zoukankan      html  css  js  c++  java
  • 深入理解系统调用

    作业要求:

    • 找一个系统调用,系统调用号为学号最后2位相同的系统调用
    • 通过汇编指令触发该系统调用
    • 通过gdb跟踪该系统调用的内核处理过程
    • 重点阅读分析系统调用入口的保存现场、恢复现场和系统调用返回,以及重点关注系统调用过程中内核堆栈状态的变化

    一、选择系统调用

    本人学号尾数为31,但是查找syscall_32.tbl表后发现31号系统调用为stty,进一步搜素在系统调用描述文件里面找到此系统调用和32号gtty都为sys_ni_syscall,进一步查资料发现上述两个系统调用已经被淘汰,所以它所对应的服务例程就要被指定为sys_ni_syscall
    系统调用表
    stty被指定为sys_ni_syscall

    知识拓展:
    即使31号和32号系统调用已经被淘汰了,但是我们并不能将它们的位置分配给其他的系统调用,因为一些老的代码可能还会使用到它们。否则,如果某个用户应用试图调用这些已经被淘汰的系统调用,所得到的结果,比如打开了一个文件,就会与预期完全不同,这将令人感到非常奇怪。其实,sys_ni_syscall中的"ni"即表示"not implemented(没有实现)


    下面转而分析31号上面的系统调用,即30号utime

    # The format is:
    # <number> <abi> <name> <entry point> <compat entry point>
    30	i386	utime			sys_utime32			__ia32_sys_utime32
    

    utime作用为修改文件的访问时间和修改时间。其对应的32位entry pointsys_utime32,搜索sys_utime32utimes.c文件中找到了其实现,它是通过调用do_utimes来实现的。do_utimes的代码实现如下:

    /*
     * do_utimes - change times on filename or file descriptor
     * @dfd: open file descriptor, -1 or AT_FDCWD
     * @filename: path name or NULL
     * @times: new times or NULL
     * @flags: zero or more flags (only AT_SYMLINK_NOFOLLOW for the moment)
     *
     * If filename is NULL and dfd refers to an open file, then operate on
     * the file.  Otherwise look up filename, possibly using dfd as a
     * starting point.
     *
     * If times==NULL, set access and modification to current time,
     * must be owner or have write permission.
     * Else, update from *times, must be owner or super user.
     */
    long do_utimes(int dfd, const char __user *filename, struct timespec64 *times,
    	       int flags)
    {
    	int error = -EINVAL;
    
    	if (times && (!nsec_valid(times[0].tv_nsec) ||
    		      !nsec_valid(times[1].tv_nsec))) {
    		goto out;
    	}
    
    	if (flags & ~AT_SYMLINK_NOFOLLOW)
    		goto out;
    
    	if (filename == NULL && dfd != AT_FDCWD) {
    		struct fd f;
    
    		if (flags & AT_SYMLINK_NOFOLLOW)
    			goto out;
    
    		f = fdget(dfd);
    		error = -EBADF;
    		if (!f.file)
    			goto out;
    
    		error = utimes_common(&f.file->f_path, times);
    		fdput(f);
    	} else {
    		struct path path;
    		int lookup_flags = 0;
    
    		if (!(flags & AT_SYMLINK_NOFOLLOW))
    			lookup_flags |= LOOKUP_FOLLOW;
    retry:
    		error = user_path_at(dfd, filename, lookup_flags, &path);
    		if (error)
    			goto out;
    
    		error = utimes_common(&path, times);
    		path_put(&path);
    		if (retry_estale(error, lookup_flags)) {
    			lookup_flags |= LOOKUP_REVAL;
    			goto retry;
    		}
    	}
    
    out:
    	return error;
    }
    

    二、 触发系统调用(直接触发+汇编触发)

    使用下面的代码直接触发utime系统调用:

    #include <sys/stat.h>
    #include <utime.h>
    #include <stdio.h>
    
    int main(int argc, char *argv[])
    {
        char *pathname;
        struct stat sb;
        struct utimbuf utb;
    
        if (argc != 2 || strcmp(argv[1], "--help") == 0){
            printf("%s file
    ", argv[0]);
            return 1;
        }
    
        pathname = argv[1];
    
