiTree(biNode* &root){ 17     char c; 18     cin >> c; 19     if(c == ‘#‘){ 20         root = NULL; 21     }else{ 22        if( !(root = (biNode*)malloc(sizeof(biNode))) ) exit(OVERFLOW); //分配存储空间 23        root->val = c;       24        //生成根节点 25        createBiTree(root->left);            //生成左子树 26        createBiTree(root->right);           //生成右子树 27     } 28 } 29  30 //前序遍历（根左右）递归 31 void preSeqOrderRec(biNode *root){ 32     if(root == NULL){ 33         return ; 34     } 35     printf("%c ",root->val); 36     preSeqOrderRec(root->left); 37     preSeqOrderRec(root->right); 38 } 39  40 //前序遍历（根左右）非递归 41 void preSeqOrderNoRec(biNode *root){ 42     if(root == NULL) 43         return; 44     stack<biNode*> st; 45     while(root || !st.empty()){ 46         while(root){ 47             st.push(root); 48             printf("%c ",root->val); 49             root = root->left; 50         } 51         root = st.top(); 52         st.pop(); 53         root = root->right; 54     } 55 } 56  57 //中序遍历（左根右）递归 58 void inSeqOrderRec(biNode *root){ 59     if(root == NULL){ 60         return ; 61     } 62     inSeqOrderRec(root->left); 63     printf("%c ",root->val); 64     inSeqOrderRec(root->right); 65 } 66  67 //中序遍历（左根右）非递归 68 void intSeqOrderNoRec(biNode *root){ 69     if(root == NULL) 70         return; 71     stack<biNode*> st; 72     while(root || !st.empty()){ 73         while(root){ 74             st.push(root); 75             root = root->left; 76         } 77         root = st.top(); 78         st.pop(); 79         printf("%c ",root->val); 80         root = root->right; 81     } 82 } 83  84 //后序遍历（左右根）递归 85 void postSeqOrderRec(biNode *root){ 86     if(root == NULL){ 87         return ; 88     } 89     postSeqOrderRec(root->left);     90     postSeqOrderRec(root->right); 91     printf("%c ",root->val); 92 } 93  94 //后序遍历（左右根）非递归 95 void postSeqOrderNoRec(biNode *root){ 96     if(root == NULL){ 97         return ; 98     } 99     stack<biNode*> st;100     biNode* p;101     p = root;102     do103     {104        while (p){//左子树进栈105         st.push(p);106         p = p->left;107        }108        while (!st.empty() && st.top()->right == p){109         p = st.top();    //栈顶结点出栈110         st.pop();111         printf("%c ",p->val);112        }113        if (!st.empty())114         p = st.top()->right; //开始遍历右子树115     }while(!st.empty());116 }117 118 //层序遍历119 void levelSeqVisit(biNode *root){120     if(root == NULL)121         return ;122     queue<biNode*> que;123     que.push(root);124     biNode *p;125     while(!que.empty()){126         p = que.front();127         que.pop();128         printf("%c ",p->val);129         if(p->left)130             que.push(p->left);131         if(p->right)132             que.push(p->right);133     }134 }135 136 //所有节点个数137 int getNodeCount(biNode* root){138     if(root == NULL)139         return 0;140     int count = 1;141     count += getNodeCount(root->left);142     count += getNodeCount(root->right);143     return count;144 }145 146 //得到叶子节点个数147 int getLeafCount(biNode* root){148     if(root == NULL)149         return 0;150     int count = 0;151     if(root->left == NULL && root->right == NULL){152         count ++;153     }else{154         count += getLeafCount(root->left);155         count += getLeafCount(root->right);156     }157     return count;158 }159 160 //树的高度161 int getDepth(biNode *root){162     if(root == NULL)163         return 0;164     int leftDepth = getDepth(root->left);165     int rightDepth = getDepth(root->right);166     return leftDepth>rightDepth ? (leftDepth+1) : (rightDepth+1);167 }168 169 //某节点所在层次170 int getLevelByNode(biNode *root,char toFind,int &count){171     172     if(root==NULL || toFind==NULL)173         return 0;174     if(root->val == toFind ){175         count++;176         return 1;177     }178     if(getLevelByNode(root->left,toFind,count) || getLevelByNode(root->right,toFind,count)){179         count++;180         return 1;181     }182 183     return 0;184 }185 186 //是否为平衡树187 bool isBalanceTree(biNode* root){188     if(root == NULL)189         return false;190     int leftDepth  = getDepth(root->left);191     int rightDepth = getDepth(root->right);192     if(leftDepth-rightDepth>1 || rightDepth-leftDepth<-1)193         return false;194     return true;195 }196 197 //是否为平衡树（优化版）198 bool isBalanceTreeOptimize(biNode* root, int* Depth){199     if(root == NULL){200         *Depth = 0;201         return true;202     }203     int left=0,right=0;204     if(isBalanceTreeOptimize(root->left,&left) && isBalanceTreeOptimize(root->right,&right)){205         int diff = left - right;206         if(diff<=1 && diff>=-1){207             *Depth = 1 + (left>right ? left : right);208             return true;209         }210     }211     return false;212 }213 214 //是否为完全二叉树215 bool isCompleteTree(biNode *root){216     queue<biNode*> que;217     que.push(root);218     biNode* p;219     bool isFirstLeaf = false;220     while(!que.empty()){221         p = que.front();222         que.pop();223         //第一个叶子节点224         if(p->left==NULL && p->right==NULL){225             isFirstLeaf = true;226         }227         bool LOrR  = p->left != NULL || p->right != NULL;228         bool LAndR = p->left != NULL && p->right != NULL; 229         //第一个叶子节点之后的节点，都是叶子节点230         if(isFirstLeaf && LOrR){231             return false;232         }233         //第一个叶子之前的节点，都有两个孩子234         if(!isFirstLeaf && !LAndR){235             return false;236         }237         if(p->left != NULL)238             que.push(p->left);239         if(p->right != NULL)240             que.push(p->right);241     }242     return true;243 }244 245 //是否满二叉树246 bool isFullTree(biNode* root){247     if(root==NULL){248         return true;249     }250     int lDepth = getDepth(root->left);251     int rDepth = getDepth(root->right);252     int diff = lDepth - rDepth;253     if(diff==0 && isFullTree(root->left) && isFullTree(root->right)){254         return true;255     }256     return false;257 }258 259 int main(){260      biNode* T;261      262      //ab#c##d##263      printf("\n创建树:\n"); 264      createBiTree(T);265      266      printf("\n前序遍历（递归）：\n");267      preSeqOrderRec(T);268      printf("\n前序遍历（非递归）：\n");269      preSeqOrderNoRec(T);270 271      printf("\n中序遍历（递归）：\n");272      inSeqOrderRec(T);273      printf("\n中序遍历（非递归）：\n");274      intSeqOrderNoRec(T);275 276      printf("\n后序遍历（递归）：\n");277      postSeqOrderRec(T);278      printf("\n后序遍历（非递归）：\n");279      postSeqOrderNoRec(T);280 281      282      printf("\n节点数为：\n%d",getNodeCount(T));283      printf("\n叶子节点数为：\n%d",getLeafCount(T));284 285      printf("\n树的高度为：\n%d",getDepth(T));286 287      printf("\n层序遍历：\n");288      levelSeqVisit(T);289 290      int level = 0 ;291      getLevelByNode(T,‘d‘,level);292      printf("\n某个节点所在层次：\n%d",level);293 294      printf("\n是否为平衡数：%d\n",isBalanceTree(T));295 296      int depth = 0;297      bool isBanlance = isBalanceTreeOptimize(T,&depth);298      printf("\n是否为平衡树优化版：%d,且高度为：%d\n",isBanlance,depth);299 300      printf("\n是否为完全二叉树：%d\n",isCompleteTree(T));301 302      printf("\n是否为满二叉树：%d\n",isFullTree(T));303 304      printf("\n");305 }