题目描述

• 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。

算法分析

• 后续遍历二叉树，遍历过程中求子树高度，判断是否平衡。

提交代码：

class Solution {
public:
	bool IsBalanced_Solution(TreeNode* pRoot) {
		if (!pRoot)
			return true;

		int depth = 0;
		return IsBalanced(pRoot, &depth);
	}


	bool IsBalanced(TreeNode* pRoot, int *depth) {
		if (!pRoot)
		{
			*depth = 0;
			return true;
		}
		// 后序遍历
		int left = *depth, right = *depth;
		if (IsBalanced(pRoot->left, &left) &&
			IsBalanced(pRoot->right, &right))
		{
			*depth = left > right ? left + 1 : right + 1;
			if (abs(left - right) > 1)
				return false;
			else
				return true;
		}

		return false;
	}
};

测试代码：

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

	Solution s;
	printf("Solution1 begins: ");
	if (s.IsBalanced_Solution(pRoot) == expected)
		printf("Passed.\n");
	else
		printf("Failed.\n");

	//printf("Solution2 begins: ");
	//if (IsBalanced_Solution(pRoot) == expected)
	//	printf("Passed.\n");
	//else
	//	printf("Failed.\n");
}

// 完全二叉树
//             1
//         /      \
//        2        3
//       /\       / \
//      4  5     6   7
void Test1()
{
	TreeNode* pNode1 = CreateBinaryTreeNode(1);
	TreeNode* pNode2 = CreateBinaryTreeNode(2);
	TreeNode* pNode3 = CreateBinaryTreeNode(3);
	TreeNode* pNode4 = CreateBinaryTreeNode(4);
	TreeNode* pNode5 = CreateBinaryTreeNode(5);
	TreeNode* pNode6 = CreateBinaryTreeNode(6);
	TreeNode* 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()
{
	TreeNode* pNode1 = CreateBinaryTreeNode(1);
	TreeNode* pNode2 = CreateBinaryTreeNode(2);
	TreeNode* pNode3 = CreateBinaryTreeNode(3);
	TreeNode* pNode4 = CreateBinaryTreeNode(4);
	TreeNode* pNode5 = CreateBinaryTreeNode(5);
	TreeNode* pNode6 = CreateBinaryTreeNode(6);
	TreeNode* 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()
{
	TreeNode* pNode1 = CreateBinaryTreeNode(1);
	TreeNode* pNode2 = CreateBinaryTreeNode(2);
	TreeNode* pNode3 = CreateBinaryTreeNode(3);
	TreeNode* pNode4 = CreateBinaryTreeNode(4);
	TreeNode* pNode5 = CreateBinaryTreeNode(5);
	TreeNode* 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()
{
	TreeNode* pNode1 = CreateBinaryTreeNode(1);
	TreeNode* pNode2 = CreateBinaryTreeNode(2);
	TreeNode* pNode3 = CreateBinaryTreeNode(3);
	TreeNode* pNode4 = CreateBinaryTreeNode(4);
	TreeNode* 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()
{
	TreeNode* pNode1 = CreateBinaryTreeNode(1);
	TreeNode* pNode2 = CreateBinaryTreeNode(2);
	TreeNode* pNode3 = CreateBinaryTreeNode(3);
	TreeNode* pNode4 = CreateBinaryTreeNode(4);
	TreeNode* 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()
{
	TreeNode* 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;
}