《剑指offer》第二十六题：树的子结构

// 面试题26：树的子结构
// 题目：输入两棵二叉树A和B，判断B是不是A的子结构。

#include <cstdio>

struct BinaryTreeNode
{
    double          m_dbValue;
    BinaryTreeNode* m_pLeft;
    BinaryTreeNode* m_pRight;
};

bool DoesTree1HaveTree2(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2);
bool Equal(double num1, double num2);

bool HasSubtree(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2)
{
    if (pRoot1 == nullptr || pRoot2 == nullptr)
        return false;

    bool result = false;

    if (Equal(pRoot1->m_dbValue, pRoot2->m_dbValue)) //如果匹配到B树根节点,继续匹配其他节点
        result = DoesTree1HaveTree2(pRoot1, pRoot2);
    if (!result)
        result = HasSubtree(pRoot1->m_pLeft, pRoot2); //在A树左节点寻找匹配
    if (!result)
        result = HasSubtree(pRoot1->m_pRight, pRoot2); //在A树右节点寻找匹配

    return result;
}

bool DoesTree1HaveTree2(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2)
{
    if (pRoot2 == nullptr)
        return true;

    if (pRoot1 == nullptr) //A树叶节点为空
        return false;

    if (!Equal(pRoot1->m_dbValue, pRoot2->m_dbValue))
        return false;

    return DoesTree1HaveTree2(pRoot1->m_pLeft, pRoot2->m_pLeft) 
        && DoesTree1HaveTree2(pRoot1->m_pRight, pRoot2->m_pRight);
}

bool Equal(double num1, double num2)
{
    if (num1 - num2 < 0.0000001 && num1 - num2 > -0.0000001)
        return true;
    else
        return false;
}

// ====================辅助测试代码====================
BinaryTreeNode* CreateBinaryTreeNode(double dbValue)
{
    BinaryTreeNode* pNode = new BinaryTreeNode();
    pNode->m_dbValue = dbValue;
    pNode->m_pLeft = nullptr;
    pNode->m_pRight = nullptr;

    return pNode;
}

void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight)
{
    if (pParent != nullptr)
    {
        pParent->m_pLeft = pLeft;
        pParent->m_pRight = pRight;
    }
}

void DestroyTree(BinaryTreeNode* pRoot)
{
    if (pRoot != nullptr)
    {
        BinaryTreeNode* pLeft = pRoot->m_pLeft;
        BinaryTreeNode* pRight = pRoot->m_pRight;

        delete pRoot;
        pRoot = nullptr;

        DestroyTree(pLeft);
        DestroyTree(pRight);
    }
}

// ====================测试代码====================
void Test(const char* testName, BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2, bool expected)
{
    if (HasSubtree(pRoot1, pRoot2) == expected)
        printf("%s passed.
", testName);
    else
        printf("%s failed.
", testName);
}

// 树中结点含有分叉，树B是树A的子结构
//                  8                8
//              /                  / 
//             8         7         9   2
//           /   
//          9     2
//               / 
//              4   7
void Test1()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNodeA6 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNodeA7 = CreateBinaryTreeNode(7);

    ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3);
    ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5);
    ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7);

    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeB1, pNodeB2, pNodeB3);

    Test("Test1", pNodeA1, pNodeB1, true);

    DestroyTree(pNodeA1);
    DestroyTree(pNodeB1);
}

// 树中结点含有分叉，树B不是树A的子结构
//                  8                8
//              /                  / 
//             8         7         9   2
//           /   
//          9     3
//               / 
//              4   7
void Test2()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNodeA6 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNodeA7 = CreateBinaryTreeNode(7);

    ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3);
    ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5);
    ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7);

    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeB1, pNodeB2, pNodeB3);

    Test("Test2", pNodeA1, pNodeB1, false);

    DestroyTree(pNodeA1);
    DestroyTree(pNodeB1);
}

// 树中结点只有左子结点，树B是树A的子结构
//                8                  8
//              /                   / 
//             8                   9   
//           /                    /
//          9                    2
//         /      
//        2        
//       /
//      5
void Test3()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNodeA1, pNodeA2, nullptr);
    ConnectTreeNodes(pNodeA2, pNodeA3, nullptr);
    ConnectTreeNodes(pNodeA3, pNodeA4, nullptr);
    ConnectTreeNodes(pNodeA4, pNodeA5, nullptr);

    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeB1, pNodeB2, nullptr);
    ConnectTreeNodes(pNodeB2, pNodeB3, nullptr);