        //获取当前文件时间
        if (stat(pathname, &sb) == -1)
            return 1;
    
        //把最近修改时间改成访问时间
        utb.actime = sb.st_atime;
        utb.modtime = sb.st_atime;        /* Make modify time same as access time */
        // 调用utime
        if (utime(pathname, &utb) == -1)  /* Update file times */
            return 1;
    
        return 0;
    }
    

    程序执行效果

    对上述的程序进行修改,使用汇编来调用utime,其实就是使用汇编指令传递utime的参数,并使用系统调用通过软中断0x80陷入内核,跳转到系统调用处理程序system_call(sys_utime32)函数,并执行相应的服务例程,但由于是代表用户进程,所以这个执行过程并不属于中断上下文,而是处于进程上下文:

    #include <sys/stat.h>
    #include <utime.h>
    #include <stdio.h>
    #include <string.h>
    int main(int argc, char *argv[])
    {
        char *pathname;
        struct stat sb;
        struct utimbuf utb;
    
        if (argc != 2 || strcmp(argv[1], "--help") == 0){
            printf("%s file
    ", argv[0]);
            return 1;
        }
    
        pathname = argv[1];
    
        //获取当前文件时间
        if (stat(pathname, &sb) == -1)
            return 1;
    
        //把最近修改时间改成访问时间
        utb.actime = sb.st_atime;
        utb.modtime = sb.st_atime;        /* Make modify time same as access time */
        int flag;
    
        asm volatile(
        "movl %1, %%ebx
    	"  // 将pathname放入ebx
        "movl %2, %%ecx
    	"  // 将utimbuf 的引用放入ecx
        "movl $30, %%eax
    	" //通过EAX寄存器返回系统调用值
        "int $0x80
    	"       // 通过软中断0x80陷入内核
        "movl %%eax, %0
    	"  // 将输出通过eax赋值给flag
        :"=m"(flag)
        :"b"(pathname),"c"(&utb)
        );
    
        if (flag == -1)  /* Update file times */
            return 1;
    
        return 0;
    }
    

    使用汇编修改最近改动时间

    三、 通过gdb跟踪该系统调用的内核处理过程

    3.1、 gdb环境配置

    首先执行qemu-system-x86_64 -kernel ../arch/x86/boot/bzImage -initrd rootfs.cpio.gz启动qemu(注意路径),然后把本地使用汇编触发utime系统调用的编译过可执行程序copy到rootfs/home/目录下,然后再在rootfs/home/目录下建一个b.test文件。然后使用以下命令重新打包根文件系统镜像(rootfs下执行),再重启qemu。

    find . -print0 | cpio --null -ov --format=newc | gzip -9 > ../rootfs.cpio.gz
    // 重新运行qemu
    qemu-system-x86_64 -kernel ../arch/x86/boot/bzImage -initrd rootfs.cpio.gz
    

    启动qemu,注意与自己机器上的路径

    copy assembly

    重启后的qemu

    关掉qemu,在终端使用qemu-system-x86_64 -kernel ./arch/x86/boot/bzImage -initrd ./busybox-1.31.1/rootfs.cpio.gz -S -s -nographic -append "console=ttyS0"以shell的形式运行qemu进行调试(退出使用killall qemu-system-x86_64)。再新开一个终端,执行以下命令加载vmlinux和连接gdb server,然后尝试着在start_kernel处打断点,可以看到qemu执行到Booting the kernel会停下来:

    gdb
    file vmlinux
    target remote:1234
    b start_kernel
    c
    ....
    

