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假设你正在爬楼梯。需要 n 阶你才能到达楼顶。

每次你可以爬 1 或 2 个台阶。你有多少种不同的方法可以爬到楼顶呢？

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public int climbStairs(int n) {
       if (n<3){
           return n;
       }
       int[] dp=new int[n+1];
       dp[1]=1;
       dp[2]=2;
       for(int i=3;i<=n;i++){
           dp[i]=dp[i-1]+dp[i-2];
       }
       return dp[n];
   }

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public int climbStairs(int n) {
       if (n<3){
           return n;
       }
       int p1=2; //f(n-1)
       int p2=1; //f(n-2)
       for(int i=3;i<=n;i++){
          int cur=p1+p2;
          p2=p1;
          p1=cur;
       }
       return p1;
   }

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你是一个专业的小偷，计划偷窃沿街的房屋。每间房内都藏有一定的现金，影响你偷窃的唯一制约因素就是相邻的房屋装有相互连通的防盗系统，如果两间相邻的房屋在同一晚上被小偷闯入，系统会自动报警。

给定一个代表每个房屋存放金额的非负整数数组，计算你 不触动警报装置的情况下 ，一夜之内能够偷窃到的最高金额。

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public int rob(int[] nums) {
        int n=nums.length;
        if (n==0){
            return 0;
        }else if (n==1){
            return nums[0];
        }else if (n==2){
            return Math.max(nums[0],nums[1]);
        }
        int[] dp=new int[n+1];

        dp[1]=nums[0];
        dp[2]=Math.max(nums[0],nums[1]);

        for (int i=3;i<=n;i++){
            dp[i]= Math.max(dp[i-1],dp[i-2]+nums[i-1]);
        }

        return dp[n];
    }

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public int rob(int[] nums) {
       int p1=0; //f(n-1)
       int p2=0; //f(n-2)

       for (int i=0;i<nums.length;i++){
           int cur=Math.max(p2+nums[i],p1);
           p2=p1;
           p1=cur;
       }

       return p1;
   }

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你是一个专业的小偷，计划偷窃沿街的房屋，每间房内都藏有一定的现金。这个地方所有的房屋都围成一圈，这意味着第一个房屋和最后一个房屋是紧挨着的。同时，相邻的房屋装有相互连通的防盗系统，如果两间相邻的房屋在同一晚上被小偷闯入，系统会自动报警。

给定一个代表每个房屋存放金额的非负整数数组，计算你在不触动警报装置的情况下，能够偷窃到的最高金额。

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public int rob(int[] nums) {
    if (nums==null||nums.length==0){
        return 0;
    }
    if (nums.length==1){
        return nums[0];
    }
    return Math.max(helper(nums,0,nums.length-2),helper(nums,1,nums.length-1));
}

public int helper(int[] nums,int start,int end){
    int p1=0;// f(n-1)
    int p2=0;// f(n-2)
    for (int i=start;i<=end;i++){
        int cur=Math.max(p2+nums[i],p1);
        p2=p1;
        p1=cur;
    }
    return p1;
}

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给定一个整数数组 nums ，找到一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。

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public int maxSubArray(int[] nums) {
        if (nums==null||nums.length==0){
            return 0;
        }

        int max=0;
        for (int i=1;i<nums.length;i++){
            nums[i]=Math.max(nums[i-1],0)+nums[i];
            max=Math.max(max,nums[i]);
        }
        return max;
    }

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给定不同面额的硬币 coins 和一个总金额 amount。编写一个函数来计算可以凑成总金额所需的最少的硬币个数。如果没有任何一种硬币组合能组成总金额，返回 -1。

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public int coinChange(int[] coins, int amount) {
       int[] dp=new int[amount+1];
       int max=amount+1;
       Arrays.fill(dp,max);
       dp[0]=0;
       for (int i=1;i<dp.length;i++){
           for (int coin : coins) {
               if (i >= coin) {
                   dp[i]=Math.min(dp[i],dp[i-coin]+1);
               }
           }
       }
       return dp[amount]>amount?-1:dp[amount];
   }

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给定一个三角形，找出自顶向下的最小路径和。每一步只能移动到下一行中相邻的结点上。

