Question

If a list is already sorted in ascending order, a modified sequential search algorithm can be used that compares against each element in turn, stopping if a list element exceeds the target value. Write a pseudocode version of this short sequential search algorithm.

Short answer

Use a loop to compare each element in the sorted list to the target, stopping if an element exceeds the target.

Step-by-step solution

Initialize Variables

Start by initializing a variable `found` to `False`. This will keep track of whether we have found the target value. Initialize an index `i` to `0` to indicate the starting point of the search in the list.

Loop Through the List

Use a loop to go through each element in the sorted list. The loop should terminate if the end of the list is reached or if the element being inspected exceeds the target value.

Compare Elements

Inside the loop, compare the current element (at index `i`) to the target value. If it matches the target value, set `found` to `True` and terminate the loop.

Check for Exceeding Element

If the current element exceeds the target value, terminate the loop immediately, as no further elements in a sorted list can be the target.

Increment Index

If neither condition in Steps 3 or 4 is satisfied, increment the index `i` to check the next element. Continue to the next iteration of the loop.

Return Result

After the loop ends, check the value of `found`. If it is `True`, the target was found; otherwise, it wasn't. Return or print the appropriate result.

Key concepts

Sequential Search

A sequential search is a basic and straightforward algorithm used to find a target value within a list. In this method, each element of the list is inspected one by one to determine if it matches the target value. Sequential search is intuitive and works well for small to medium-sized lists. However, it is not the most efficient algorithm for large datasets, due to its linear time complexity.

• This search begins at the first element of the list.
• It continues checking each subsequent element until the desired value is found or the end of the list is reached.
• If the list is unsorted, it is possible that every element needs to be checked.

For sorted lists, the process can often be shortened, as we’ll discuss further. Despite its simplicity, sequential search remains a fundamental concept that helps in understanding more complex search algorithms.

Pseudocode

Pseudocode is a helpful tool for planning and visualizing algorithms before implementing them in a programming language. It combines the features of programming language and human language, making it easy to understand and follow the logic of an algorithm.

• Pseudocode does not require strict syntax, allowing flexibility in expressing ideas.
• It helps programmers and non-programmers alike to visually understand the steps and flow of an algorithm.
• Using pseudocode, one can focus on algorithm design without being bogged down by language-specific syntax.

In the context of a sequential search in a sorted list, pseudocode clearly outlines the initialization of variables, looping through the list, and the conditions to stop the search. This makes it easier to transition into actual coding.

Sorted List

A sorted list is an arrangement of data where elements follow a specific sequence or order. This is typically numerical or alphabetical. For a sequential search, having a sorted list can drastically enhance performance by allowing the search to terminate early if a condition is met.

• In a sorted list, elements are ordered from the smallest to the largest (or vice versa).
• This ordering allows for the effective use of certain search algorithms, such as binary search.
• In a modified sequential search, once an element greater than the target is found, the search stops.

Therefore, using the natural order of a sorted list allows for logical decisions to be made early, reducing unnecessary comparisons.

Ascending Order

Ascending order is a sequence arrangement where elements increase in value, often used for numerical lists, letters, or dates.

• From smallest to largest, such as 1, 2, 3, ..., or a, b, c, ...
• In ascending order, each subsequent element is equal to or greater than the previous element.
• When written in ascending order, it becomes possible to optimize searches like sequential search.

In algorithm design, taking advantage of ascending order can prevent unnecessary full-list scans. For example, in the discussed exercise, if an element larger than the target is found, it indicates that subsequent elements will also exceed the target, thus halting the search early.