    可能出现的错误及解决方法:

    • ERROR:执行file vmlinux可能会报一下错误:
    • 解决方法:
    vi ~/.gdbinit
    ================添加以下内容==============
    add-auto-load-safe-path /home/dfx/linux-5.4.34/scripts/gdb/vmlinux-gdb.py
    set auto-load safe-path /
    python sys.path.append("/home/dfx/linux-5.4.34/scripts/gdb/vmlinux-gdb.py")
    
    3.2、系统调用分析

    使用gcc a.c -static -m32a.c编译成32位的可执行文件,然后再使用 objdump -S a.out > a32.s反汇编查看utime的调用过程。

    mian函数调用utime
    utime call 0x80ea9f0
    可以看到utime并没有使用syscall,而是调用0x80ea9f0,使用gdb 运行x 0x80ea9f0查看该地址的值如下
    查看0x80ea9f0地址值

    无奈,只好转而分析一下64位的utime,使用上述方法重新得到64的反汇编代码如下(部分):

    000000000043f250 <utime>:
      43f250:       b8 84 00 00 00          mov    $0x84,%eax
      43f255:       0f 05                   syscall
      43f257:       48 3d 01 f0 ff ff       cmp    $0xfffffffffffff001,%rax
      43f25d:       0f 83 4d 52 00 00       jae    4444b0 <__syscall_error>
      43f263:       c3                      retq
      43f264:       66 2e 0f 1f 84 00 00    nopw   %cs:0x0(%rax,%rax,1)
      43f26b:       00 00 00 
      43f26e:       66 90                   xchg   %ax,%ax
    
    

    从上面的代码可以看到,utime的系统调用号为0x84(132),查看系统调用表可以发现对应的系统调用函数为__x64_sys_utime
    64位系统调用表

    3.3、使用gdb调试跟踪

    __x64_sys_utime打断点,然后在qemu运行64位的程序(注意要重新打包rootfs),可以看到成功跟踪到了utime.c文件的相关代码


    可以看到调用的是do_futimesat在utime.c中可以发现下面这段注释:

    futimesat()、utimes()和utime()是utimensat()的旧版本为与传统C库兼容而提供的。
    在现代体系中,我们总是使用libc包装器utimensat ()
    

    即utime是为了对c语言库进行兼容,现在使用utimensat,其为第320号系统调用,并且不管是utime还是utimensat,都是调用的do_utimes()函数。
    utimensat在系统调用表中的信息
    utimensat函数体

    =======================do_utimes描述==========================
    
    /*
     * do_utimes - change times on filename or file descriptor
     * @dfd: open file descriptor, -1 or AT_FDCWD
     * @filename: path name or NULL
     * @times: new times or NULL
     * @flags: zero or more flags (only AT_SYMLINK_NOFOLLOW for the moment)
     *
     * If filename is NULL and dfd refers to an open file, then operate on
     * the file.  Otherwise look up filename, possibly using dfd as a
     * starting point.
     *
     * If times==NULL, set access and modification to current time,
     * must be owner or have write permission.
     * Else, update from *times, must be owner or super user.
     */
    

    具体的跟踪过程如下两段代码所示(第一段先整体查看调用流程,并监视堆栈的变化,第二段进入部分函数内部,查看细节):

    (gdb) b __x64_sys_utime
    Note: breakpoints 1, 2, 3, 4, 5 and 6 also set at pc 0xffffffff81206f07.
    Breakpoint 8 at 0xffffffff81206f07: file fs/utimes.c, line 204.
    (gdb) c
    Continuing.
    
    (gdb) bt
    #0  __x64_sys_utime (regs=0xffffc900001b7f58) at fs/utimes.c:204
    #1  0xffffffff81002603 in do_syscall_64 (nr=<optimized out>, regs=0xffffc900001b7f58) at arch/x86/entry/common.c:290
    #2  0xffffffff81c0007c in entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:175
    #3  0x0000000000000000 in ?? ()
    (gdb) n
    