相邻的结点 在这里指的是 下标 与 上一层结点下标 相同或者等于 上一层结点下标 + 1 的两个结点。

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[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

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public int minimumTotal(List<List<Integer>> triangle) {
        int n = triangle.size();
        int[][] f = new int[n][n];
        //左边特殊处理
        f[0][0] = triangle.get(0).get(0);
        for (int i = 1; i < n; ++i) {
            f[i][0] = f[i - 1][0] + triangle.get(i).get(0);
            for (int j = 1; j < i; ++j) {
                f[i][j] = Math.min(f[i - 1][j - 1], f[i - 1][j]) + triangle.get(i).get(j);
            }
            //右边特殊处理
            f[i][i] = f[i - 1][i - 1] + triangle.get(i).get(i);
        }
        int minTotal = f[n - 1][0];
        for (int i = 1; i < n; ++i) {
            minTotal = Math.min(minTotal, f[n - 1][i]);
        }
        return minTotal;
    }

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给定一个无序的整数数组，找到其中最长上升子序列的长度。

示例:
输入: [10,9,2,5,3,7,101,18]
输出: 4 
解释: 最长的上升子序列是 [2,3,7,101]，它的长度是 4。

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public int lengthOfLIS(int[] nums) {
       if (nums.length==0){
           return 0;
       }
       int res=0;
       int[] dp=new int[nums.length];
       Arrays.fill(dp,1);
       for (int end=0;end<nums.length;end++){
           for (int start=0;start<end;start++){
               if (nums[start]<nums[end]){
                   dp[end]=Math.max(dp[end],dp[start]+1);
               }
           }
           res=Math.max(res,dp[end]);
       }
       return res;
   }

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给定一个包含非负整数的 m x n 网格，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。

说明：每次只能向下或者向右移动一步。

示例:

输入:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
输出: 7
解释: 因为路径 1→3→1→1→1 的总和最小。

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public int minPathSum(int[][] grid) {
        int m=grid.length;
        int n=grid[0].length;
        int[][] dp=new int[m][n];
        dp[0][0]=grid[0][0];
        //第一行
        for (int col=1;col<n;col++){
            dp[0][col]=dp[0][col-1]+grid[0][col];
        }
        //第一列
        for (int row=1;row<m;row++){
            dp[row][0]=dp[row-1][0]+grid[row][0];
        }
        for (int row=1;row<m;row++){
            for (int col=1;col<n;col++){
                dp[row][col]=Math.min(dp[row-1][col],dp[row][col-1])+grid[row][col];
            }
        }
        return dp[m-1][n-1];


    }

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一些恶魔抓住了公主（P）并将她关在了地下城的右下角。地下城是由 M x N 个房间组成的二维网格。我们英勇的骑士（K）最初被安置在左上角的房间里，他必须穿过地下城并通过对抗恶魔来拯救公主。

骑士的初始健康点数为一个正整数。如果他的健康点数在某一时刻降至 0 或以下，他会立即死亡。

有些房间由恶魔守卫，因此骑士在进入这些房间时会失去健康点数（若房间里的值为负整数，则表示骑士将损失健康点数）；其他房间要么是空的（房间里的值为 0），要么包含增加骑士健康点数的魔法球（若房间里的值为正整数，则表示骑士将增加健康点数）。

为了尽快到达公主，骑士决定每次只向右或向下移动一步。
编写一个函数来计算确保骑士能够拯救到公主所需的最低初始健康点数。

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public int calculateMinimumHP(int[][] dungeon) {
     int n = dungeon.length, m = dungeon[0].length;
     int[][] dp = new int[n + 1][m + 1];
     for (int i = 0; i <= n; ++i) {
         Arrays.fill(dp[i], Integer.MAX_VALUE);
     }
     dp[n][m - 1] = dp[n - 1][m] = 1;
     for (int i = n - 1; i >= 0; --i) {
         for (int j = m - 1; j >= 0; --j) {
             int minn = Math.min(dp[i + 1][j], dp[i][j + 1]);
             dp[i][j] = Math.max(minn - dungeon[i][j], 1);
         }
     }
     return dp[0][0];
 }

