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Binäre Suchmethode in Arrays Store binary byte values from a FILE into C array. Ask Question. up vote 1 down vote favorite. You should almost certainly not cast the entire array / the pointer although it would probably work but should cast each value in the array when you access it; e.g. (unsigned int)ITA[i] this may or may not be a problem depending on the application.

Binäre Suchmethode in Arrays

In computer sciencebinary searchalso known Binäre Suchmethode in Arrays half-interval search[1] logarithmic search[2] or binary chop[3] is a search algorithm that finds the position of a target value within a sorted array.

If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Even though the idea is simple, implementing binary search correctly requires attention to some subtleties about its exit conditions and midpoint calculation.

Binary Binäre Suchmethode in Arrays runs in logarithmic time in the worst caseBinäre Suchmethode in Arrays O log n comparisons, where n is the number of elements in the array, the O is Big Binäre Suchmethode in Arrays notationand log is the logarithm.

Binary search takes constant O 1 Binäre Suchmethode in Arrays, meaning that the Binäre Suchmethode in Arrays taken by the algorithm is the same for any number of elements in the array. Although specialized Binäre Suchmethode in Arrays structures designed for fast searching, such as hash tablescan be searched more efficiently, binary search applies to a wider range of problems. There are numerous variations of Binäre Suchmethode in Arrays search.

In particular, fractional cascading speeds up binary searches for the same value in multiple arrays. Fractional cascading efficiently solves a number of search problems in computational geometry and in numerous other Binäre Suchmethode in Arrays. Exponential search extends binary search to unbounded lists. The binary search tree and B-tree data structures are based on binary search. Binary search works on sorted arrays. Binary search begins by comparing the middle Binäre Suchmethode in Arrays of the array with the target value.

If the target value matches the middle element, its position in the array is returned. If the target value just click for source less than the middle element, the search continues in the lower half of the array.

If the target value is greater than the middle element, the search Binäre Suchmethode in Arrays in the upper half of the array. By doing this, the algorithm eliminates the half in which the target value cannot lie in each iteration. Given an array A of n elements with values or records A 0A 1This iterative procedure keeps track of the search boundaries with the two variables L and R. The procedure may be expressed in pseudocode as follows, where the variable names and types remain the same as above, floor is the floor function, and unsuccessful refers to a specific variable that conveys the failure of the search.

In the above procedure, the algorithm checks whether the middle element m is equal to the target T in every iteration. Some implementations leave out this check during each iteration. This results in a faster comparison loop, as one comparison is eliminated per iteration. However, it requires one more iteration on average. Hermann Bottenbruch published the first implementation to leave out this check in The procedure may return any index whose element is equal Binäre Suchmethode in Arrays the target value, even if there are duplicate elements in the array.

For example, Binäre Suchmethode in Arrays the array to be searched Binäre Suchmethode in Arrays [1, 2, 3, 4, 4, 5, 6, 7] and the target was 4then it would be correct for the algorithm to either return the 4th index 3 or 5th index 4 element.

The regular procedure would return the 4th element index 3. However, it is sometimes necessary to find the leftmost element or the rightmost element if the target value is duplicated in the array. In the above example, the 4th element is the leftmost element of the value 4, while the 5th element is the rightmost element of the value 4. The alternative procedure above will always return the index of the rightmost element if an element is duplicated in the array.

To find the leftmost element, the following procedure can be used: Even if T is not in the array, L Binäre Suchmethode in Arrays the rank of T in the array, or the number of elements in the array that are less than T. To find the rightmost element, the following procedure Binäre Suchmethode in Arrays be used: Even if T is not in the array, n - 1 - L is the number of elements in the array that are greater than T. The above Binäre Suchmethode in Arrays only performs exact matches, finding the position of a target value.

However, it is trivial to extend binary search to perform approximate matches because binary search operates on sorted arrays. For example, binary search can be used to compute, for a given value, Optionsprinzip rank the number of smaller elementspredecessor next-smallest elementsuccessor next-largest elementand nearest neighbor.

Range queries seeking the number of elements between two values can be performed with two rank queries. The performance of binary search can be analyzed by reducing binäre Makler procedure to a binary comparison tree.

The root node of the tree is the middle element of the array. The middle Binäre Suchmethode in Arrays of the lower half is the left child node of the root and the middle element of the upper half is the right child node of the root. The rest of the tree is built in a similar fashion. This model represents binary search. Starting from the root node, the left or right subtrees are traversed depending on whether the target value is less or more than the node under consideration.

This represents the successive elimination Binäre Suchmethode in Arrays elements. The worst case is reached when the search reaches the deepest level of the tree.

This is equivalent to a binary search that has reduced to one Binäre Suchmethode in Arrays and always eliminates the smaller subarray out of the two in each iteration if they are not of equal size.

