剑指offer 39 - 二叉树的深度

1.先遍历二叉树的左子树的深度，然后再遍历二叉树右子树的深度。最后判断左子树和右子树的深度，如果左子树比右子树深则返回左子树深度+1,否则返回右子树深度+1。

2.判断该树是不是平衡树，我们用后序遍历的方式遍历整棵二叉树。在遍历某结点的左右子结点之后，我们可以根据它的左右子结点的深度判断它是不是平衡的，并得到当前结点的深度。当最后遍历到树的根结点的时候，也就判断了整棵二叉树是不是平衡二叉树了。

#include <iostream>
#include<vector>
using namespace std;

struct	BinaryTreeNode
{
int	m_nValue;
BinaryTreeNode*		m_pLeft;
BinaryTreeNode*		m_pRight;
};

BinaryTreeNode* CreateBinaryTreeNode(int	value)
{
BinaryTreeNode	*head = new  BinaryTreeNode[sizeof(BinaryTreeNode )];
head->m_nValue = value;
head->m_pLeft = head->m_pRight	=	NULL;

return head;
}

void ConnectTreeNodes(BinaryTreeNode*    root ,BinaryTreeNode*   left, BinaryTreeNode*   right)
{
if(root != NULL)
{
root->m_pLeft = left;
root->m_pRight = right;
}
}

void DestroyTree(BinaryTreeNode*    root)
{
if(root !=NULL)
{
BinaryTreeNode* left = root->m_pLeft;
BinaryTreeNode* right= root->m_pRight;

delete root;
root=NULL;
DestroyTree(left);
DestroyTree( right);
}
}

bool  isBalanced(BinaryTreeNode* pRoot,int *depth)     //节点深度作为参数，一边遍历一边判断是否平衡
{
if(pRoot==NULL)
{
*depth=0;
return  true;
}
int left,right;
if( isBalanced(pRoot->m_pLeft,&left)   &&	isBalanced(pRoot->m_pRight,&right) )
{
int diff = left - right;
if(diff <= 1 && diff >= -1)  //此处不能写（-1<=diff<=1），错误
{
*depth = left>right ? (left+1) :(right+1);
return true;
}
}
return false;
}

int  TreeDepth(BinaryTreeNode* pRoot)    //节点深度  后序遍历
{
if(pRoot==NULL)
return 0;

int nLeft= TreeDepth(pRoot->m_pLeft);
int     nRight= TreeDepth(pRoot->m_pRight);

return  nLeft>nRight ? (nLeft+1) :(nRight+1);

}
bool IsBalanced(BinaryTreeNode* pRoot)    //方法2. 需要重复遍历节点多次
{
if(pRoot== NULL)
return true;

int nLeftDepth = TreeDepth(pRoot->m_pLeft);
int nRightDepth = TreeDepth(pRoot->m_pRight);
int diff = nRightDepth-nLeftDepth;

if (diff>1 || diff<-1)
return false;

return IsBalanced(pRoot->m_pLeft)&&IsBalanced(pRoot->m_pRight);
}

// ====================测试代码====================
void Test(char* testName, BinaryTreeNode* pRoot,bool result)
{
if(testName != NULL)
printf("%s begins:", testName);

int depth = 0;
if(result ==  isBalanced(pRoot,&depth))
printf("%s\n","passed");
else
printf("%s\n","failed");

printf("\n");
}

//            1
//         /      \
//        2        3
//       / \         \
//      4  5     	    6
//			   \
//				7
void Test1()
{
BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);

ConnectTreeNodes(pNode1, pNode2, pNode3);
ConnectTreeNodes(pNode2, pNode4, pNode5);
ConnectTreeNodes(pNode3, NULL, pNode6);
ConnectTreeNodes(pNode5, NULL, pNode7);

Test("Test1", pNode1,true);

DestroyTree(pNode1);
}

//               1
//              /
//             2
//            /
//           3
//          /
//         4
//        /
//       5
void Test2()
{
BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);

ConnectTreeNodes(pNode1, pNode2, NULL);
ConnectTreeNodes(pNode2, pNode3, NULL);
ConnectTreeNodes(pNode3, pNode4, NULL);
ConnectTreeNodes(pNode4, pNode5, NULL);

Test("Test2",pNode1, false);

DestroyTree(pNode1);
}

// 1
//  \
//   2
//    \
//     3
//      \
//       4
//        \
//         5
void Test3()
{
BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);

ConnectTreeNodes(pNode1, NULL, pNode2);
ConnectTreeNodes(pNode2, NULL, pNode3);
ConnectTreeNodes(pNode3, NULL, pNode4);
ConnectTreeNodes(pNode4, NULL, pNode5);

Test("Test3",pNode1, false);

DestroyTree(pNode1);
}

// 树中只有1个结点
void Test4()
{
BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
Test("test4",pNode1, true);

DestroyTree(pNode1);
}

// 树中没有结点
void Test5()
{
Test("Test5",NULL,true);
}

int main(int argc, char* argv[])
{
Test1();
Test2();
Test3();
Test4();
Test5();

return 0;
}