面试题 04.10. 检查子树

本文介绍了如何设计一个高效的算法来判断一棵拥有数万节点的二叉树T2是否为另一棵大二叉树T1的子树。通过递归和深度优先搜索实现,同时提供了示例和解题思路。

检查子树。你有两棵非常大的二叉树:T1,有几万个节点;T2,有几万个节点。设计一个算法,判断 T2 是否为 T1 的子树。

如果 T1 有这么一个节点 n,其子树与 T2 一模一样,则 T2 为 T1 的子树,也就是说,从节点 n 处把树砍断,得到的树与 T2 完全相同。

注意:此题相对书上原题略有改动。

示例1:

输入:t1 = [1, 2, 3], t2 = [2]
输出:true
示例2:

输入:t1 = [1, null, 2, 4], t2 = [3, 2]
输出:false
提示:

树的节点数目范围为[0, 20000]。

来源:力扣(LeetCode)
链接:https://leetcode.cn/problems/check-subtree-lcci
著作权归领扣网络所有。商业转载请联系官方授权,非商业转载请注明出处。

解题思路

一个深搜 再用一个函数判断是不是子树

代码

class Solution
{
public:
    bool checkSubTree(TreeNode *t1, TreeNode *t2)
    {
        if (!t2)
        {
            return true;
        }
        if (!t1)
        {
            return false;
        }
        return judge(t1, t2) || checkSubTree(t1->left, t2) || checkSubTree(t1->right, t2);
    }

    bool judge(TreeNode *t1, TreeNode *t2)
    {
        if (!t2)
        {
            return true;
        }

        if (t2->val == t1->val)
        {
            return judge(t1->left, t2->left) && judge(t1->right, t2->right);
        }
        else
        {
            return false;
        }
    }
};

