判断一个二叉树是否是平衡二叉树

题目：判断一个二叉排序树是否是平衡二叉树

思路:利用递归判断左右子树的深度是否相差1来判断是否是平衡二叉树。

#include<stdio.h>  2 #include "stdafx.h"  3   4 struct BinaryTreeNode  5 {  6     int              m_nValue;  7     BinaryTreeNode*  m_pLeft;  8     BinaryTreeNode*  m_pRight;  9 }; 10  11 BinaryTreeNode* CreateBinaryTreeNode(int value) 12 { 13     BinaryTreeNode* pNode = new BinaryTreeNode(); 14     pNode->m_nValue = value; 15     pNode->m_pLeft = NULL; 16     pNode->m_pRight = NULL; 17 } 18  19 void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight) 20 { 21     if(pParent != NULL) 22     { 23         pParent->m_pLeft = pLeft; 24         pParent->m_pRight = pRight; 25     } 26 } 27  28 void PrintTreeNode(BinaryTreeNode* pNode) 29 { 30     if(pNode != NULL) 31     { 32         printf("value of this node is: %d\n", pNode->m_nValue); 33          34         if(pNode->m_pLeft != NULL) 35             printf("value of its left child is: %d.\n", pNode->m_pLeft->m_nValue); 36         else 37             printf("left child is null.\n"); 38          39         if(pNode->m_pRight != NULL) 40             printf("value of its right child is: %d.\n",pNode->m_pRight->m_nValue); 41         else 42             printf("right child is null.\n"); 43     } 44     else 45     { 46         printf("this node is null.\n"); 47     } 48     printf("\n"); 49 } 50  51 void PrintTree(BinaryTreeNode* pRoot) 52 { 53     PrintTreeNode(pRoot); 54      55     if(pRoot != NULL) 56     { 57         if(pRoot->m_pLeft != NULL) 58             PrintTree(pRoot->m_pLeft); 59          60         if(pRoot->m_pRight != NULL)  61             PrintTree(pRoot->m_pRight); 62     } 63 } 64  65 void DestroyTree(BinaryTreeNode* pRoot) 66 { 67     if(pRoot != NULL) 68     { 69         BinaryTreeNode* pLeft = pRoot->m_pLeft; 70         BinaryTreeNode* pRight = pRoot->m_pRight; 71          72         delete pRoot; 73         pRoot = NULL; 74          75         DestroyTree(pLeft); 76         DestroyTree(pRight); 77     } 78 } 79  80  81 //========================方法1============================== 82 int TreeDepth(BinaryTreeNode* pRoot) 83 { 84     if(pRoot == NULL) 85         return 0; 86      87     int nLeft = TreeDepth(pRoot->m_pLeft); 88     int nRight = TreeDepth(pRoot->m_pRight); 89      90     return (nLeft > nRight) ? (nLeft + 1) : (nRight + 1); 91 } 92  93 bool IsBalanced_Solution1(BinaryTreeNode* pRoot) 94 { 95     if(pRoot == NULL) 96         return true; 97      98     int left = TreeDepth(pRoot->m_pLeft); 99     int right = TreeDepth(pRoot->m_pRight);100     int diff = left - right;101     if(diff > 1 || diff < -1)102         return false;103     104     return IsBalanced_Solution1(pRoot->m_pLeft)105         && IsBalanced_Solution1(pRoot->m_pRight);106 }107 108 //=====================方法2===========================109 bool IsBalanced(BinaryTreeNode* pRoot, int* pDepth);110 111 bool IsBalanced_Solution2(BinaryTreeNode* pRoot)112 {113     int depth = 0;114     return IsBalanced(pRoot, &depth);115 }116 117 bool IsBalanced(BinaryTreeNode* pRoot, int* pDepth)118 {119     if(pRoot == NULL)120     {121         *pDepth = 0;122         return true;123     }124     125     int left, right;126     if(IsBalanced(pRoot->m_pLeft, &left)127         && IsBalanced(pRoot->m_pRight, &right))128     {129         int diff = left - right;130         if(diff <= 1 && diff >= -1)131         {132             *pDepth = 1+ (left > right ? left : right);133             return true;134         }135     }136     137     return false;138 }139 140 // 不是完全二叉树，但是平衡二叉树141 //             1142 //         /      \143 //        2        3144 //       /\         \145 //      4  5         6146 //        /147 //       7148 149 int main()150 {151     BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);152     BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);153     BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);154     BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);155     BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);156     BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);157     BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);158 159     ConnectTreeNodes(pNode1, pNode2, pNode3);160     ConnectTreeNodes(pNode2, pNode4, pNode5);161     ConnectTreeNodes(pNode3, pNode6, pNode7);162     163     printf("Solution1 begins: ");164      if(IsBalanced_Solution1(pNode1))165          printf("is balanced.\n");166      else167          printf("not balanced.\n");168      169      printf("Solution2 begins: ");170      if(IsBalanced_Solution2(pNode1))171          printf("is balanced.\n");172      else173          printf("not balanced.\n");174      printf("\n");175      176      DestroyTree(pNode1);177      178     return 0;179 }180