树的子结构

最新推荐文章于 2025-07-26 21:01:30 发布

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最新推荐文章于 2025-07-26 21:01:30 发布

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文章标签：数据结构与算法测试

本文提供了一种高效的算法来判断一棵二叉树是否为另一棵二叉树的子树。通过优化递归过程，避免了不必要的遍历，显著提高了算法的效率。文章包括完整的C++代码实现及单元测试。

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#include<stdio.h>

struct BinaryTreeNode
{
	int m_nValue;
	BinaryTreeNode* m_pLeft;
	BinaryTreeNode* m_pRight;
};

BinaryTreeNode* createBinaryTreeNode(int value)
{
	BinaryTreeNode* pNewNode = new BinaryTreeNode();
	pNewNode->m_nValue = value;
	pNewNode->m_pLeft = NULL;
	pNewNode->m_pRight = NULL;
	return pNewNode;
}
void connectBinaryTreeNode(BinaryTreeNode* pParent,BinaryTreeNode* pLeftChild,
						   BinaryTreeNode* pRightChild)
{
	if(!pParent)
		return;

	pParent->m_pLeft = pLeftChild;
	pParent->m_pRight = pRightChild;
}
/*
bool hasTheSubTeeWithRoot(BinaryTreeNode* pBigTree, BinaryTreeNode* pSmallTree);
//判断pSmallTree是不是pBigTree的子树
bool isSubtreeInBinaryTree(BinaryTreeNode* pBigTree, BinaryTreeNode* pSmallTree)
{
	if(pSmallTree == NULL || pBigTree == NULL)
		return false;

	bool result = false;
	bool result1 = false;
	bool result2 = false;
	result = hasTheSubTeeWithRoot(pBigTree,pSmallTree);
	if(pBigTree->m_pLeft)
		result1 = isSubtreeInBinaryTree(pBigTree->m_pLeft,pSmallTree);
	if(pBigTree->m_pRight)
		result2 = isSubtreeInBinaryTree(pBigTree->m_pRight,pSmallTree);
	
	return	(result || result1 || result2);
}
//两棵树已包含根节点为条件，判断是否为子树
bool hasTheSubTeeWithRoot(BinaryTreeNode* pBigTree, BinaryTreeNode* pSmallTree)
{
	if(pSmallTree == NULL)
		return true;
	if(pBigTree == NULL)
		return false;

	bool result = false;
	bool result1 = false;
	bool result2 = false;
	if(pBigTree->m_nValue == pSmallTree->m_nValue)
	{
		result = true;
		result1 = hasTheSubTeeWithRoot(pBigTree->m_pLeft,pSmallTree->m_pLeft);
		result2 = hasTheSubTeeWithRoot(pBigTree->m_pRight,pSmallTree->m_pRight);
	}
	return result && result1 && result2;
}
*/

//以上注释的代码能实现基本功能，但效率很差,原因是上述方法即使一开始确定
//是子树，也会继续遍历较大树下面的每个节点。
//下面方法可以避免这个问题
bool hasTheSubTeeWithRoot(BinaryTreeNode* pBigTree, BinaryTreeNode* pSmallTree);
bool isSubtreeInBinaryTree(BinaryTreeNode* pBigTree, BinaryTreeNode* pSmallTree)
{ 
	bool result = false;
	if(pBigTree != NULL && pSmallTree != NULL)
	{
		if(pBigTree->m_nValue == pSmallTree->m_nValue)
			result = hasTheSubTeeWithRoot(pBigTree,pSmallTree);
		if(!result)	//如果查找出子树就停止往下查找
			result = isSubtreeInBinaryTree(pBigTree->m_pLeft,pSmallTree);
		if(!result)
			result = isSubtreeInBinaryTree(pBigTree->m_pRight,pSmallTree);
	}
	return result;
}

bool hasTheSubTeeWithRoot(BinaryTreeNode* pBigTree, BinaryTreeNode* pSmallTree)
{
	if(pSmallTree == NULL)
		return true;
	if(pBigTree == NULL)
		return false;

	if(pBigTree->m_nValue != pSmallTree->m_nValue)
		return false;
	//用return语句递归
	return hasTheSubTeeWithRoot(pBigTree->m_pLeft,pSmallTree->m_pLeft) && hasTheSubTeeWithRoot(pBigTree->m_pRight,pSmallTree->m_pRight);
}


//单元测试
void test1()
{
	BinaryTreeNode* pNode1 = createBinaryTreeNode(8);
	BinaryTreeNode* pNode2 = createBinaryTreeNode(8);
	BinaryTreeNode* pNode3 = createBinaryTreeNode(7);
	BinaryTreeNode* pNode4 = createBinaryTreeNode(9);
	BinaryTreeNode* pNode5 = createBinaryTreeNode(2);
	BinaryTreeNode* pNode6 = createBinaryTreeNode(4);
	BinaryTreeNode* pNode7 = createBinaryTreeNode(7);

	connectBinaryTreeNode(pNode1,pNode2,pNode3);
	connectBinaryTreeNode(pNode2,pNode4,pNode5);
	connectBinaryTreeNode(pNode5,pNode6,pNode7);

	BinaryTreeNode* pNode21 = createBinaryTreeNode(8);
	BinaryTreeNode* pNode22 = createBinaryTreeNode(9);
	BinaryTreeNode* pNode23 = createBinaryTreeNode(2);
	connectBinaryTreeNode(pNode21,pNode22,pNode23);

	if(isSubtreeInBinaryTree(pNode1,pNode21))
		printf("the smalltree is a subtree in bigtree");
	else
		printf("not subtree");
}
void test2()
{
	BinaryTreeNode* pNode1 = createBinaryTreeNode(8);
	BinaryTreeNode* pNode2 = createBinaryTreeNode(8);
	BinaryTreeNode* pNode3 = createBinaryTreeNode(7);
	BinaryTreeNode* pNode4 = createBinaryTreeNode(9);
	BinaryTreeNode* pNode5 = createBinaryTreeNode(2);
	BinaryTreeNode* pNode6 = createBinaryTreeNode(4);
	BinaryTreeNode* pNode7 = createBinaryTreeNode(7);

	connectBinaryTreeNode(pNode1,pNode2,pNode3);
	connectBinaryTreeNode(pNode2,pNode4,pNode5);
	connectBinaryTreeNode(pNode5,pNode6,pNode7);

	BinaryTreeNode* pNode21 = createBinaryTreeNode(8);
	BinaryTreeNode* pNode22 = createBinaryTreeNode(9);
	BinaryTreeNode* pNode23 = createBinaryTreeNode(2);
	BinaryTreeNode* pNode24 = createBinaryTreeNode(1);
	BinaryTreeNode* pNode25 = createBinaryTreeNode(2);
	connectBinaryTreeNode(pNode21,pNode22,pNode23);
	connectBinaryTreeNode(pNode22,pNode24,pNode25);

	if(isSubtreeInBinaryTree(pNode1,pNode21))
		printf("the smalltree is a subtree in bigtree");
	else
		printf("not subtree");
}
int main()
{
	test1();
	printf("\n\n");
	test2();
	return 0;
}

二叉树相关的代码有大量的指针操作，每一次使用指针的时候，我们都要问自己这个

指针有没有可能是NULL，如果是NULL该怎么处理。

==参考剑指offer