ubuntu@raspberrypi:~$ bash ./PX4-Autopilot/Tools/setup/ubuntu.sh --fix-missing [ubuntu.sh] Starting... [ubuntu.sh] arch: aarch64 [ubuntu.sh] Ubuntu 20.04 [ubuntu.sh] Installing PX4 general dependencies Hit:1 http://mirrors.tuna.tsinghua.edu.cn/ros/ubuntu focal InRelease Hit:2 http://mirrors.tuna.tsinghua.edu.cn/ros2/ubuntu focal InRelease Hit:3 https://mirrors.tuna.tsinghua.edu.cn/ubuntu-ports focal InRelease Hit:4 https://mirrors.tuna.tsinghua.edu.cn/ubuntu-ports focal-updates InRelease Hit:5 https://mirrors.tuna.tsinghua.edu.cn/ubuntu-ports focal-backports InRelease Hit:6 https://mirrors.tuna.tsinghua.edu.cn/ubuntu-ports focal-security InRelease Reading package lists... Reading package lists... Building dependency tree... Reading state information... ccache is already the newest version (3.7.7-1). file is already the newest version (1:5.38-4). g++ is already the newest version (4:9.3.0-1ubuntu2). gcc is already the newest version (4:9.3.0-1ubuntu2). make is already the newest version (4.2.1-1.2). python3 is already the newest version (3.8.2-0ubuntu2). python3-dev is already the newest version (3.8.2-0ubuntu2). zip is already the newest version (3.0-11build1). astyle is already the newest version (3.1-2build1). cppcheck is already the newest version (1.90-4build1). lcov is already the newest version (1.14-2). ninja-build is already the newest version (1.10.0-1build1). shellcheck is already the newest version (0.7.0-2build2). build-essential is already the newest version (12.8ubuntu1.1). cmake is already the newest version (3.16.3-1ubuntu1.20.04.1). gdb is already the newest version (9.2-0ubuntu1~20.04.2). git is already the newest version (1:2.25.1-1ubuntu3.14). git set to manually installed. libssl-dev is already the newest version (1.1.1f-1ubuntu2.24). libxml2-dev is already the newest version (2.9.10+dfsg-5ubuntu0.20.04.10). libxml2-utils is already the newest version (2.9.10+dfsg-5ubuntu0.20.04.10). python3-setuptools is already the newest version (45.2.0-1ubuntu0.3). rsync is already the newest version (3.1.3-8ubuntu0.9). rsync set to manually installed. unzip is already the newest version (6.0-25ubuntu1.2). python3-pip is already the newest version (20.0.2-5ubuntu1.11). python3-wheel is already the newest version (0.34.2-1ubuntu0.1). 0 upgraded, 0 newly installed, 0 to remove and 163 not upgraded. [ubuntu.sh] Installing PX4 Python3 dependencies Collecting argcomplete (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 1)) Downloading argcomplete-3.6.2-py3-none-any.whl.metadata (16 kB) Collecting cerberus (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 2)) Downloading Cerberus-1.3.7-py3-none-any.whl.metadata (5.5 kB) Collecting coverage (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 3)) Downloading coverage-7.6.1-cp38-cp38-manylinux_2_17_aarch64.manylinux2014_aarch64.whl.metadata (8.3 kB) Requirement already satisfied: empy<4,>=3.3 in /usr/lib/python3/dist-packages (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 4)) (3.3.2) Requirement already satisfied: future in /usr/lib/python3/dist-packages (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 5)) (0.18.2) Requirement already satisfied: jinja2>=2.8 in /usr/lib/python3/dist-packages (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 6)) (2.10.1) Requirement already satisfied: jsonschema in /usr/lib/python3/dist-packages (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 7)) (3.2.0) Collecting kconfiglib (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 8)) Downloading kconfiglib-14.1.0-py2.py3-none-any.whl.metadata (39 kB) Collecting lxml (from -r /home/ubuntu/PX4-Autopilot/Tools/setup/requirements.txt (line 9)) Downloading lxml-6.0.0.tar.gz (4.1 