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public class MyServer {
    public static void main(String[] args) throws Exception{

        EventLoopGroup bossGroup = new NioEventLoopGroup(1);
        EventLoopGroup workerGroup = new NioEventLoopGroup();

        try {

            ServerBootstrap serverBootstrap = new ServerBootstrap();
            serverBootstrap.group(bossGroup,workerGroup)
                    .channel(NioServerSocketChannel.class)
                    .childHandler(new ChannelInitializer<SocketChannel>() {
                        @Override
                        protected void initChannel(SocketChannel ch) throws Exception {
                            ChannelPipeline pipeline = ch.pipeline();

                            //入站编码处理器
                            pipeline.addLast(new MyByteToLongDecoder());
                            //出站的handler进行编码
                            pipeline.addLast(new MyLongToByteEncoder());
                            //自定义的handler 处理业务逻辑
                            pipeline.addLast(new MyServerHandler());

                        }
                    });

            ChannelFuture channelFuture = serverBootstrap.bind(7000).sync();
            channelFuture.channel().closeFuture().sync();

        }finally {
            bossGroup.shutdownGracefully();
            workerGroup.shutdownGracefully();
        }

    }
}

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protected MultithreadEventExecutorGroup(int nThreads, Executor executor,
                                           EventExecutorChooserFactory chooserFactory, Object... args) {
       if (nThreads <= 0) {
           //参数合法性检测
           throw new IllegalArgumentException(String.format("nThreads: %d (expected: > 0)", nThreads));
       }

       if (executor == null) {
           //如果线程池为空，则创建一个线程池，
           //这个线程池非常的特殊，他为每个任务都单独创建一个任务
           executor = new ThreadPerTaskExecutor(newDefaultThreadFactory());
       }

    //这个children实际上是一个NioEventLoop数组
       children = new EventExecutor[nThreads];

       for (int i = 0; i < nThreads; i ++) {
           boolean success = false; //用于标记是否创建成功
           try {
               //这里的newChild实际是子类NioEventLoopGroup实现的
               children[i] = newChild(executor, args);
               success = true;
           } catch (Exception e) {
               // TODO: Think about if this is a good exception type
               throw new IllegalStateException("failed to create a child event loop", e);
           } finally {
               if (!success) {
                   //如果在创建的NioEventLoop数组数组中途出现了异常
                   //那么就将成功创建的NioEventLoop关闭掉
                   for (int j = 0; j < i; j ++) {
                       children[j].shutdownGracefully();
                   }

                   for (int j = 0; j < i; j ++) {
                       EventExecutor e = children[j];
                       try {
                           while (!e.isTerminated()) {
                               e.awaitTermination(Integer.MAX_VALUE, TimeUnit.SECONDS);
                           }
                       } catch (InterruptedException interrupted) {
                           // Let the caller handle the interruption.
                           Thread.currentThread().interrupt();
                           break;
                       }
                   }
               }
           }
       }

    //chooser实际上是每次进行相关操作时线程的选择的实现，默认使用的是轮询策略
       chooser = chooserFactory.newChooser(children);

       final FutureListener<Object> terminationListener = new FutureListener<Object>() {
           @Override
           public void operationComplete(Future<Object> future) throws Exception {
               if (terminatedChildren.incrementAndGet() == children.length) {
                   terminationFuture.setSuccess(null);
               }
           }
       };

       for (EventExecutor e: children) {
           e.terminationFuture().addListener(terminationListener);
       }

       Set<EventExecutor> childrenSet = new LinkedHashSet<EventExecutor>(children.length);
       Collections.addAll(childrenSet, children);
       readonlyChildren = Collections.unmodifiableSet(childrenSet);
   }

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   protected EventLoop newChild(Executor executor, Object... args) throws Exception {
       EventLoopTaskQueueFactory queueFactory = args.length == 4 ? (EventLoopTaskQueueFactory) args[3] : null;
       return new NioEventLoop(this, executor, (SelectorProvider) args[0],
           ((SelectStrategyFactory) args[1]).newSelectStrategy(), (RejectedExecutionHandler) args[2], queueFactory);
}

