剑指Offer之 - 二叉树的深度

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题目：
1、求二叉树的最大深度和最小深度。
2、判断一棵二叉树是不是平衡二叉树。
代码：
#include <iostream>using namespace std;struct BinaryTreeNode{int m_nValue;BinaryTreeNode *m_pLeft;BinaryTreeNode *m_pRight;BinaryTreeNode(){}BinaryTreeNode(int value):m_nValue(value),m_pLeft(NULL),m_pRight(NULL){}};//功能：求二叉树的最大深度和最小深度int TreeDepthMax(BinaryTreeNode *pRoot){if(pRoot == NULL)return 0;int nLeft = TreeDepthMax(pRoot->m_pLeft);int nRight = TreeDepthMax(pRoot->m_pRight);return (nLeft > nRight) ? (nLeft + 1) : (nRight + 1);}int TreeDepthMin(BinaryTreeNode *pRoot){if(pRoot == NULL)return 0;if(pRoot->m_pLeft == NULL || pRoot->m_pRight == NULL)return 1;int nLeft = TreeDepthMin(pRoot->m_pLeft);int nRight = TreeDepthMin(pRoot->m_pRight);if(!pRoot->m_pLeft)//左为空，返回右+1return nRight + 1;if(!pRoot->m_pRight)//右为空，返回左+1return nLeft + 1;return (nLeft > nRight) ? nRight + 1 : nLeft + 1;//左右都不为空，返回小的+1}//功能：判断一棵树是不是平衡二叉树，即任意结点的左右子树的深度相差不超过1//思路1：求出每个结点的左右子树深度，然后再比较，效率较低bool IsBalanced(BinaryTreeNode *pRoot){if(pRoot == NULL)return true;int left = TreeDepthMax(pRoot->m_pLeft);int right = TreeDepthMax(pRoot->m_pRight);int diff = left - right;if(diff > 1 || diff < -1)return false;return IsBalanced(pRoot->m_pLeft) && IsBalanced(pRoot->m_pRight);}//思路2：记录下每个结点的深度，并作为形参传入//用从下至上遍历的方式遍历二叉树的每一个结点，在遍历到一个结点之前我们已经遍历了它的左右子树。只要在遍历每个结点的时候记录它的深度//我们就可以一边遍历一边判断每个结点是不是平衡的。bool IsBalancedTree(BinaryTreeNode *pRoot , int *depth){if(pRoot == NULL){*depth = 0;return true;}int left = 0 , right = 0;if(IsBalancedTree(pRoot->m_pLeft , &left) && IsBalancedTree(pRoot->m_pRight , &right)){int diff = left - right;if(diff <= 1 && diff >= -1){*depth = 1 + (left > right ? left : right);return true;}}return false;}bool IsBalancedTree(BinaryTreeNode *pRoot){int depth = 0;bool result = IsBalancedTree(pRoot , &depth);return result;}int main(){BinaryTreeNode *p1 = new BinaryTreeNode(1);BinaryTreeNode *p2 = new BinaryTreeNode(2);BinaryTreeNode *p3 = new BinaryTreeNode(3);BinaryTreeNode *p4 = new BinaryTreeNode(4);BinaryTreeNode *p5 = new BinaryTreeNode(5);p1->m_pLeft = p2;p1->m_pRight = p3;p3->m_pRight = p4;p4->m_pRight = p5;int depth = TreeDepthMax(p1);int minDepth = TreeDepthMin(p1);cout<<depth<<endl;cout<<minDepth<<endl;cout<<IsBalancedTree(p1)<<endl;cout<<IsBalanced(p1)<<endl;}
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