要编译Android Studio Vulkan示例，可以按照以下步骤进行操作：

1. 在Android Studio中创建一个新的Android项目。
2. 在项目的app/build.gradle文件中添加以下依赖项：

dependencies {
    implementation 'androidx.appcompat:appcompat:1.3.0'
    implementation 'androidx.constraintlayout:constraintlayout:2.0.4'

    implementation 'androidx.vectordrawable:vectordrawable:1.1.0'
    implementation 'androidx.vectordrawable:vectordrawable-animated:1.1.0'

    implementation 'org.lwjgl:lwjgl-glfw:3.3.0'
    implementation 'org.lwjgl:lwjgl-glfw:3.3.0:natives-windows'
    implementation 'org.lwjgl:lwjgl-glfw:3.3.0:natives-linux'
    implementation 'org.lwjgl:lwjgl-glfw:3.3.0:natives-osx'

    implementation 'org.lwjgl:lwjgl-opengl:3.3.0'
    implementation 'org.lwjgl:lwjgl-opengl:3.3.0:natives-windows'
    implementation 'org.lwjgl:lwjgl-opengl:3.3.0:natives-linux'
    implementation 'org.lwjgl:lwjgl-opengl:3.3.0:natives-osx'

    implementation 'org.lwjgl:lwjgl-vulkan:3.3.0'
    implementation 'org.lwjgl:lwjgl-vulkan:3.3.0:natives-windows'
    implementation 'org.lwjgl:lwjgl-vulkan:3.3.0:natives-linux'
    implementation 'org.lwjgl:lwjgl-vulkan:3.3.0:natives-osx'

    implementation 'org.lwjgl:lwjgl-stb:3.3.0'
    implementation 'org.lwjgl:lwjgl-stb:3.3.0:natives-windows'
    implementation 'org.lwjgl:lwjgl-stb:3.3.0:natives-linux'
    implementation 'org.lwjgl:lwjgl-stb:3.3.0:natives-osx'
}

3. 在app/src/main/java目录下创建一个新的Java类，例如VulkanExample.java，并将以下示例代码添加到该类中：

import org.lwjgl.*;
import org.lwjgl.glfw.*;
import org.lwjgl.opengl.*;
import org.lwjgl.system.*;

import java.nio.*;

import static org.lwjgl.glfw.Callbacks.*;
import static org.lwjgl.glfw.GLFW.*;
import static org.lwjgl.opengl.GL11.*;
import static org.lwjgl.opengl.GL15.*;
import static org.lwjgl.opengl.GL20.*;
import static org.lwjgl.opengl.GL30.*;
import static org.lwjgl.opengl.GL32.*;
import static org.lwjgl.system.MemoryStack.*;
import static org.lwjgl.system.MemoryUtil.*;

public class VulkanExample {

    private long window;

    public void run() {
        init();
        loop();

        glfwFreeCallbacks(window);
        glfwDestroyWindow(window);

        glfwTerminate();
        glfwSetErrorCallback(null).free();
    }

    private void init() {
        GLFWErrorCallback.createPrint(System.err).set();

        if (!glfwInit()) {
            throw new IllegalStateException("Unable to initialize GLFW");
        }

        glfwDefaultWindowHints();
        glfwWindowHint(GLFW_VISIBLE, GLFW_FALSE);
        glfwWindowHint(GLFW_RESIZABLE, GLFW_TRUE);

        window = glfwCreateWindow(800, 600, "Vulkan Example", NULL, NULL);
        if (window == NULL) {
            throw new RuntimeException("Failed to create the GLFW window");
        }

        glfwSetFramebufferSizeCallback(window, (window, width, height) -> {
            glViewport(0, 0, width, height);
        });

        try (MemoryStack stack = stackPush()) {
            IntBuffer pWidth = stack.mallocInt(1);
            IntBuffer pHeight = stack.mallocInt(1);

            glfwGetWindowSize(window, pWidth, pHeight);

            GLFWVidMode vidmode = glfwGetVideoMode(glfwGetPrimaryMonitor());

            glfwSetWindowPos(
                    window,
                    (vidmode.width() - pWidth.get(0)) / 2,
                    (vidmode.height() - pHeight.get(0)) / 2
            );
        }

        glfwMakeContextCurrent(window);
        glfwSwapInterval(1);

        glfwShowWindow(window);
    }

    private void loop() {
        GL.createCapabilities();

        glClearColor(0.0f, 0.0f, 0.0f, 0.0f);

        while (!glfwWindowShouldClose(window)) {
            glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

            glfwSwapBuffers