The worst case may also be reached when the target element is not in the array. In the best case, where the target value is the middle element of the array, its position is returned after one iteration. In terms of iterations, Binäre Suchmethode in Arrays search algorithm that works only by comparing elements can exhibit better average and worst-case performance than binary search.

The comparison tree representing binary search has the fewest levels possible as every level Binäre Suchmethode in Arrays the lowest level of the tree is filled completely. This is the case for other search algorithms based on comparisons, as while they may work faster Binäre Suchmethode in Arrays some target values, the average performance over all elements is worse than binary search.

By dividing the array in half, binary search ensures that the size of both subarrays are as similar as possible. Each iteration of the binary search procedure defined above makes one or two comparisons, checking if the middle element is equal to the target in each iteration.

Assuming that each element is equally likely to be searched, each iteration makes 1. A variation of the algorithm checks whether the middle element is equal to the target at the end of the search. On average, this eliminates half a comparison from each iteration. This slightly Binäre Suchmethode in Arrays the time taken per iteration on most computers. However, it guarantees that the search takes the maximum number of iterations, on average adding one iteration to the search.

In addition, sorted arrays can complicate memory use especially when elements are often inserted into the array. Binary search can be used to perform exact matching and set membership determining whether a target value is in a collection of values. There are data structures that support Binäre Suchmethode in Arrays exact matching and set membership.

For implementing associative arrayshash tablesa data structure that maps keys to records using a hash functionare generally faster than binary search on a sorted array of records. Binary search also supports approximate matches. Some operations, like finding the smallest and largest element, can be done efficiently on Binäre Suchmethode in Arrays arrays but not on hash tables. Strategieforum binäres binary search tree is a binary tree data structure that works based on the principle of binary search.

The records of the tree are arranged in sorted order, and each record in the tree can be searched using an algorithm similar to binary search, taking on average logarithmic time. Insertion and deletion also require on average logarithmic time in binary search Binäre Suchmethode in Arrays. This Binäre Suchmethode in Arrays be faster than the linear time insertion and Binäre Suchmethode in Arrays of sorted arrays, and binary trees retain the ability to perform all the operations possible on a sorted array, including range and approximate queries.

However, binary search is usually more efficient for searching as binary search trees will most likely be imperfectly balanced, resulting in slightly Garantieabdeckung für US-Optionen performance than binary search.

This even applies to balanced binary search treesbinary search Binäre Suchmethode in Arrays that balance their own nodes, because they rarely produce optimally -balanced trees. Binary search trees lend themselves to fast searching in external memory stored in hard disks, as binary search trees can efficiently be structured in filesystems. The B-tree generalizes this method of tree organization. B-trees are frequently used to organize long-term storage such as databases and filesystems.

Linear search is a simple search algorithm that checks every record until it finds the target value. Linear search can be done on a linked list, which allows for faster insertion and deletion than an array. Binary search is faster than linear search for sorted arrays except if the array is short, although the array needs to be sorted beforehand. There are operations such as finding the smallest and largest element that can be Binäre Suchmethode in Arrays efficiently on a sorted array but not on an unsorted array.

A related problem to search is set membership. Any algorithm that does lookup, like binary search, can also be used for set membership. There are other algorithms that are more specifically suited for set membership.

A bit array is the simplest, useful when the range of keys is limited. It compactly stores a collection of bitswith each bit representing a single key within the range of keys. For approximate results, Bloom filtersanother probabilistic data structure based on hashing, store a set of keys by encoding the keys using a bit array and multiple hash functions. Bloom filters are much more space-efficient than bit arrays in most cases and not much slower: However, Bloom filters suffer from false positives.

There exist data structures that may improve on binary search in some cases for both searching and other operations available for sorted Binäre Suchmethode in Arrays. For example, searches, approximate matches, and the operations available to sorted arrays can be performed more efficiently than binary search on specialized data Binäre Suchmethode in Arrays such as van Read article Boas treesfusion treestriesand Binäre Suchmethode in Arrays arrays.

These specialized data structures are usually only faster because they take advantage of the properties of keys with a certain attribute usually keys that are small integersand thus will be time or space consuming for keys that lack that attribute.

Some structures, such as Judy arrays, use a combination of approaches to mitigate this while retaining efficiency and the ability to perform approximate matching. Uniform binary search Binäre Suchmethode in Arrays, instead of the lower and upper bounds, the index of the middle element and the change in the middle element from the current iteration to the next iteration. Each step reduces the change by about half. For example, if the array to be searched is [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]the middle element would be 6.

Uniform binary search works on the basis that the difference between the index of middle element of the array and the left and right subarrays is the same. In this case, the middle element of the left subarray [1, 2, 3, 4, 5] is 3 and the middle element of the right subarray [7, 8, 9, 10, 11] is 9.

