面试题39—相关题目（判断平衡二叉树）

**题目：输入一颗二叉树的根节点，判断该树是不是平衡二叉树。
代码示例：**

#include "BinaryTree.h"#include<iostream>using namespace std;// ====================方法1====================int TreeDepth(BinaryTreeNode* pRoot){    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_Solution1(BinaryTreeNode* pRoot){    if (pRoot == NULL)        return true;    int left = TreeDepth(pRoot->m_pLeft);    int right = TreeDepth(pRoot->m_pRight);    int diff = left - right;    if (diff > 1 || diff < -1)        return false;    return IsBalanced_Solution1(pRoot->m_pLeft)        && IsBalanced_Solution1(pRoot->m_pRight);}// ====================方法2====================bool IsBalanced(BinaryTreeNode* pRoot, int* pDepth);bool IsBalanced_Solution2(BinaryTreeNode* pRoot){    int depth = 0;    return IsBalanced(pRoot, &depth);}bool IsBalanced(BinaryTreeNode* pRoot, int* pDepth){    if (pRoot == NULL)    {        *pDepth = 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)        {            *pDepth = 1 + (left > right ? left : right);            return true;        }    }    return false;}// ====================测试代码====================void Test(char* testName, BinaryTreeNode* pRoot, bool expected){    if (testName != NULL)        printf("%s begins:\n", testName);    printf("Solution1 begins: ");    if (IsBalanced_Solution1(pRoot) == expected)        printf("Passed.\n");    else        printf("Failed.\n");    printf("Solution2 begins: ");    if (IsBalanced_Solution2(pRoot) == expected)        printf("Passed.\n");    else        printf("Failed.\n");}// 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);    ConnectTreeNodes(pNode1, pNode2, pNode3);    ConnectTreeNodes(pNode2, pNode4, pNode5);    ConnectTreeNodes(pNode3, pNode6, pNode7);    Test("Test1", pNode1, true);    DestroyTree(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);    ConnectTreeNodes(pNode1, pNode2, pNode3);    ConnectTreeNodes(pNode2, pNode4, pNode5);    ConnectTreeNodes(pNode3, NULL, pNode6);    ConnectTreeNodes(pNode5, pNode7, NULL);    Test("Test2", pNode1, true);    DestroyTree(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);    ConnectTreeNodes(pNode1, pNode2, pNode3);    ConnectTreeNodes(pNode2, pNode4, pNode5);    ConnectTreeNodes(pNode5, pNode6, NULL);    Test("Test3", pNode1, false);    DestroyTree(pNode1);}//               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);    ConnectTreeNodes(pNode1, pNode2, NULL);    ConnectTreeNodes(pNode2, pNode3, NULL);    ConnectTreeNodes(pNode3, pNode4, NULL);    ConnectTreeNodes(pNode4, pNode5, NULL);    Test("Test4", pNode1, false);    DestroyTree(pNode1);}// 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);    ConnectTreeNodes(pNode1, NULL, pNode2);    ConnectTreeNodes(pNode2, NULL, pNode3);    ConnectTreeNodes(pNode3, NULL, pNode4);    ConnectTreeNodes(pNode4, NULL, pNode5);    Test("Test5", pNode1, false);    DestroyTree(pNode1);}// 树中只有1个结点void Test6(){    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);    Test("Test6", pNode1, true);    DestroyTree(pNode1);}// 树中没有结点void Test7(){    Test("Test7", NULL, true);}int main(){    Test1();    Test2();    Test3();    Test4();    Test5();    Test6();    Test7();    return 0;}