Bài 1. Gọi
trong đó
Bài 2. Cho
Bài 3. (Bất đẳng thức nội suy Kolmogorov) Giả sử
và
a) Chứng minh rằng
b) Chứng minh rằng
c) Chứng minh rằng
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Notice the first limitation of the technique - it states that no raw CR and LF can be placed in the body section. This means that the technique cannot be used to send (POST) requests whose body complies with the "multipart/form-data" content-type format (this format uses raw CRs and LFs to mark headers and boundaries). In other words, a (POST) request whose body is a valid "multipart/form-data" stream is guaranteed (as far as today's knowledge extends) not to be sent from a Flash player. Web application authors can therefore use HTML forms whose ENCTYPE attribute is set to "multipart/form-data", and enforce that the submission contains a valid multipart/form-data body. Once these mechanisms are in place, and a request passes through, it is known not to originate from a Flash player, so the attack
described here is irrelevant.
T. Suppose we lump together every red node with its parent (which must be black); then, we obtain a tree T'which is no longer a binary tree. The tree T' will be a (2,4)-tree (or 2-3-4 tree), where each internal node has 2, 3, or 4 children. If the RB tree shown above is T, then its 2-3-4 counterpart isred, unless it is the root in which case we color it black. Call the newly inserted node z.z or its parent is black, then there is nothing to do. All properties are still satisfied.z‘s parent is red. Then, we have the double red problem. We fix this problem by considering the following cases.z‘s uncle is red, then we recolor z‘s parent and uncle black, grandparent red (it had to be black before), and consider the grandparent the new z. We potentially have a new double red problem but it is now higher up in the tree. If z‘s grand parent is the root then we color it black and we are done. The following picture illustrates this case.z‘s uncle is black then there are two subcases which can be resolved with either a single rotation or a double rotation as seen in the following pictures.z‘s sibling is black with both black children and the parent is red. In this case, we color the sibling red, parent black, and we are done:z‘s sibling is black with both black children and the parent is black. In this case, we color the sibling red, parent double black, and move the double black problem up the tree.z‘s sibling is red we perform a single rotation, give the sibling the parent’s color, and the parent red color. As z‘s new sibling is black, we are back to one of the previous cases.| Cô Hường, mẹ thí sinh Trần Thị Thu Hằng. |
| Trước hôm lên Hà Nội, Hằng (ngoài cùng bên trái) phải cùng mẹ mò cua, mót rau lấy tiền đi thi. |
| Việc bị cắt cáp trộm ảnh hưởng lớn đến uy tín và tài chính của doanh nghiệp viễn thông. Ảnh minh họa. |