MB) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 4.1/4.1 MB 4.0 MB/s eta 0:00:00 Installing build dependencies ... done Getting requirements to build wheel ... error error: subprocess-exited-with-error × Getting requirements to build wheel did not run successfully. │ exit code: 1 ╰─> [3 lines of output] Building lxml version 6.0.0. Building without Cython. Error: Please make sure the libxml2 and libxslt development packages are installed. [end of output] note: This error originates from a subprocess, and is likely not a problem with pip. error: subprocess-exited-with-error × Getting requirements to build wheel did not run successfully. │ exit code: 1 ╰─> See above for output. note: This error originates from a subprocess, and is likely not a problem with pip.
08-10
<think>我们正在解决在Ubuntu 20.04上安装PX4-Autopilot的Python依赖时遇到的lxml安装失败问题。 根据引用[1]和引用[2],我们知道PX4-Autopilot的依赖安装是通过执行`ubuntu.sh`脚本或手动安装`requirements.txt`中的依赖。 但是,在安装lxml时可能会遇到问题,因为lxml是一个需要编译的Python包,它依赖系统库(如libxml2和libxslt)的开发文件。 步骤: 1. 确保系统已更新,并安装必要的编译工具和依赖库。 2. 安装lxml所需的系统依赖。 3. 尝试重新安装lxml。 具体操作: 1. 更新系统并安装编译工具: ```bash sudo apt update sudo apt upgrade -y sudo apt install -y build-essential python3-dev ``` 2. 安装lxml的系统依赖: ```bash sudo apt install -y libxml2-dev libxslt1-dev ``` 如果上述安装后仍然有问题,可以尝试安装zlib1g-dev(有时压缩相关的库也需要): ```bash sudo apt install -y zlib1g-dev ``` 3. 然后尝试重新安装lxml。由于我们是在PX4-Autopilot的环境中,可以进入PX4-Autopilot目录,并重新运行安装依赖的脚本,或者单独安装lxml。 方法一:重新运行PX4的安装脚本(如果之前是使用脚本安装的): ```bash cd PX4-Autopilot/Tools/setup # 确保已经安装了上述系统依赖,然后重新运行脚本(注意:如果之前使用了参数,这里也要加上) bash ubuntu.sh --no-sim-tools # 或者根据你的需要加上其他参数 ``` 方法二:单独安装lxml(使用pip): ```bash pip install lxml --upgrade --force-reinstall ``` 或者,如果你使用的是系统的pip3: ```bash pip3 install lxml --upgrade --force-reinstall ``` 4. 如果上述方法仍然失败,可以考虑使用预编译的二进制包(wheel)来安装,避免编译过程: ```bash sudo apt install -y python3-lxml ``` 但是,请注意,使用系统包管理器安装的lxml可能不是最新版本,但通常兼容性较好。 5. 如果问题仍然存在,检查错误日志,通常会有更详细的错误信息。根据错误信息进一步排查。 注意:在PX4-Autopilot的依赖安装中,requirements.txt中指定了lxml(引用[2]中requirements.txt包含lxml),所以确保安装时使用正确的Python环境(可能是PX4使用的Python环境,通常建议使用系统的Python3或虚拟环境)。 如果以上步骤都不能解决问题,可能需要考虑Python环境的问题,例如是否在虚拟环境中,或者是否有多个Python版本冲突。 根据引用[3]中提到的rosdep安装依赖的方法,这里不适用,因为lxml不是ROS包,而是一个Python包。 希望这些步骤能帮助你解决lxml安装失败的问题。 相关问题: 1. 如何解决在Ubuntu上安装Python包时的编译错误? 2. PX4-Autopilot的依赖安装脚本`ubuntu.sh`具体做了哪些工作? 3. 在Ubuntu 20.04上安装PX4-Autopilot还需要注意哪些常见问题?</think>### 解决PX4-Autopilot安装中lxml依赖失败问题(Ubuntu 20.04) #### 问题原因分析 在Ubuntu 20.04安装PX4-Autopilot时,`lxml`安装失败通常是由于缺少编译依赖或Python环境冲突导致。`lxml`是一个需要编译的Python包,依赖系统级的C库(如libxml2/libxslt)[^1]。 #### 解决方案步骤 1. **安装系统级编译依赖** ```bash sudo apt update sudo apt install -y libxml2-dev libxslt1-dev python3-dev zlib1g-dev ``` 这些库提供`lxml`编译所需的头文件和链接库[^2]。 2. **修复Python环境** ```bash # 确保pip和setuptools最新 pip install --upgrade pip setuptools wheel # 强制重装lxml(使用系统编译环境) CFLAGS="-O2" pip install --no-cache-dir --force-reinstall lxml ``` 3. **使用系统包管理器安装(备选方案)** ```bash sudo apt install python3-lxml ``` 此方法会安装Ubuntu官方维护的预编译版本,兼容性更好但版本可能较低[^1]。 4. **验证PX4依赖安装** ```bash cd PX4-Autopilot/Tools/setup # 跳过仿真工具安装(避免gazebo版本冲突) bash ubuntu.sh --no-sim-tools ``` #### 常见错误处理 - **错误提示**:`Command 'x86_64-linux-gnu-gcc' failed` - 解决方案:安装`build-essential`包 ```bash sudo apt install -y build-essential ``` - **错误提示**:`libxml/xmlversion.h not found` - 解决方案:确认`libxml2-dev`已正确安装 ```bash sudo apt install --reinstall libxml2-dev ``` #### 预防措施 1. 使用Python虚拟环境避免依赖冲突: ```bash python3 -m venv px4_env source px4_env/bin/activate ``` 2. 在安装前检查系统更新: ```bash sudo apt update && sudo apt upgrade -y ``` #### 验证安装 运行以下命令确认lxml安装成功: ```bash python -c "import lxml; print(lxml.__version__)" # 应输出类似:4.9.4 ``` > **关键提示**:Ubuntu 20.04默认Python3为3.8版本,PX4依赖需确保所有操作使用`python3`和`pip3`命令[^1][^2]。
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