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Exhibit 13.17. Notes on the C quicksort. in .NET Produce Data Matrix in .NET Exhibit 13.17. Notes on the C quicksort.




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384 Exhibit 13.17. Notes on the C quicksort. using .net vs 2010 toembed barcode data matrix for asp.net web,windows application upc barcode CHAPTER 13. LOGIC PROGRAMMING 1. The parameters first and last must be pointers to the beginning and end of an array of integers. On exit from quicksort, the values in this array are in sorted order.

Pointers, rather than subscripts, are used to index the array. 2. A sentinel value equal to maxint must follow the last data element to stop the left-to-right scanning pointer in the case that the pivot value is the largest value in the array.

3. The inner while loops identify the leftmost and rightmost elements that are stored in the wrong part of the array. These two elements are then swapped.

4. After exit from the for loop, all items to the left of small are small (less than or equal to pivot value) and all items to the right of large are large. The large scanner points to a small element, and small either points to the same thing or points to the large element on large s right.

5. Before returning, the pivot element is swapped into the middle, between the small and large elements. This is its nal resting place.

The small and large areas remain to be sorted by future recursive calls on quicksort.. an array. The action of 2d Data Matrix barcode for .NET moving through the elements of the list is accomplished in Prolog by recursively binding a local name, Tail, to the list with its head removed.

This recursive binding takes the place of the increment ( ++ ) and decrement ( -- ) operations in C, both of which have assignment as a side e ect. Binding and concatenation are used in Prolog in place of the assignment operations in C. As Prolog s split pulls each item o the unsorted list, it binds the item to a local variable name, Head.

Since the function is called recursively, once for each element on the unsorted list, enough bindings are created to hold all the list elements. As each call to split returns, the bound item is appended to the list returned by the lower level. In contrast, the C version uses iteration instead of recursion to perform the split operation.

New storage is not created; rather, assignment is used to swap pairs of values in the original storage area. The sequential execution of C statements is echoed exactly in the sequential application of the subgoals in each Prolog rule. Thus the main routine, quicksort, looks almost the same in the two languages.

Finally, in the C code, explicit if statements are used to end recursion in quicksort and to end the split operation, and while statements are used to determine whether an element belongs in the small or the large part of the array. In Prolog all this is accomplished by the elaborate pattern matching algorithm (uni cation) that is built into the proof system. Prolog uses uni cation to.

13.5. PROLOG select which rule to ap VS .NET ECC200 ply when split is called, which determines whether the next step will add an element to the small list or the large list, or end the recursion..

Cuts and the not Predicate Two major theoretical r Data Matrix 2d barcode for .NET esults have had a strong bearing on Prolog: clausal logic is complete but not decidable. So although every true clausal theorem can be proved, no e ective procedure can ever exist that will always produce a proof and terminate in a nite amount of time.

This means that if the Prolog proof system relied on resolution alone, a programmer might not know of not knowing whether a given query would ever be answered. Prolog does have a way, called a cut, to control the proof process so that a programmer can avoid being trapped in lengthy deductions that seem likely to be fruitless. However, when the cut operation is used for this purpose in Prolog, it destroys the completeness of the proof system and leaves open the possibility that a provable goal might fail.

Cuts A cut is written as ! and may appear as one of the conditions in a rule. 3 Informally, a cut prunes o one branch of the proof-search tree by telling the proof system to abandon a chain of reasoning under certain conditions. In some ways it is analogous to a break instruction.

Perhaps the best way to think of a cut is to imagine that it is a barrier, placed by the programmer in a rule, to stop fruitless backtracking. Consider a rule with several terms: P : Q, R, S, !, T, U, V. In trying to satisfy this rule, the proof system starts by searching for a uni cation of conditions Q, R, and S.

Backtracking might occur several times during this search, and control might go back as far as condition Q. If Prolog fails to satisfy this part of the rule, it will go on to try the next rule for P . However, if the conditions Q, R, and S on the left are eventually satis ed, control passes through the cut to the conditions T , U , and V on the right.

At this point, all variable bindings for conditions Q, R, and S are frozen, or committed, and the information that would permit Prolog to backtrack back through these conditions is discarded. The proof system now begins to try to nd a uni cation for conditions T , U , and V that is consistent with the frozen bindings. Again, a great deal of backtracking can happen among these clauses, and, perhaps, some uni cation of the whole rule may be found.

In this case, the rule succeeds, and a uni cation is returned. If (during backtracking) control ever returns to the cut, it means that the attempt to unify conditions T , U , and V with the frozen bindings has failed. At this point, the two pruning actions of the cut take place: 1.

Instead of returning to reinstantiate the left part of the rule, the entire rule fails immediately.. Do not confuse this mea ning of the term cut with the meaning of cut in a resolution step of clausal logic..
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