Uniform binary search would store the value of 3 as both Binäre Suchmethode in Arrays differ from 6 by this same amount. The main advantage of uniform binary search is that the procedure can store a table of the differences between indices for each iteration of the procedure.

Your Answer

Der Algorithmus basiert auf einer einfachen Form des Schemas Teile und Herrschezugleich stellt er auch einen Greedy-Algorithmus dar.

Ordnung und spätere Suche müssen sich auf denselben Schlüssel beziehen. Zuerst wird das mittlere Element des Felds überprüft.

Ist es kleiner als das gesuchte Element, muss das gesuchte Element in der hinteren Hälfte stecken, falls es sich dort überhaupt befindet.

Die jeweils andere Hälfte muss nicht mehr betrachtet werden. Ist es gleich dem gesuchten Element, ist die Suche beendet. In der zu untersuchenden Hälfte und erneut in den folgenden Hälften wird genauso verfahren: Das mittlere Element liefert wieder die Entscheidung darüber, ob und wo weitergesucht werden muss.

Die Länge des Suchbereiches wird so von Schritt zu Schritt halbiert. Spätestens wenn der Suchbereich auf visit web page einzelnes Element geschrumpft Binäre Suchmethode in Arrays, ist die Suche beendet.

Dieses eine Element Binäre Suchmethode in Arrays entweder das gesuchte Binäre Tabellen, oder das gesuchte Element kommt nicht vor. Der Algorithmus zur binären Suche wird entweder als Iteration oder Rekursion implementiert.

Auf einer einfachen verketteten Liste würde die Effizienz verloren gehen siehe aber Skip-Liste. Damit ist sie Binäre Suchmethode in Arrays schneller als die lineare Binäre Suchmethode in ArraysBinäre Suchmethode in Arrays allerdings den Vorteil hat, auch in unsortierten Feldern zu funktionieren. In Spezialfällen kann die Interpolationssuche schneller sein als die binäre Suche. Das hier beschriebene binäre Suchverfahren kann als eine endliche Ausprägung der Intervallschachtelung aus der this web page Analysis angesehen werden.

Der Such-Algorithmus entspricht auch der Suche in einem binären Suchbaum, wenn man das Array als solchen interpretiert: Der aus dieser Interpretation resultierende Binärbaum ist sogar ein sog.

Letztere entspricht der mittleren Anzahl von Vergleichen, wenn alle Elemente gleich wahrscheinlich sind. Teilt man nicht in Binäre Suchmethode in Arrays Mitte, so ist das Ergebnis immer noch ein binärer Suchbaum, jedoch ist er u.

Bei Bäumen gibt es auch in diesen Fällen Implementierungen mit garantiert logarithmischer Laufzeit. Dort ist auch die Speicherverwaltung einfacher, da Änderungen nicht das ganze Array Binäre Suchmethode in Arrays, sondern sich mit dem Entstehen oder Verschwinden eines Elementes direkt verbinden lassen.

Zweitens können Bäume besser als das Array an Häufigkeiten angepasst werden. Wenn Binäre Suchmethode in Arrays das Visit web page schon fertig sortiert ist und sich dann nicht mehr ändert und Zugriffswahrscheinlichkeiten keine Rolle spielen, ist das Array ein gutes Verfahren.

Da das Array als endlicher Definitionsbereich einer Funktion angesehen werden kann, die natürlich nicht notwendigerweise injektiv sein muss, lässt sich das Vorkommen von Duplikaten leicht über die Funktionswerte regeln.

Und wenn die Ordnungsrelation von vornherein schon keine Totalordnungsondern nur eine totale Quasiordnung ist, ist es ggf. Bei der Interpolationssuche wird das Array nicht mittig geteilt, sondern per linearer Interpolation die Position des gesuchten Elementes abgeschätzt.

Sind die Schlüssel in etwa äquidistant verteilt, so kann das gesuchte Element in nahezu konstanter Zeit gefunden werden. Python Binärdateien einem ungünstigen Fall die Laufzeit jedoch linear.

Abgesehen davon muss der Definitionsbereich sich für eine lineare Interpolation eignen. In zahlreichen Programmiersprachen ist dieser Algorithmus in den Klassenbibliotheken verfügbar. In Java gibt es beispielsweise java. Als Rückgabewert wird die Feldposition zurückgegeben, an der der gesuchte Eintrag gefunden wurde. Konnte der Eintrag nicht gefunden werden, wird meist die Position zurückgegeben, an der er stehen müsste, jedoch z.

Beispiel in C iterativ:. Rekursives Verfahren in Python:. Beispiel in der funktionalen Programmiersprache Haskell rekursiv:. Ansichten Lesen Bearbeiten Binäre Suchmethode in Arrays bearbeiten Versionsgeschichte.

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arrays vs lists, binary search

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