#数据结构与算法学习笔记#剑指Offer16：是否为二叉树的子树+测试用例（Java、C/C++）

2018.8.13

这道题的思路和遍历差不多，用递归的思想做即可。若要判断二叉树B是否为A的子树，先遍历A的每一个结点并进行匹配，若出现左右结点相同则根据右子树结构进行递归遍历，满足所有结点与右子树相等则返回true。

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题目描述

输入两棵二叉树A，B，判断B是不是A的子结构。（ps：我们约定空树不是任意一个树的子结构）

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Java实现代码：

/**
 * 
 * @author ChopinXBP 
 * 输入两棵二叉树A，B，判断B是不是A的子结构。（ps：我们约定空树不是任意一个树的子结构）
 *  
 *
 */

public class HasBintree {
	
	public static class TreeNode {
	    int val = 0;
	    TreeNode left = null;
	    TreeNode right = null;

	    public TreeNode(int val) {
	        this.val = val;

	    }

	}
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		TreeNode root1 = new TreeNode(0);
		TreeNode pNode1 = root1;
		pNode1.left = new TreeNode(8);
		pNode1 = root1.left;
		pNode1.left = new TreeNode(8);
		pNode1 = root1.left;
		pNode1.left = new TreeNode(9);
		pNode1 = root1.left;
		pNode1.left = new TreeNode(2);
		pNode1 = root1.left;
		pNode1.left = new TreeNode(5);

		
		TreeNode root2 = new TreeNode(8);
		TreeNode pNode2 = root2;
		pNode2.right = new TreeNode(9);
		pNode2 = root2.right;
		pNode2.left = new TreeNode(3);
		pNode2.right = new TreeNode(2);
		
		boolean result = Solution(root1, root2);
		System.out.println(result);
	}
	
	public static boolean Solution(TreeNode root1, TreeNode root2){
		//判断边界
		if(root1 == null || root2 == null) return false;
		//以当前结点所在子树进行匹配||以当前结点左子结点所在子树进行匹配||以当前结点右子结点所在子树进行匹配
		return isSameTree(root1, root2) || Solution(root1.left, root2) || Solution(root1.right, root2);

	}

	//判断root1在该结点对应的子树是否与root2匹配
	public static boolean isSameTree(TreeNode root1, TreeNode root2){
		if(root2 == null) return true;							//遍历到root2的边界
		else if(root1 == null && root2 != null) return false;	//遍历到root1的边界

		//当前结点&&左子树所有结点&&右子树所有结点
		if(root1.val == root2.val){
			return isSameTree(root1.left, root2.left) && isSameTree(root1.right, root2.right);
		}else{
			return false;
		}
	}
}

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C++解法示例：

bool HasSubtree(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2)
{
    bool result = false;

    if(pRoot1 != NULL && pRoot2 != NULL)
    {
        if(pRoot1->m_nValue == pRoot2->m_nValue)
            result = DoesTree1HaveTree2(pRoot1, pRoot2);
        if(!result)
            result = HasSubtree(pRoot1->m_pLeft, pRoot2);
        if(!result)
            result = HasSubtree(pRoot1->m_pRight, pRoot2);
    }

    return result;
}

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

    if(pRoot1 == NULL)
        return false;

    if(pRoot1->m_nValue != pRoot2->m_nValue)
        return false;

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

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测试代码：

// ====================测试代码====================
void Test(char* testName, BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2, bool expected)
{
    if(HasSubtree(pRoot1, pRoot2) == expected)
        printf("%s passed.\n", testName);
    else
        printf("%s failed.\n", 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, NULL);
    ConnectTreeNodes(pNodeA2, pNodeA3, NULL);
    ConnectTreeNodes(pNodeA3, pNodeA4, NULL);
    ConnectTreeNodes(pNodeA4, pNodeA5, NULL);

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

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

    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, NULL);
    ConnectTreeNodes(pNodeA2, pNodeA3, NULL);
    ConnectTreeNodes(pNodeA3, pNodeA4, NULL);
    ConnectTreeNodes(pNodeA4, pNodeA5, NULL);

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

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

    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, NULL, pNodeA2);
    ConnectTreeNodes(pNodeA2, NULL, pNodeA3);
    ConnectTreeNodes(pNodeA3, NULL, pNodeA4);
    ConnectTreeNodes(pNodeA4, NULL, pNodeA5);

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

    ConnectTreeNodes(pNodeB1, NULL, pNodeB2);
    ConnectTreeNodes(pNodeB2, NULL, 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, NULL, pNodeA2);
    ConnectTreeNodes(pNodeA2, NULL, pNodeA3);
    ConnectTreeNodes(pNodeA3, NULL, pNodeA4);
    ConnectTreeNodes(pNodeA4, NULL, pNodeA5);

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

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

    Test("Test7", NULL, 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, NULL, pNodeA2);
    ConnectTreeNodes(pNodeA2, pNodeA3, pNodeA4);

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

    DestroyTree(pNodeA1);
}

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

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

    return 0;
}

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