    Breakpoint 7, do_utimes (dfd=-100, filename=0x4a1024 "./b.test", times=0xffffc900001b7ee0, flags=0) at fs/utimes.c:90
    90	{
    (gdb) n
    93		if (times && (!nsec_valid(times[0].tv_nsec) ||
    (gdb) n
    94			      !nsec_valid(times[1].tv_nsec))) {
    (gdb) n
    93		if (times && (!nsec_valid(times[0].tv_nsec) ||
    (gdb) n
    98		if (flags & ~AT_SYMLINK_NOFOLLOW)
    (gdb) n
    101		if (filename == NULL && dfd != AT_FDCWD) {
    (gdb) n
    119				lookup_flags |= LOOKUP_FOLLOW;
    (gdb) n
    121			error = user_path_at(dfd, filename, lookup_flags, &path);
    (gdb) n
    122			if (error)
    (gdb) n
    125			error = utimes_common(&path, times);
    (gdb) n
    126			path_put(&path);
    (gdb) n
    127			if (retry_estale(error, lookup_flags)) {
    (gdb) n
    135	}
    (gdb) bt
    #0  do_utimes (dfd=-100, filename=0x4a1024 "./b.test", times=0xffffc900001b7ee0, flags=0) at fs/utimes.c:119
    #1  0xffffffff81206f64 in __do_sys_utime (times=<optimized out>, filename=<optimized out>) at fs/utimes.c:215
    #2  __se_sys_utime (times=<optimized out>, filename=<optimized out>) at fs/utimes.c:204
    #3  __x64_sys_utime (regs=<optimized out>) at fs/utimes.c:204
    #4  0xffffffff81002603 in do_syscall_64 (nr=<optimized out>, regs=0x4a1024) at arch/x86/entry/common.c:290
    #5  0xffffffff81c0007c in entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:175
    #6  0x0000000000000000 in ?? ()
    
    (gdb) n
    __x64_sys_utime (regs=0xffff8880070a4140) at fs/utimes.c:204
    204	SYSCALL_DEFINE2(utime, char __user *, filename, struct utimbuf __user *, times)
    (gdb) bt
    #0  __x64_sys_utime (regs=0xffff8880070a4140) at fs/utimes.c:204
    #1  0xffffffff81002603 in do_syscall_64 (nr=<optimized out>, regs=0x0 <fixed_percpu_data>) at arch/x86/entry/common.c:290
    #2  0xffffffff81c0007c in entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:175
    #3  0x0000000000000000 in ?? ()
    (gdb) n
    do_syscall_64 (nr=18446612682188144960, regs=0xffffc900001b7f58) at arch/x86/entry/common.c:300
    300		syscall_return_slowpath(regs);
    (gdb) n
    301	}
    (gdb) bt
    #0  do_syscall_64 (nr=<optimized out>, regs=<optimized out>) at arch/x86/entry/common.c:301
    #1  0xffffffff81c0007c in entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:175
    #2  0x0000000000000000 in ?? ()
    (gdb) n
    entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:184
    184		movq	RCX(%rsp), %rcx
    (gdb) bt
    #0  entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:184
    #1  0x0000000000000000 in ?? ()
    (gdb) n
    185		movq	RIP(%rsp), %r11
    (gdb) n
    187		cmpq	%rcx, %r11	/* SYSRET requires RCX == RIP */
    (gdb) n
    188		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    205		shl	$(64 - (__VIRTUAL_MASK_SHIFT+1)), %rcx
    (gdb) n
    206		sar	$(64 - (__VIRTUAL_MASK_SHIFT+1)), %rcx
    (gdb) n
    210		cmpq	%rcx, %r11
    (gdb) n
    211		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    213		cmpq	$__USER_CS, CS(%rsp)		/* CS must match SYSRET */
    (gdb) n
    214		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    216		movq	R11(%rsp), %r11
    (gdb) n
    217		cmpq	%r11, EFLAGS(%rsp)		/* R11 == RFLAGS */
    (gdb) n
    218		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    238		testq	$(X86_EFLAGS_RF|X86_EFLAGS_TF), %r11
    (gdb) n
    239		jnz	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    243		cmpq	$__USER_DS, SS(%rsp)		/* SS must match SYSRET */
    (gdb) n
    244		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:253
    253		POP_REGS pop_rdi=0 skip_r11rcx=1
    (gdb) bt
    #0  syscall_return_via_sysret () at arch/x86/entry/entry_64.S:253
    #1  0x0000000000000000 in ?? ()
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:259
    259		movq	%rsp, %rdi
    (gdb) n
    260		movq	PER_CPU_VAR(cpu_tss_rw + TSS_sp0), %rsp
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:262
    262		pushq	RSP-RDI(%rdi)	/* RSP */
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:263
    263		pushq	(%rdi)		/* RDI */
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:271
    271		SWITCH_TO_USER_CR3_STACK scratch_reg=%rdi
    (gdb) n
    273		popq	%rdi
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:274
    274		popq	%rsp
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:275
    275		USERGS_SYSRET64
    (gdb) n
    0x000000000043f257 in ?? ()
    (gdb) n
    Cannot find bounds of current function
    (gdb) 
    
