在配置servlet不同路径时遇上以下两个错误：
java.lang.NoSuchMethodError: javax.servlet.ServletContext.getVirtualServerName()Ljava/lang/String；
java.lang.ClassNotFoundException: org.apache.jsp.index_jsp；
对于第一个问题，我上网查阅了很多资料后发现，可能是tomcat版本冲突导致，catalina log如下：
19-Feb-2018 08:26:44.175 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Server version: Apache Tomcat/8.5.28
19-Feb-2018 08:26:44.175 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Server built: Feb 6 2018 23:10:25 UTC
19-Feb-2018 08:26:44.175 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Server number: 8.5.28.0
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log OS Name: Windows 7
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log OS Version: 6.1
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Architecture: x86
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Java Home: C:\Program Files\Java\jdk1.8.0_141\jre
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log JVM Version: 1.8.0_141-b15
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log JVM Vendor: Oracle Corporation
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log CATALINA_BASE: F:\apache-tomcat-8.5.28
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log CATALINA_HOME: F:\apache-tomcat-8.5.28
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.util.logging.config.file=F:\apache-tomcat-8.5.28\conf\logging.properties
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.util.logging.manager=org.apache.juli.ClassLoaderLogManager
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djdk.tls.ephemeralDHKeySize=2048
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.protocol.handler.pkgs=org.apache.catalina.webresources
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dignore.endorsed.dirs=
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dcatalina.base=F:\apache-tomcat-8.5.28
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dcatalina.home=F:\apache-tomcat-8.5.28
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.io.tmpdir=F:\apache-tomcat-8.5.28\temp
19-Feb-2018 08:26:44.191 信息 [main] org.apache.catalina.core.AprLifecycleListener.lifecycleEvent Loaded APR based Apache Tomcat Native library [1.2.16] using APR version [1.6.3].
19-Feb-2018 08:26:44.206 信息 [main] org.apache.catalina.core.AprLifecycleListener.lifecycleEvent APR capabilities: IPv6 [true], sendfile [true], accept filters [false], random [true].
19-Feb-2018 08:26:44.206 信息 [main] org.apache.catalina.core.AprLifecycleListener.lifecycleEvent APR/OpenSSL configuration: useAprConnector [false], useOpenSSL [true]
19-Feb-2018 08:26:44.830 信息 [main] org.apache.catalina.core.AprLifecycleListener.initializeSSL OpenSSL successfully initialized [OpenSSL 1.0.2m 2 Nov 2017]
19-Feb-2018 08:26:45.080 信息 [main] org.apache.coyote.AbstractProtocol.init Initializing ProtocolHandler ["http-nio-8080"]
19-Feb-2018 08:26:45.517 信息 [main] org.apache.tomcat.util.net.NioSelectorPool.getSharedSelector Using a shared selector for servlet write/read
19-Feb-2018 08:26:45.581 信息 [main] org.apache.coyote.AbstractProtocol.init Initializing ProtocolHandler ["ajp-nio-8009"]
19-Feb-2018 08:26:45.597 信息 [main] org.apache.tomcat.util.net.NioSelectorPool.getSharedSelector Using a shared selector for servlet write/read
19-Feb-2018 08:26:45.597 信息 [main] org.apache.catalina.startup.Catalina.load Initialization processed in 2422 ms
19-Feb-2018 08:26:45.643 信息 [main] org.apache.catalina.core.StandardService.startInternal Starting service [Catalina]
19-Feb-2018 08:26:45.643 信息 [main] org.apache.catalina.core.StandardEngine.startInternal Starting Servlet Engine: Apache Tomcat/8.5.28
19-Feb-2018 08:26:45.675 信息 [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deploying web application directory [F:\apache-tomcat-8.5.28\webapps\docs]
19-Feb-2018 08:26:46.423 信息 [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory [F:\apache-tomcat-8.5.28\webapps\docs] has finished in [748] ms
19-Feb-2018 08:26:46.423 信息 [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deploying web application directory [F:\apache-tomcat-8.5.28\webapps\examples]
19-Feb-2018 08:26:47.059 严重 [localhost-startStop-1] org.apache.catalina.core.ContainerBase.addChildInternal ContainerBase.addChild: start:
org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/examples]]
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:167)
at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:752)
at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:728)
at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:734)
at org.apache.catalina.startup.HostConfig.deployDirectory(HostConfig.java:1141)
at org.apache.catalina.startup.HostConfig$DeployDirectory.run(HostConfig.java:1875)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)
at java.util.concurrent.FutureTask.run(FutureTask.java:266)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624)
at java.lang.Thread.run(Thread.java:748)
Caused by: org.apache.catalina.LifecycleException: Failed to start component [Pipeline[StandardEngine[Catalina].StandardHost[localhost].StandardContext[/examples]]]
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:167)
at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5125)
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
... 10 more
Caused by: org.apache.catalina.LifecycleException: Failed to start component [org.apache.catalina.authenticator.FormAuthenticator[/examples]]
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:167)
at org.apache.catalina.core.StandardPipeline.startInternal(StandardPipeline.java:182)
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
... 12 more
Caused by: java.lang.NoSuchMethodError: javax.servlet.ServletContext.getVirtualServerName()Ljava/lang/String;
at org.apache.catalina.authenticator.AuthenticatorBase.startInternal(AuthenticatorBase.java:1186)
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
