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Chapter 8: Problem 9

The _________ search algorithm repeatedly divides the portion of an array being searched in half.

Short Answer

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Question: Explain the binary search algorithm and provide a step-by-step procedure for its operation. Answer: The binary search algorithm is an efficient search method that uses a divide and conquer approach to find a target element in a sorted array. It operates by repeatedly dividing the array into halves and comparing the middle element with the target value. If the middle element matches the target, the search is successful. If it is greater or smaller than the target, the search continues in the right or left half of the array, respectively. The step-by-step procedure includes initializing variables representing array indices (left, right, middle), performing the search (while left <= right), and checking the middle element at each step. If the target is not found after the search process, return -1 or a message indicating the target value is not in the array.

Step by step solution

01

Understanding the Binary Search Algorithm

The binary search algorithm is an efficient search algorithm that uses the divide and conquer approach to search for a target element in a sorted array. It repeatedly divides the array into halves and compares the middle element with the target value. If the middle element is the target, the search is successful. If the middle element is greater or smaller than the target, the search continues in the right or left half of the array, respectively.
02

Initialize Variables

First, create three variables: left, right, and middle to represent the array indices. Set the values of left to 0, and right to the last index of the array. Throughout the search process, these variables will be adjusted accordingly.
03

Perform Binary Search

While left <= right, follow these substeps, which make up the primary binary search algorithm process: - Calculate the middle index by using the formula: middle = (left + right) // 2 (// denotes integer division). - Compare the middle element with the target value. - If the middle element is equal to the target value, return the index middle. - If the middle element is greater than the target value, update the right index: right = middle - 1. - If the middle element is smaller than the target value, update the left index: left = middle + 1.
04

Target Not Found

If the while loop in step 3 completes and the target value has not been found, return -1 or a message indicating the target value is not in the array. This means that the target element is not present in the sorted array, and the binary search has been unsuccessful. Following these steps, the binary search algorithm can be used to efficiently search for a target element in a sorted array.

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Most popular questions from this chapter

Why is the bubble sort inefficient for large arrays?

If an array is sorted in _________ order, the values are stored from lowest to highest.

T F If data are sorted in ascending order, it means they are ordered from lowest value to highest value.

Complete the following table calculating the average and maximum number of comparisons the linear search will perform, and the maximum number of comparisons the binary search will perform. $$\begin{array}{l|lllll} \hline & 50 & 500 & 10,000 & 100,000 & 10,000,000 \\ \text { Array Size } \rightarrow & \text { Elements } & \text { Elements } & \text { Elements } & \text { Elements } & \text { Elements } \\ \hline \begin{array}{l} \text { Linear Search } \\ \text { (Average } \\ \text { Comparisons) } \end{array} & & & & \\ \hline \begin{array}{l} \text { Linear Search } \\ \text { (Maximum } \\ \text { Comparisons) } \end{array} & & & & & \\ \hline \begin{array}{l} \text { Binary Search } \\ \text { (Maximum } \\ \text { Comparisons) } \end{array} & & & & & \\ \hline \end{array}$$

In an average case involving an array of N elements, how many times will a linear search function have to read the array to locate a specific value?
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