    
    
    Breakpoint 1, __x64_sys_utime (regs=0xffffc900001b7f58) at fs/utimes.c:204
    204	SYSCALL_DEFINE2(utime, char __user *, filename, struct utimbuf __user *, times)
    (gdb) n
    
    Breakpoint 7, do_utimes (dfd=-100, filename=0x4a1024 "./b.test", times=0xffffc900001b7ee0, flags=0) at fs/utimes.c:90
    90	{
    (gdb) n
    93		if (times && (!nsec_valid(times[0].tv_nsec) ||
    (gdb) n
    94			      !nsec_valid(times[1].tv_nsec))) {
    (gdb) n
    93		if (times && (!nsec_valid(times[0].tv_nsec) ||
    (gdb) n
    98		if (flags & ~AT_SYMLINK_NOFOLLOW)
    (gdb) n
    101		if (filename == NULL && dfd != AT_FDCWD) {
    (gdb) n
    119				lookup_flags |= LOOKUP_FOLLOW;
    (gdb) n
    121			error = user_path_at(dfd, filename, lookup_flags, &path);
    (gdb) n
    122			if (error)
    (gdb) n
    125			error = utimes_common(&path, times);
    (gdb) n
    126			path_put(&path);
    (gdb) n
    127			if (retry_estale(error, lookup_flags)) {
    (gdb) s
    retry_estale (flags=<optimized out>, error=<optimized out>) at ./include/linux/namei.h:91
    91		return error == -ESTALE && !(flags & LOOKUP_REVAL);
    (gdb) n
    do_utimes (dfd=118112576, filename=0x64 <error: Cannot access memory at address 0x64>, times=0xffffc900001b7ee0, flags=0) at fs/utimes.c:135
    135	}
    (gdb) n
    __x64_sys_utime (regs=0xffff8880070a4140) at fs/utimes.c:204
    204	SYSCALL_DEFINE2(utime, char __user *, filename, struct utimbuf __user *, times)
    (gdb) n
    do_syscall_64 (nr=18446612682188144960, regs=0xffffc900001b7f58) at arch/x86/entry/common.c:300
    300		syscall_return_slowpath(regs);
    (gdb) s
    syscall_return_slowpath (regs=<optimized out>) at arch/x86/entry/common.c:300
    300		syscall_return_slowpath(regs);
    (gdb) s
    get_current () at ./arch/x86/include/asm/current.h:15
    15		return this_cpu_read_stable(current_task);
    (gdb) s
    syscall_return_slowpath (regs=<optimized out>) at arch/x86/entry/common.c:256
    256		u32 cached_flags = READ_ONCE(ti->flags);
    (gdb) n
    270		if (unlikely(cached_flags & SYSCALL_EXIT_WORK_FLAGS))
    (gdb) n
    273		local_irq_disable();
    (gdb) s
    arch_local_irq_disable () at arch/x86/entry/common.c:273
    273		local_irq_disable();
    (gdb) s
    native_irq_disable () at ./arch/x86/include/asm/irqflags.h:49
    49		asm volatile("cli": : :"memory");
    (gdb) s
    syscall_return_slowpath (regs=<optimized out>) at arch/x86/entry/common.c:274
    274		prepare_exit_to_usermode(regs);
    (gdb) n
    do_syscall_64 (nr=<optimized out>, regs=<optimized out>) at arch/x86/entry/common.c:300
    300		syscall_return_slowpath(regs);
    (gdb) n
    301	}
    (gdb) n
    entry_SYSCALL_64 () at arch/x86/entry/entry_64.S:184
    184		movq	RCX(%rsp), %rcx
    (gdb) n
    185		movq	RIP(%rsp), %r11
    (gdb) n
    187		cmpq	%rcx, %r11	/* SYSRET requires RCX == RIP */
    (gdb) n
    188		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    205		shl	$(64 - (__VIRTUAL_MASK_SHIFT+1)), %rcx
    (gdb) n
    206		sar	$(64 - (__VIRTUAL_MASK_SHIFT+1)), %rcx
    (gdb) n
    210		cmpq	%rcx, %r11
    (gdb) n
    211		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    213		cmpq	$__USER_CS, CS(%rsp)		/* CS must match SYSRET */
    (gdb) n
    214		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    216		movq	R11(%rsp), %r11
    (gdb) n
    217		cmpq	%r11, EFLAGS(%rsp)		/* R11 == RFLAGS */
    (gdb) n
    218		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    238		testq	$(X86_EFLAGS_RF|X86_EFLAGS_TF), %r11
    (gdb) n
    239		jnz	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    243		cmpq	$__USER_DS, SS(%rsp)		/* SS must match SYSRET */
    (gdb) n
    244		jne	swapgs_restore_regs_and_return_to_usermode
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:253
    253		POP_REGS pop_rdi=0 skip_r11rcx=1
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:259
    259		movq	%rsp, %rdi
    (gdb) n
    260		movq	PER_CPU_VAR(cpu_tss_rw + TSS_sp0), %rsp
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:262
    262		pushq	RSP-RDI(%rdi)	/* RSP */
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:263
    263		pushq	(%rdi)		/* RDI */
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:271
    271		SWITCH_TO_USER_CR3_STACK scratch_reg=%rdi
    (gdb) n
    273		popq	%rdi
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:274
    274		popq	%rsp
    (gdb) n
    syscall_return_via_sysret () at arch/x86/entry/entry_64.S:275
    275		USERGS_SYSRET64
    (gdb) n
    0x000000000043f257 in ?? ()
    (gdb) n
    Cannot find bounds of current function
    (gdb) 
    
