/*题目1：输入一棵二叉树的结点，求该树的深度。从根节点到叶节点依次经过的结点（含根、叶结点）形成树的一条路径，最长路径的长度为树的深度*//*题目2：输入一棵二叉树的根结点，判断该树是不是平衡二叉树。如果某二叉树中任意结点的左右子树的深度相差不超过1，那么它就是一棵平衡二叉树。*/#include <iostream>using namespace std;//定义一个二叉树结点struct BinaryTreeNode{ int m_nValue; BinaryTreeNode *m_pLeft; BinaryTreeNode *m_pRight;};//创建一个二叉树结点BinaryTreeNode *CreateBinaryTreeNode(int Value){ BinaryTreeNode *pNode = new BinaryTreeNode; pNode -> m_nValue = Value; pNode -> m_pLeft = NULL; pNode -> m_pRight = NULL; return pNode;}//创建二叉树void ConnectBinaryTreeNode(BinaryTreeNode *pRoot, BinaryTreeNode *pLeft, BinaryTreeNode *pRight){ pRoot -> m_pLeft = pLeft; pRoot -> m_pRight = pRight;}//释放二叉树空间void DestroyBinaryTreeNode(BinaryTreeNode *pRoot){ if(pRoot) { DestroyBinaryTreeNode(pRoot -> m_pLeft); DestroyBinaryTreeNode(pRoot -> m_pRight); delete pRoot; }}//计算二叉树的深度int BinaryTreeDepth(BinaryTreeNode *pRoot){ if(pRoot == NULL) return 0; int Left = BinaryTreeDepth(pRoot -> m_pLeft); int Right = BinaryTreeDepth(pRoot -> m_pRight); return 1 + (Left > Right ? Left : Right);}//判断二叉树是不是平衡二叉树bool IsBalancedBinaryTree(BinaryTreeNode *pRoot, int *pDepth){ //递归退出条件，同时存储对应结点的二叉树深度 if(pRoot == NULL) { *pDepth = 0; return true; } int Left = 0; int Right = 0; //递归判断是否符合平衡二叉树的条件，同时存储二叉树深度(后序遍历二叉树) if(IsBalancedBinaryTree(pRoot -> m_pLeft, &Left) && IsBalancedBinaryTree(pRoot -> m_pRight, &Right)) { int dif = Left - Right; if(dif <= 1 && -1 <= dif) { *pDepth = 1 + (Left > Right ? Left : Right); return true; } } return false;}//重载二叉树判断函数，同时传入相应参数bool IsBalancedBinaryTree(BinaryTreeNode *pRoot){ int pDepth = 0; return IsBalancedBinaryTree(pRoot, &pDepth);}//========================测试代码========================void Test(char *TestName, BinaryTreeNode *pRoot, int ExpectedDepth, bool ExpectedResult){ if(TestName != NULL) cout << TestName << " begins:" << endl; if(BinaryTreeDepth(pRoot) == ExpectedDepth) cout << "Depth Passed!" << endl; else cout << "Depth Failed!" << endl; if(IsBalancedBinaryTree(pRoot) == ExpectedResult) cout << "Test Passed!" << endl; else cout << "Test Failed!" << endl;}//完全二叉树// 1// / \// 2 3// / \ / \// 4 5 6 7void 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); ConnectBinaryTreeNode(pNode1, pNode2, pNode3); ConnectBinaryTreeNode(pNode2, pNode4, pNode5); ConnectBinaryTreeNode(pNode3, pNode6, pNode7); Test("Test1", pNode1, 3, true); DestroyBinaryTreeNode(pNode1);}//不是完全二叉树,但是平衡二叉树// 1// / \// 2 3// / \ \// 4 5 6// /// 7void Test2(){ 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); ConnectBinaryTreeNode(pNode1, pNode2, pNode3); ConnectBinaryTreeNode(pNode2, pNode4, pNode5); ConnectBinaryTreeNode(pNode3, NULL, pNode6); ConnectBinaryTreeNode(pNode5, pNode7, NULL); Test("Test2", pNode1, 4, true); DestroyBinaryTreeNode(pNode1);}//不是平衡二叉树// 1// / \// 2 3// / \// 4 5// /// 6void Test3(){ 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); ConnectBinaryTreeNode(pNode1, pNode2, pNode3); ConnectBinaryTreeNode(pNode2, pNode4, pNode5); ConnectBinaryTreeNode(pNode5, pNode6, NULL); Test("Test3", pNode1, 4, false); DestroyBinaryTreeNode(pNode1);}//任意结点的右子树深度均为1，不是平衡二叉树// 1// /// 2// /// 3// /// 4// /// 5void Test4(){ BinaryTreeNode *pNode1 = CreateBinaryTreeNode(1); BinaryTreeNode *pNode2 = CreateBinaryTreeNode(2); BinaryTreeNode *pNode3 = CreateBinaryTreeNode(3); BinaryTreeNode *pNode4 = CreateBinaryTreeNode(4); BinaryTreeNode *pNode5 = CreateBinaryTreeNode(5); ConnectBinaryTreeNode(pNode1, pNode2, NULL); ConnectBinaryTreeNode(pNode2, pNode3, NULL); ConnectBinaryTreeNode(pNode3, pNode4, NULL); ConnectBinaryTreeNode(pNode4, pNode5, NULL); Test("Test4", pNode1, 5, false); DestroyBinaryTreeNode(pNode1);}//任意结点的左子树深度均为1，不是平衡二叉树// 1// \// 2// \// 3// \// 4// \// 5void Test5(){ BinaryTreeNode *pNode1 = CreateBinaryTreeNode(1); BinaryTreeNode *pNode2 = CreateBinaryTreeNode(2); BinaryTreeNode *pNode3 = CreateBinaryTreeNode(3); BinaryTreeNode *pNode4 = CreateBinaryTreeNode(4); BinaryTreeNode *pNode5 = CreateBinaryTreeNode(5); ConnectBinaryTreeNode(pNode1, NULL, pNode2); ConnectBinaryTreeNode(pNode2, NULL, pNode3); ConnectBinaryTreeNode(pNode3, NULL, pNode4); ConnectBinaryTreeNode(pNode4, NULL, pNode5); Test("Test5", pNode1, 5, false); DestroyBinaryTreeNode(pNode1);}//树上只有一个结点void Test6(){ BinaryTreeNode *pNode1 = CreateBinaryTreeNode(1); Test("Test6", pNode1, 1, true); DestroyBinaryTreeNode(pNode1);}//输入空树void Test7(){ Test("Test7", NULL, 0, true);}int main(){ Test1(); Test2(); Test3(); Test4(); Test5(); Test6(); Test7(); return 0;}