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public ServerBootstrap group(EventLoopGroup parentGroup, EventLoopGroup childGroup) {
    super.group(parentGroup);
    ObjectUtil.checkNotNull(childGroup, "childGroup");
    if (this.childGroup != null) {
        throw new IllegalStateException("childGroup set already");
    }
    this.childGroup = childGroup;
    return this;
}

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private ChannelFuture doBind(final SocketAddress localAddress) {
    //对Channel进行初始化和注册操作
       final ChannelFuture regFuture = initAndRegister();
       final Channel channel = regFuture.channel();
       if (regFuture.cause() != null) {
           return regFuture;
       }

       if (regFuture.isDone()) {
           // At this point we know that the registration was complete and successful.
           ChannelPromise promise = channel.newPromise();
           doBind0(regFuture, channel, localAddress, promise);
           return promise;
       } else {
           // Registration future is almost always fulfilled already, but just in case it's not.
           final PendingRegistrationPromise promise = new PendingRegistrationPromise(channel);
           regFuture.addListener(new ChannelFutureListener() {
               @Override
               public void operationComplete(ChannelFuture future) throws Exception {
                   Throwable cause = future.cause();
                   if (cause != null) {
                       // Registration on the EventLoop failed so fail the ChannelPromise directly to not cause an
                       // IllegalStateException once we try to access the EventLoop of the Channel.
                       promise.setFailure(cause);
                   } else {
                       // Registration was successful, so set the correct executor to use.
                       // See https://github.com/netty/netty/issues/2586
                       promise.registered();

                       doBind0(regFuture, channel, localAddress, promise);
                   }
               }
           });
           return promise;
       }
   }

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final ChannelFuture initAndRegister() {
    Channel channel = null;
    try {
        //利用Channel工厂创建一个Channel，实际上是通过反射实例化的
        channel = channelFactory.newChannel();
        init(channel);
    } catch (Throwable t) {
        if (channel != null) {
            channel.unsafe().closeForcibly();
            return new DefaultChannelPromise(channel, GlobalEventExecutor.INSTANCE).setFailure(t);
        }
   
        return new DefaultChannelPromise(new FailedChannel(), GlobalEventExecutor.INSTANCE).setFailure(t);
    }

    ChannelFuture regFuture = config().group().register(channel);
    if (regFuture.cause() != null) {
        if (channel.isRegistered()) {
            channel.close();
        } else {
            channel.unsafe().closeForcibly();
        }
    }
    return regFuture;
}

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void init(Channel channel) {
       setChannelOptions(channel, options0().entrySet().toArray(newOptionArray(0)), logger);
       setAttributes(channel, attrs0().entrySet().toArray(newAttrArray(0)));

       ChannelPipeline p = channel.pipeline();

       final EventLoopGroup currentChildGroup = childGroup;
       final ChannelHandler currentChildHandler = childHandler;
       final Entry<ChannelOption<?>, Object>[] currentChildOptions =
               childOptions.entrySet().toArray(newOptionArray(0));
       final Entry<AttributeKey<?>, Object>[] currentChildAttrs = childAttrs.entrySet().toArray(newAttrArray(0));

       p.addLast(new ChannelInitializer<Channel>() {
           @Override
           public void initChannel(final Channel ch) {
               final ChannelPipeline pipeline = ch.pipeline();
               ChannelHandler handler = config.handler();
               if (handler != null) {
                   pipeline.addLast(handler);
               }

               ch.eventLoop().execute(new Runnable() {
                   @Override
                   public void run() {
                       pipeline.addLast(new ServerBootstrapAcceptor(
                               ch, currentChildGroup, currentChildHandler, currentChildOptions, currentChildAttrs));
                   }
               });
           }
       });
   }

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@Override
public final void register(EventLoop eventLoop, final ChannelPromise promise) {
    ObjectUtil.checkNotNull(eventLoop, "eventLoop");
    if (isRegistered()) {
        promise.setFailure(new IllegalStateException("registered to an event loop already"));
        return;
    }
    if (!isCompatible(eventLoop)) {
        promise.setFailure(
                new IllegalStateException("incompatible event loop type: " + eventLoop.getClass().getName()));
        return;
    }

