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Note how similar this process is to looking up a topic in the index of a book. Each page of the index is labeled with a word or letter that represents the topics listed on that page. The page labels are analogous to the keys in the internal nodes of the search tree. The actual page number listed next to the topic in the book s index is analogous to the disk address of file name that leads you to the actual data. The last step of the search process is searching through that page in the book, or through that file on the disk. This analogy is closer if the book s index itself had an index. Each internal level of the multiway tree corresponds to another index level. Algorithm 12.2 Inserting into a B-Tree To insert a record with key k using a B-tree index of order m: 1. If the tree is empty, create a root node with two dummy leaves, insert k there, and return true (indicating that the insertion was successful). 2. Let x be the root. 3. Repeat steps 4 6 until x is a leaf node. 4. Apply the binary search to node x for the key k i , where k i 1 < k k i (regarding k 0 = and k m = ).

Patents A patent protects an inventor s intellectual property for a limited period of time After 20 years, the patented idea becomes public property, and anyone can use it During the lifetime of the patent, the patent gives the owner the right to prevent others from making or using the invention, unless the owner grants permission The purpose of seeking a patent, which often costs many thousands of dollars in legal and filing fees, is to gain protection from competition, so the inventor can bring the invention to market and profit from it A patent is a short-term monopoly right granted to reward the genius of the inventor To be patentable, an invention must be novel, nonobvious, and useful Many suitcases today have wheels on them, so they can be rolled about as well as carried.

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public static void sort(int[] a) { // POSTCONDITION: a[0] <= a[1] <= ... <= a[a.length-1]; sort(a, 0, a.length); } private static void sort(int[] a, int p, int q) { // PRECONDITION: 0 <= p <= q <= a.length // POSTCONDITION: a[p..q) is sorted; if (q - p < 2) { return; } int m = partition(a, p, q); // step 2 sort(a, p, m); // step 4 sort(a, m+1, q); // step 5 } private static int partition(int[] a, int p, int q) { // RETURNS: index m of pivot element a[m]; // POSTCONDITION: a[i] <= a[m] <= a[j] for p <= i <= m <= j < q; int pivot = a[p], i = p, j = q; // steps 1-2 while (i < j) { // step 3 while (i < j && a[--j] >= pivot) ; // step 4 if (i < j) { a[i] = a[j]; // step 5 } while (i < j && a[++i] <= pivot) ; // step 6 if (i < j) { a[j] = a[i]; // step 7 } } a[j] = pivot; // step 8 return j; }

If someone tried to patent a three-wheeled suitcase, arguing that only two- and four-wheeled suitcases existed prior to the patent application, the patent would probably be denied as being obvious A three-wheeled suitcase might be novel, and it might be useful, but once someone comes up with the idea of a wheeled suitcase, the number of wheels seems to be a minor detail something obvious to someone in the business of designing suitcases Since 1981, software has been patentable in the United States, if the software is part of a patentable device In general, software is not patentable because scientific truths and the mathematical expressions of scientific truths are not patentable The 1981 case involved a patent for a rubber curing device which incorporated a computer for control Since software was part of a patentable rubber molding device, the software was patentable.

Note the empty loop at line 22 and line 26. All the action is managed within the loop condition, so no statements are in its body.

For even as we celebrate tonight, we know the challenges that tomorrow will bring are the greatest of our lifetime two wars, a planet in peril, the worst financial crisis in a century Even as we stand here tonight, we know there are brave Americans waking up in the deserts of Iraq and the mountains of Afghanistan to risk their lives for us There are mothers and fathers who will lie awake after their children fall asleep and wonder how they ll make the mortgage, or pay.

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