《剑指offer》第五十五题（平衡二叉树）

// 面试题55（二）：平衡二叉树
// 题目：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>
#include "BinaryTree.h"

// ====================方法1====================
//迭代的从上到下，判断每个节点是否是平衡树，会导致一个节点的深度重复计算

int TreeDepth(const BinaryTreeNode* pRoot)//检测节点深度
{
    if (pRoot == nullptr)
        return 0;

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

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

bool IsBalanced_Solution1(const BinaryTreeNode* pRoot)//记录
{
    if (pRoot == nullptr)
        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====================
//从下到上检测，如果节点是平衡树，就记录其深度，每个节点被计算一次
bool IsBalanced(const BinaryTreeNode* pRoot, int* pDepth);

bool IsBalanced_Solution2(const BinaryTreeNode* pRoot)
{
    int depth = 0;
    return IsBalanced(pRoot, &depth);
}

bool IsBalanced(const BinaryTreeNode* pRoot, int* pDepth)
{
    if (pRoot == nullptr)
    {
        *pDepth = 0;
        return true;
    }

    int left, right;
    if (IsBalanced(pRoot->m_pLeft, &left)
        && IsBalanced(pRoot->m_pRight, &right))//if条件是找到子节点开始从下向上判断节点是不是平衡树
    {
        int diff = left - right;
        if (diff <= 1 && diff >= -1)//如果是，记录最大深度
        {
            *pDepth = 1 + (left > right ? left : right);
            return true;
        }
    }

    return false;
}

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

    printf("Solution1 begins: ");
    if (IsBalanced_Solution1(pRoot) == expected)
        printf("Passed.
");
    else
        printf("Failed.
");

    printf("Solution2 begins: ");
    if (IsBalanced_Solution2(pRoot) == expected)
        printf("Passed.
");
    else
        printf("Failed.
");
}

// 完全二叉树
//             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, 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
//        /
//       7
void 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, nullptr, pNode6);
    ConnectTreeNodes(pNode5, pNode7, nullptr);

    Test("Test2", pNode1, true);

    DestroyTree(pNode1);
}

// 不是平衡二叉树
//             1
//         /      
//        2        3
//       /         
//      4  5        
//        /
//       6
void 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, nullptr);

    Test("Test3", pNode1, false);

    DestroyTree(pNode1);
}


//               1
//              /
//             2
//            /
//           3
//          /
//         4
//        /
//       5
void Test4()
{
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);

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

    Test("Test4", pNode1, false);

    DestroyTree(pNode1);
}

// 1
//  
//   2
//    
//     3
//      
//       4
//        
//         5
void Test5()
{
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNode1, nullptr, pNode2);
    ConnectTreeNodes(pNode2, nullptr, pNode3);
    ConnectTreeNodes(pNode3, nullptr, pNode4);
    ConnectTreeNodes(pNode4, nullptr, 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", nullptr, true);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();
    system("pause");
    return 0;
}