    Test("Test3", pNodeA1, pNodeB1, true);

    DestroyTree(pNodeA1);
    DestroyTree(pNodeB1);
}

// 树中结点只有左子结点，树B不是树A的子结构
//                8                  8
//              /                   / 
//             8                   9   
//           /                    /
//          9                    3
//         /      
//        2        
//       /
//      5
void Test4()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNodeA1, pNodeA2, nullptr);
    ConnectTreeNodes(pNodeA2, pNodeA3, nullptr);
    ConnectTreeNodes(pNodeA3, pNodeA4, nullptr);
    ConnectTreeNodes(pNodeA4, pNodeA5, nullptr);

    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3);

    ConnectTreeNodes(pNodeB1, pNodeB2, nullptr);
    ConnectTreeNodes(pNodeB2, pNodeB3, nullptr);

    Test("Test4", pNodeA1, pNodeB1, false);

    DestroyTree(pNodeA1);
    DestroyTree(pNodeB1);
}

// 树中结点只有右子结点，树B是树A的子结构
//       8                   8
//                            
//         8                   9   
//                             
//           9                   2
//                  
//             2        
//              
//               5
void Test5()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNodeA1, nullptr, pNodeA2);
    ConnectTreeNodes(pNodeA2, nullptr, pNodeA3);
    ConnectTreeNodes(pNodeA3, nullptr, pNodeA4);
    ConnectTreeNodes(pNodeA4, nullptr, pNodeA5);

    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeB1, nullptr, pNodeB2);
    ConnectTreeNodes(pNodeB2, nullptr, pNodeB3);

    Test("Test5", pNodeA1, pNodeB1, true);

    DestroyTree(pNodeA1);
    DestroyTree(pNodeB1);
}

// 树A中结点只有右子结点，树B不是树A的子结构
//       8                   8
//                            
//         8                   9   
//                           / 
//           9               3   2
//                  
//             2        
//              
//               5
void Test6()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNodeA1, nullptr, pNodeA2);
    ConnectTreeNodes(pNodeA2, nullptr, pNodeA3);
    ConnectTreeNodes(pNodeA3, nullptr, pNodeA4);
    ConnectTreeNodes(pNodeA4, nullptr, pNodeA5);

    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNodeB4 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeB1, nullptr, pNodeB2);
    ConnectTreeNodes(pNodeB2, pNodeB3, pNodeB4);

    Test("Test6", pNodeA1, pNodeB1, false);

    DestroyTree(pNodeA1);
    DestroyTree(pNodeB1);
}

// 树A为空树
void Test7()
{
    BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNodeB4 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeB1, nullptr, pNodeB2);
    ConnectTreeNodes(pNodeB2, pNodeB3, pNodeB4);

    Test("Test7", nullptr, pNodeB1, false);

    DestroyTree(pNodeB1);
}

// 树B为空树
void Test8()
{
    BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNodeA1, nullptr, pNodeA2);
    ConnectTreeNodes(pNodeA2, pNodeA3, pNodeA4);

    Test("Test8", pNodeA1, nullptr, false);

    DestroyTree(pNodeA1);
}

// 树A和树B都为空
void Test9()
{
    Test("Test9", nullptr, nullptr, false);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();
    Test8();
    Test9();

    return 0;
}

分析：递归简洁。

/*
struct TreeNode {
    int val;
    struct TreeNode *left;
    struct TreeNode *right;
    TreeNode(int x) :
            val(x), left(NULL), right(NULL) {
    }
};*/
class Solution {
public:
    bool HasSubtree(TreeNode* pRoot1, TreeNode* pRoot2)
    {
        if (pRoot1 == nullptr || pRoot2 == nullptr)
            return false;
        
        bool result = false;
        
        if (pRoot1->val == pRoot2->val)
            result = DoesTree1HaveTree2(pRoot1, pRoot2);
        if (!result)
            result = HasSubtree(pRoot1->left, pRoot2);
        if (!result)
            result = HasSubtree(pRoot1->right, pRoot2);
        
        return result;
    }
    bool DoesTree1HaveTree2(TreeNode* pRoot1, TreeNode* pRoot2)
    {
        if (pRoot2 == nullptr)
            return true;
        if (pRoot1 == nullptr)
            return false;
        
        if (pRoot1->val != pRoot2->val)
            return false;
        
        return DoesTree1HaveTree2(pRoot1->left, pRoot2->left) 
            && DoesTree1HaveTree2(pRoot1->right, pRoot2->right);
    }
};