    AbstractChannel.this.eventLoop = eventLoop;

    if (eventLoop.inEventLoop()) {
        register0(promise);
    } else {
        try {
            eventLoop.execute(new Runnable() {
                @Override
                public void run() {
                    register0(promise);
                }
            });
        } catch (Throwable t) {
            logger.warn(
                    "Force-closing a channel whose registration task was not accepted by an event loop: {}",
                    AbstractChannel.this, t);
            closeForcibly();
            closeFuture.setClosed();
            safeSetFailure(promise, t);
        }
    }
}
private void register0(ChannelPromise promise) {
    try {
        if (!promise.setUncancellable() || !ensureOpen(promise)) {
            return;
        }
        boolean firstRegistration = neverRegistered;
        doRegister();
        neverRegistered = false;
        registered = true;
        pipeline.invokeHandlerAddedIfNeeded();
        safeSetSuccess(promise);
        pipeline.fireChannelRegistered();
        if (isActive()) {
            if (firstRegistration) {
                pipeline.fireChannelActive();
            } else if (config().isAutoRead()) {
                beginRead();
            }
        }
    } catch (Throwable t) {
        closeForcibly();
        closeFuture.setClosed();
        safeSetFailure(promise, t);
    }
}

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protected void doRegister() throws Exception {
    boolean selected = false;
    for (;;) {
        try {
            selectionKey = javaChannel().register(eventLoop().unwrappedSelector(), 0, this);
            return;
        } catch (CancelledKeyException e) {
            if (!selected) {
                eventLoop().selectNow();
                selected = true;
            } else {
                throw e;
            }
        }
    }
}

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private void execute(Runnable task, boolean immediate) {
    boolean inEventLoop = inEventLoop();
    addTask(task);
    if (!inEventLoop) {
        startThread();
        if (isShutdown()) {
            boolean reject = false;
            try {
                if (removeTask(task)) {
                    reject = true;
                }
            } catch (UnsupportedOperationException e) {
            }
            if (reject) {
                reject();
            }
        }
    }
    if (!addTaskWakesUp && immediate) {
        wakeup(inEventLoop);
    }
}

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protected void run() {
    int selectCnt = 0;
    for (;;) {
        try {
            int strategy;
            try {
                strategy = selectStrategy.calculateStrategy(selectNowSupplier, hasTasks());
                switch (strategy) {
                case SelectStrategy.CONTINUE:
                    continue;
                case SelectStrategy.BUSY_WAIT:
                case SelectStrategy.SELECT:
                    long curDeadlineNanos = nextScheduledTaskDeadlineNanos();
                    if (curDeadlineNanos == -1L) {
                        curDeadlineNanos = NONE; // nothing on the calendar
                    }
                    nextWakeupNanos.set(curDeadlineNanos);
                    try {
                        if (!hasTasks()) {
                            strategy = select(curDeadlineNanos);
                        }
                    } finally {
                        nextWakeupNanos.lazySet(AWAKE);
                    }
                    // fall through
                default:
                }
            } catch (IOException e) {
                rebuildSelector0();
                selectCnt = 0;
                handleLoopException(e);
                continue;
            }

            selectCnt++;
            cancelledKeys = 0;
            needsToSelectAgain = false;
            final int ioRatio = this.ioRatio;
            boolean ranTasks;
            if (ioRatio == 100) {
                try {
                    if (strategy > 0) {
                        processSelectedKeys();
                    }
                } finally {
                    // Ensure we always run tasks.
                    ranTasks = runAllTasks();
                }
            } else if (strategy > 0) {
                final long ioStartTime = System.nanoTime();
                try {
                    processSelectedKeys();
                } finally {
                    final long ioTime = System.nanoTime() - ioStartTime;
                    ranTasks = runAllTasks(ioTime * (100 - ioRatio) / ioRatio);
                }
            } else {
                ranTasks = runAllTasks(0); // This will run the minimum number of tasks
            }
            if (ranTasks || strategy > 0) {
                if (selectCnt > MIN_PREMATURE_SELECTOR_RETURNS && logger.isDebugEnabled()) {
                    logger.debug("Selector.select() returned prematurely {} times in a row for Selector {}.",
                            selectCnt - 1, selector);
                }
                selectCnt = 0;
            } else if (unexpectedSelectorWakeup(selectCnt)) { // Unexpected wakeup (unusual case)
                selectCnt = 0;
            }
        } catch (CancelledKeyException e) {
            if (logger.isDebugEnabled()) {
                logger.debug(CancelledKeyException.class.getSimpleName() + " raised by a Selector {} - JDK bug?",
                        selector, e);
            }
        } catch (Throwable t) {
            handleLoopException(t);
        }
        try {
            if (isShuttingDown()) {
                closeAll();
                if (confirmShutdown()) {
                    return;
                }
            }
        } catch (Throwable t) {
            handleLoopException(t);
        }
    }
}

