Question

Assume an array of structures is in order by the customerID ficld of the record, where customer IDs go from 101 to 500 . A) Write the most efficient pseudocode algorithm you can to find the record with a specific customerlD if every single customer ID from 101 to 500 is used and the array has 400 elements. B) Write the most efficient pscudocode algorithm you can to find a record with a customer ID near the end of the IDs, say 494 , if not every single customer 10 in the range of 101 to 500 is used and the array size is only 300 .

Short answer

Question: Explain the differences between the direct access method and the binary search method when searching for a record with a specific customerID in an ordered array. Answer: The direct access method is an efficient way of searching for a record when the array has a continuous range of unique keys, such as customerID in this case, and the size of the array is known. It calculates the index of the target record by subtracting the minimum key value from the target key, and directly accesses the element at that index. This method provides quick access in constant time, but requires that the key range is continuous and all keys are used. On the other hand, the binary search method is applicable when the key range is not continuous or not all keys are used. Binary search works by repeatedly dividing the search interval in half and comparing the middle element with the target key. If the middle element matches the target key, the record is found. If the target key is less (or greater) than the middle element, the search continues with the left (or right) half of the interval. Binary search takes logarithmic time in terms of the array size, but it works even when the key range is not continuous or all keys are not used.

Step-by-step solution

(Part A: Direct Access Algorithm)

: 1. Initialize the customerID (ID) 2. Calculate the index (I) as follows: I = ID - 101 3. Access the record in the array with the index (I) 4. If the record exists, return the record. Otherwise, the record does not exist in the array.

(Part B: Binary Search Algorithm)

: 1. Initialize the customerID (ID) 2. Set left pointer (L) to 0 3. Set right pointer (R) to size of the array minus 1 (array_size - 1) 4. While L <= R: a. Calculate the middle index (M) as follows: M = floor((L + R)/2) b. Check the customerID of the record in the array with index M. If it matches the target ID, return the record. c. If the target ID is less than the ID at index M, set R to M - 1. d. If the target ID is greater than the ID at index M, set L to M + 1. 5. If the loop exits without finding the target ID, the record does not exist in the array.

Key concepts

Direct Access Method

The Direct Access Method is like knowing the exact location of a book on a bookshelf. It allows instant retrieval of information, making it extremely efficient. This method is especially useful when dealing with arrays that have continuous and ordered indexes.
When we already know every possible index corresponds to a valid entry, as in part A of the exercise, this method becomes the perfect choice.

Here's why it works so well:

• Each index in the array directly relates to a specific data point, such as a customer ID.
• The calculation of the index is simple—it's just the ID minus the starting point of the ID range.
• Access time is constant, meaning it doesn't depend on the number of elements in the array, leading to efficiency.

If a customer ID ranges from 101 to 500, and we need the record for a specific ID, we can derive the index simply using: \[ I = ID - 101 \]This formula provides us with the exact position of the record in the array immediately, and we can access the record without searching.
Thus, the Direct Access Method is incredibly fast because it completely bypasses the searching process, provided the IDs are predictable and ordered without any gaps.

Binary Search Algorithm

The Binary Search Algorithm is a clever way to find a specific item in an ordered list, and is particularly effective when elements are not sequentially continuous.
It's like a game of "guess the number" where you efficiently narrow down the possibilities by consistently choosing the middle number.
In part B of the exercise, we use this algorithm to efficiently locate a customer ID that might not be in adjacent order.

• Binary Search works by dividing the array into halves and reducing the search space greatly.
• It uses two pointers, "left" and "right," to determine the current search scope.
• The middle index is calculated, and depending on whether the sought ID is smaller or larger, the search scope is halved.

Let's delve into the steps:
1. Start with the entire array, setting the left pointer at the first item and the right pointer at the last.
2. Find the middle of this scope by computing: \[ M = \text{floor}((L + R)/2) \]
3. Compare the middle ID with the target ID: - If it matches, you've found the record. - If the target ID is smaller, continue the search to the left. - If larger, continue to the right.
4. Adjust the pointers accordingly and repeat until you find the ID or the pointers cross.
This method is extremely efficient for large, ordered but non-sequential datasets because each step eliminates half of the remaining options, making it both powerful and fast.

Array Structures

Array Structures are essential in programming, particularly when dealing with data storage and retrieval. An array is a collection of elements, each identified by an array index. This allows for quick access, retrieval, and modification of data.
Arrays can hold different types of data, such as integers, characters, or user-defined structures, making them versatile and useful across many applications.

Key characteristics of arrays include:

• Fixed Size: Once created, the size of an array is defined and does not change.
• Indexed Access: Each element can be accessed directly using its index, which starts at 0 for the first element.
• Homogeneity: Arrays typically contain elements of the same data type, ensuring uniformity in processing.

In the context of our exercise, an array structure could be an array of customer records, where each record contains various fields like customer ID, name, and other details.
This structure allows for efficient organization and access of records using IDs.
Having array structures allows algorithms like Direct Access or Binary Search to operate effectively and retrieve data quickly without unnecessary searches.
Thus, understanding array fundamentals can greatly aid in writing efficient algorithms and optimizing performance in various programming tasks.