... 14 more
19-Feb-2018 08:26:47.075 严重 [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Error deploying web application directory [F:\apache-tomcat-8.5.28\webapps\examples]
java.lang.IllegalStateException: ContainerBase.addChild: start: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/examples]]
at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:756)
at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:728)
at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:734)
at org.apache.catalina.startup.HostConfig.deployDirectory(HostConfig.java:1141)
at org.apache.catalina.startup.HostConfig$DeployDirectory.run(HostConfig.java:1875)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)
at java.util.concurrent.FutureTask.run(FutureTask.java:266)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624)
at java.lang.Thread.run(Thread.java:748)
我先试着删除其他Tomcat版本，重新配置tomcat环境变量并重新部署Tomcat。发现并没有解决问题，再次上网查阅，发现getContextPath()在servlet2.5特有。于是试着删除原先jar包中的servlet-api.jar,然后重新部署项目。发现了第二个问题，log如下：
19-Feb-2018 09:59:51.534 严重 [http-nio-8080-exec-3] org.apache.catalina.core.StandardWrapperValve.invoke Servlet.service() for servlet [jsp] in context with path [/Happy] threw exception [java.lang.ClassNotFoundException: org.apache.jsp.index_jsp] with root cause
java.lang.ClassNotFoundException: org.apache.jsp.index_jsp
at java.net.URLClassLoader.findClass(URLClassLoader.java:381)
at org.apache.jasper.servlet.JasperLoader.loadClass(JasperLoader.java:129)
at org.apache.jasper.servlet.JasperLoader.loadClass(JasperLoader.java:60)
at org.apache.catalina.core.DefaultInstanceManager.newInstance(DefaultInstanceManager.java:159)
at org.apache.jasper.servlet.JspServletWrapper.getServlet(JspServletWrapper.java:171)
at org.apache.jasper.servlet.JspServletWrapper.service(JspServletWrapper.java:380)
at org.apache.jasper.servlet.JspServlet.serviceJspFile(JspServlet.java:386)
at org.apache.jasper.servlet.JspServlet.service(JspServlet.java:330)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:847)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:231)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:193)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:199)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:96)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:140)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:81)
at org.apache.catalina.valves.AbstractAccessLogValve.invoke(AbstractAccessLogValve.java:650)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:87)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:342)
at org.apache.coyote.http11.Http11Processor.service(Http11Processor.java:803)
at org.apache.coyote.AbstractProcessorLight.process(AbstractProcessorLight.java:66)
at org.apache.coyote.AbstractProtocol$ConnectionHandler.process(AbstractProtocol.java:790)
at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.doRun(NioEndpoint.java:1459)
at org.apache.tomcat.util.net.SocketProcessorBase.run(SocketProcessorBase.java:49)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624)
at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
at java.lang.Thread.run(Thread.java:748)
19-Feb-2018 10:03:45.289 严重 [http-nio-8080-exec-1] org.apache.catalina.core.StandardWrapperValve.invoke Servlet.service() for servlet [jsp] in context with path [/Happy] threw exception [Unable to compile class for JSP] with root cause
java.lang.ClassNotFoundException: com.sun.el.ExpressionFactoryImpl
at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1291)
at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1119)
at javax.el.FactoryFinder.newInstance(FactoryFinder.java:83)
at javax.el.FactoryFinder.find(FactoryFinder.java:193)
at javax.el.ExpressionFactory.newInstance(ExpressionFactory.java:185)
at javax.el.ExpressionFactory.newInstance(ExpressionFactory.java:156)
at org.apache.jasper.compiler.PageInfo.<init>(PageInfo.java:80)
at org.apache.jasper.compiler.Compiler.generateJava(Compiler.java:117)
at org.apache.jasper.compiler.Compiler.compile(Compiler.java:374)
at org.apache.jasper.compiler.Compiler.compile(Compiler.java:351)
at org.apache.jasper.compiler.Compiler.compile(Compiler.java:335)
at org.apache.jasper.JspCompilationContext.compile(JspCompilationContext.java:595)
at org.apache.jasper.servlet.JspServletWrapper.service(JspServletWrapper.java:368)
at org.apache.jasper.servlet.JspServlet.serviceJspFile(JspServlet.java:386)
at org.apache.jasper.servlet.JspServlet.service(JspServlet.java:330)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:847)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:231)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:193)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:199)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:96)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:140)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:81)
at org.apache.catalina.valves.AbstractAccessLogValve.invoke(AbstractAccessLogValve.java:650)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:87)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:342)
at org.apache.coyote.http11.Http11Processor.service(Http11Processor.java:803)
at org.apache.coyote.AbstractProcessorLight.process(AbstractProcessorLight.java:66)
at org.apache.coyote.AbstractProtocol$ConnectionHandler.process(AbstractProtocol.java:790)
at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.doRun(NioEndpoint.java:1459)
at org.apache.tomcat.util.net.SocketProcessorBase.run(SocketProcessorBase.java:49)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624)
at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
at java.lang.Thread.run(Thread.java:748)
再次查阅资料，发现是缺少jar包。因为jdk1.8的扩展jar包里没有servlet相关api，故IDEA会导入失败。
此时需要导入jar包，之前我是下载相关api
然后放到下图目录中
为了防止出现缺少jar包问题，建议直接去tomcat目录下的lib中找到servlet-api.jar，直接复制到ext中。然后再重新部署一下tomcat，问题解决。
总结