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Chapter 12: Problem 1

Why is a linear search called "linear"?

Short Answer

Expert verified
A linear search is called 'linear' because it checks each element in sequence, moving in a straight line through the list.

Step by step solution

01

Understand the Linear Search Algorithm

A linear search algorithm checks each element of a list sequentially until the target value is found or the list ends. It starts from the first element and moves to the next one, continuing this process until the target is found.
02

Examine the Search Method

In a linear search, the searching process is direct and straightforward. Each element is compared one by one in a straight path until the target is located. No elements are skipped or revisited.
03

Identify the Search Sequence

The search progresses in a linear sequence, meaning it moves step by step in one direction through the list. This sequential processing of elements is inherently linear.
04

Conclude Why It Is Called Linear

Since the search traverses the list in a straight line, checking each element before moving to the next, it follows a linear path. Hence, the term 'linear' accurately describes the process.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sequential Search
The linear search algorithm uses what is known as a sequential search. This means it starts from the beginning of the list and moves element by element, in the order they appear, until it finds the target or reaches the end of the list. Sequential search is simple and easy to implement. However, it can be slow, especially if the list is very long because it may need to check every single element. If you need to search data frequently, you might want to look into more efficient algorithms.
Element Comparison
A crucial part of the linear search or sequential search process involves element comparison. Every time the algorithm inspects an element, it compares it with the target value. If they match, the search ends successfully. If they don't match, the algorithm moves to the next element and repeats the process.
This comparison is straightforward but essential, as it determines whether the algorithm continues or stops. Because every element is checked one by one, the time taken for a successful or unsuccessful search averages out to about half the size of the list.
Search Sequence
The search sequence in a linear search is very structured. It begins at the first element and proceeds step by step through each subsequent element. If the target is located, the search stops immediately. If not, the search continues until all elements have been checked. This sequential approach ensures that no elements are missed, but also means that the performance depends directly on the length of the list.
Despite its simplicity, understanding the search sequence is crucial for appreciating the linear search algorithm's efficiency and limitations.

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Most popular questions from this chapter

Describe the contents of the array after the following code segment is run: int [][] matrix = new int[5][5]; for (int row \(=0\); row \(<\) matrix.length; row++) for (int col \(=0 ; \mathrm{col}<\) matrix[row].length; \(\mathrm{col}++\) ) matrix[row \(][c o l]=\) row \(*\) col;

Write a code segment that outputs the integers in a two-dimensional array named table. The output should begin each row of integers on a new line.

Draw a diagram that shows the contents of the array 87654 after each number is moved in a bubble sort, until the 8 arrives at the end of the array.

Which elements are examined during a binary search of the array 3456788599 for the target element 100 ?

Write a code segment that searches a two-dimensional array for a negative integer. The loop should terminate at the first instance of a negative integer in the array, and the variables row and col should be set to its position. Otherwise, if there are no negative integers in the array, the variables row and col should equal the number of rows and columns in the array (we assume that each row has the same number of columns).
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