    

    四、 分析总结

    utime的系统调用触发大致过程如下(错误之处望指正):

    1. utime函数触发系统调用__x64_sys_utime,其主要通过调用do_utimes来完成相应的功能。
    2. do_utimes通过文件描述符引用一个打开的文件,然后操作文件。If times==NULL,就将访问和修改设置为当前时间。然后调用do_syscall_64从寄存器%rax里面取出系统调用号,然后根据系统调用号,在系统调用表sys_call_table中找到相应的函数进行调用并将寄存器中保存的参数取出来,作为函数参数,然后陷入内核。
    3. 最后系统调用结束前,一般会调用prepare_exit_to_usermode进行准备工作,然后使用jne条件转移指令等进行一系列的restore,恢复到用户态。e.g:jne swapgs_restore_regs_and_return_to_usermode

    参考文章:

  • 相关阅读:
    [kuangbin带你飞]专题二十一 概率&期望
    [kuangbin带你飞]专题二十 斜率DP
    POJ——3984迷宫问题(BFS+回溯)
    POJ——2251Dungeon Master(三维BFS)
    HDU——2647Reward(DFS或差分约束)
    HDU——4549M斐波那契数列(矩阵快速幂+快速幂+费马小定理)
    PAT天梯赛练习题——L3-008. 喊山(邻接表+BFS)
    Opencv学习笔记——视频高斯模糊并分别输出
    Opencv学习笔记——视频进度条的随动
    NYOJ——239月老的难题(二分图最大匹配)
  • 原文地址:https://www.cnblogs.com/fxding/p/12931117.html
Copyright © 2011-2022 走看看