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protected HandlerExecutionChain getHandler(HttpServletRequest request) throws Exception {
for (HandlerMapping hm : this.handlerMappings) {
if (logger.isTraceEnabled()) {
logger.trace(
"Testing handler map [" + hm + "] in DispatcherServlet with name '" + getServletName() + "'");
}
HandlerExecutionChain handler = hm.getHandler(request);
if (handler != null) {
return handler;
}
}
return null;
}

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//判断当前的HandlerAdapter是否支持HandlerMethod
boolean supports(Object handler);
ModelAndView handle(HttpServletRequest request, HttpServletResponse response, Object handler) throws Exception;
long getLastModified(HttpServletRequest request, Object handler);

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protected HandlerAdapter getHandlerAdapter(Object handler) throws ServletException {
for (HandlerAdapter ha : this.handlerAdapters) {
if (logger.isTraceEnabled()) {
logger.trace("Testing handler adapter [" + ha + "]");
}
if (ha.supports(handler)) {
return ha;
}
}
throw new ServletException("No adapter for handler [" + handler +
"]: The DispatcherServlet configuration needs to include a HandlerAdapter that supports this handler");
}

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public ModelAndView handle(HttpServletRequest request, HttpServletResponse response, Object handler)
throws Exception {

//最终拿到了我们的Controller类
Class<?> clazz = ClassUtils.getUserClass(handler);
//判断是否使用了@SessionAttributes
Boolean annotatedWithSessionAttributes = this.sessionAnnotatedClassesCache.get(clazz);
if (annotatedWithSessionAttributes == null) {
annotatedWithSessionAttributes = (AnnotationUtils.findAnnotation(clazz, SessionAttributes.class) != null);
this.sessionAnnotatedClassesCache.put(clazz, annotatedWithSessionAttributes);
}

if (annotatedWithSessionAttributes) {
// Always prevent caching in case of session attribute management.
checkAndPrepare(request, response, this.cacheSecondsForSessionAttributeHandlers, true);
// Prepare cached set of session attributes names.
}
else {
// 禁用缓存
checkAndPrepare(request, response, true);
}

// Execute invokeHandlerMethod in synchronized block if required.
if (this.synchronizeOnSession) {
HttpSession session = request.getSession(false);
if (session != null) {
Object mutex = WebUtils.getSessionMutex(session);
synchronized (mutex) {
return invokeHandlerMethod(request, response, handler);
}
}
}

return invokeHandlerMethod(request, response, handler);
}

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protected ModelAndView invokeHandlerMethod(HttpServletRequest request, HttpServletResponse response, Object handler)
throws Exception {

ServletHandlerMethodResolver methodResolver = getMethodResolver(handler);
//获取处理请求的方法
Method handlerMethod = methodResolver.resolveHandlerMethod(request);
//创建各种组件
ServletHandlerMethodInvoker methodInvoker = new ServletHandlerMethodInvoker(methodResolver);
ServletWebRequest webRequest = new ServletWebRequest(request, response);
ExtendedModelMap implicitModel = new BindingAwareModelMap();

        //调用方法拿到结果
Object result = methodInvoker.invokeHandlerMethod(handlerMethod, handler, webRequest, implicitModel);
//获取ModelAndView
ModelAndView mav =
methodInvoker.getModelAndView(handlerMethod, handler.getClass(), result, implicitModel, webRequest);
//更新view中的属性
methodInvoker.updateModelAttributes(handler, (mav != null ? mav.getModel() : null), implicitModel, webRequest);
return mav;
}