![]() Searching is an operation or a technique that helps finds the place of a given element or value in the list. In this chapter, you will get to know the basic concepts of searching that are used in the data structure and case of programming also. If the data is kept properly in sorted order, then searching becomes very easy and efficient. You often spend time in searching for any desired item. The process of identifying or finding a particular record is called Searching. ![]() This chapter explores various searching techniques. If the middle item of the list is not the item that we’re looking for, and is larger than the middle value, we can drop the entire bottom half of the list and save ourselves that much computation time.Basic Concepts of Data Structures Data Structure Introduction Data Structures Environment Setup Fundamental Elements of Data Structure Arrays, Iteration, Invariants Data Structures and Arrays Lists, Recursion, Stacks, Queues Linked List Polynomials Using Linked List and Arrays Concepts of Stack in Data Structure Concepts of Queue in Data Structure Algorithms Principles of Program Analysis Big-O Notation and Algorithm Analysis Searching Techniques Sorting Techniques Bubble Sort Algorithm Selection Sort Algorithm Merge Sort Algorithm Quick Sort Algorithm Insertion Sort Algorithm Greedy Algorithm Trees Binary Trees AVL Trees Forests and Orchards Instead of searching through the collection, sequentially, starting with the first item in the list or array, the process starts at the middle. There are at most, at any time, \(n-1\) more items to look at if the item we’re currently evaluating is not the one we’re looking for.īinary search takes a bit of a different approach to the problem. With sequential search we start by evaluating the first entry of array for whether or not it matches the the item that we’re looking for, and if it does not we proceed through the entire collection, trying to find a match. This example is left for future work as it’s more abstract to just the search examples we’re displaying here. This can prove really useful if we can somehow, somewhere else in our data structure definitions, that we can guarantee ordering of our arrays. Modifying the table above, we can see that with the item not present in our array, we save some computational cycles in the negative case. We can see that we are able to terminate the execution of the search because we’ve found a number greater than the number we’re searching for with the assumption that the list being passed into the function is ordered, we know we can terminate the computation. However, if the item is not present we have a slight advantage in that the item that we’re looking for may never be present past another item of greater value.įor example, if we’re looking for the number 25, and through the process of searching through the array, we happen upon the number 27, we know that no other integers past number 27 will have the value that we’re looking for.ĭef ordered_sequential_search(li, item): position = 0 found = False stop = False while position item: stop = True else: position = (position + 1) return found test_li = print(ordered_sequential_search(test_li, 25)) False If we assume that the list, or array, that we’re searching over is ordered, say from low to high, the chance of the item we’re looking for being in any one of the \(n\) positions is still the same. Therefore for all inputs of size \(n\), the time needed for the entire search is at most \((cn+d) = O(n)\).Īt worst, the item \(x\) we’re searching for is the last item in the entire list of items. ![]() \(d\) steps are taken outside of the loop, for some constant \(d\).Each iteration takes \(c\) steps for some constant \(c\). ![]() # Search sequentially through a list, incrementing the position counter # if is_present is not True, otherwise set is_present to True and return def sequential_search(li, item): position = 0 is_present = False while position \(n\) after \(n\) iterations.
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