剑指Offer面试题：22.二叉搜索树的后序遍历序列

    public static bool VerifySquenceOfBST(int[] sequence, int length)
    {
        if (sequence == null || length <= 0)
        {
            return false;
        }

        int root = sequence[length - 1];

        int i = 0;
        // 在二叉搜索树中左子树的结点小于根结点
        for (; i < length - 1; i++)
        {
            if (sequence[i] > root)
            {
                break;
            }
        }
        // 在二叉搜索树中右子树的结点大于根结点
        int j = i;
        for (; j < length - 1; j++)
        {
            if (sequence[j] < root)
            {
                // 如果找到小于根节点直接返回false
                return false;
            }
        }
        // 判断左子树是不是二叉搜索树
        bool leftIsBST = true;
        if (i > 0)
        {
            leftIsBST = VerifySquenceOfBST(sequence, i);
        }
        // 判断右子树是不是二叉搜索树
        bool rightIsBST = true;
        if (j < length - 1)
        {
            // C#中无法直接操作指针，在C/C++可以直接传递sequence+i
            int[] newSequence = sequence.Skip(i).ToArray();
            rightIsBST = VerifySquenceOfBST(newSequence, length - i - 1);
        }

        return leftIsBST && rightIsBST;
    }

    //            10
    //         /      \
    //        6        14
    //       /\        /\
    //      4  8     12  16
    [TestMethod]
    public void SequenceTest1()
    {
        int[] data = { 4, 8, 6, 12, 16, 14, 10 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, true);
    }

    //           5
    //          / \
    //         4   7
    //            /
    //           6
    [TestMethod]
    public void SequenceTest2()
    {
        int[] data = { 4, 6, 7, 5 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, true);
    }

    //               5
    //              /
    //             4
    //            /
    //           3
    //          /
    //         2
    //        /
    //       1
    [TestMethod]
    public void SequenceTest3()
    {
        int[] data = { 1, 2, 3, 4, 5 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, true);
    }

    // 1
    //  \
    //   2
    //    \
    //     3
    //      \
    //       4
    //        \
    //         5
    [TestMethod]
    public void SequenceTest4()
    {
        int[] data = { 5, 4, 3, 2, 1 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, true);
    }

    // 树中只有1个结点
    [TestMethod]
    public void SequenceTest5()
    {
        int[] data = { 5 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, true);
    }

    // 错误序列
    [TestMethod]
    public void SequenceTest6()
    {
        int[] data = { 7, 4, 6, 5 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, false);
    }

    // 错误序列
    [TestMethod]
    public void SequenceTest7()
    {
        int[] data = { 4, 6, 12, 8, 16, 14, 10 };
        bool result = SequenceHelper.VerifySquenceOfBST(data, data.Length);
        Assert.AreEqual(result, false);
    }

    // 错误序列
    [TestMethod]
    public void SequenceTest8()
    {
        bool result = SequenceHelper.VerifySquenceOfBST(null, 0);
        Assert.AreEqual(result, false);
    }