《剑指offer》第五十五题II：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 <cstdio>
#include "BinaryTree.h"

// ====================方法1====================
int TreeDepth(const BinaryTreeNode* pRoot)
{
    if (pRoot == nullptr)
        return 0;

    int left = TreeDepth(pRoot->m_pLeft);
    int right = TreeDepth(pRoot->m_pRight);

    return (left > right) ? left + 1 : right + 1;
}

bool IsBalanced_Solution1(const BinaryTreeNode* pRoot)
{
    if (pRoot == nullptr)
        return true;

    int left = TreeDepth(pRoot->m_pLeft);
    int right = TreeDepth(pRoot->m_pRight);
    int dif = left - right;
    if (dif > 1 || dif < -1)
        return false;

    return IsBalanced_Solution1(pRoot->m_pLeft)
        && IsBalanced_Solution1(pRoot->m_pRight);  //需要计算所有节点
}

// ====================方法2====================
bool IsBalanced(const BinaryTreeNode* pRoot, int* pDepth);

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

bool IsBalanced(const BinaryTreeNode* pRoot, int* pDepth)  //计算某个节点的深度并判断其是否二叉树
{
    if (pRoot == nullptr)
    {
        *pDepth = 0;
        return true;
    }

    int left, right;  //左右子树深度
    if (IsBalanced(pRoot->m_pLeft, &left) 
        && IsBalanced(pRoot->m_pRight, &right))
    {
        int dif = left - right;  //深度差
        if (dif <= 1 && dif >= -1)
        {
            *pDepth = (left > right ? left + 1 : right + 1);
            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();

    return 0;
}

分析：记录当前节点深度，不用多次遍历子节点。

class Solution {
public:
    bool IsBalanced_Solution(TreeNode* pRoot) {
        
        int depth = 0;
        return IsBalanced(pRoot, &depth);
    }
    
    bool IsBalanced(TreeNode* pRoot, int* depth)
    {
        if (pRoot == nullptr)
        {
            *depth = 0;
            return true;
        }
        
        int left, right;
        if (IsBalanced(pRoot->left, &left) 
            && IsBalanced(pRoot->right, &right))
        {
            int diff = left - right;
            if (diff <= 1 && diff >= -1)
            {
                *depth = ((left > right)? left + 1 : right + 1);
                return true;
            }
        }
        return false;
    }
};