Question

Write an algorithm that finds the largest number in a list (an array) of \(n\) numbers.

Short answer

The algorithm finds the largest number in an array by first assuming the first number is the largest (maximum), then traverses the array while comparing each number to this maximum and updating it if a larger number is found. By the end of the traversal, the maximum holds the largest value in the array.

Step-by-step solution

Setup

Start by setting up the algorithm. Assume that the largest number is the first number in the array. We'll refer to this as the 'maximum' variable. This involves a variable declaration and initializing it with the first value of the array.

Traversal

Now, traverse through the list of numbers. This means going through each number in the array, starting from the second number (since we've already considered the first number as the maximum). This could be achieved using a looping statement like 'for' or 'while'.

Comparison

As each number is traversed, compare it with the 'maximum' variable. If the current number is larger than 'maximum', then update 'maximum' with this current number. This step is crucial as it allows the algorithm to keep track of the largest number encountered so far.

Continue till the end

Repeat the traversal and comparison steps for all the other numbers in the array.

Conclusion

By the end of these steps, the 'maximum' variable will hold the largest number in the array as it has compared every number and kept the largest one. This is the final result of the algorithm.

Key concepts

Array Traversal

Array traversal is a fundamental concept in computer programming that involves accessing each element of an array one by one. In the context of finding the largest number in an array, traversal allows us to inspect every number and determine which one is the greatest. Imagine you're in a classroom, and you are asked to find the tallest student, you'll have to look at each student to find them. Similarly, the algorithm starts with the first element and moves through the array, one element at a time, until it reaches the last element.

When applying array traversal, a pointer or index is typically used to keep track of the current position within the array. In a computer program, this is often done within a loop, which systematically visits each position, allowing you to perform some operation on the array's elements such as comparison or computation. Effectively, it's a digital iteration over the array's length, and every time a new item is reached, we can use this opportunity to perform our desired check or action.

Comparison Operation

Comparison operations are the tools that algorithms use to make decisions. Just like deciding if one number is larger than another in your head, an algorithm uses comparison operations to study pairs of numbers. In the case of finding the largest number, we employ a simple 'greater than' check. Each time the algorithm examines a new number from the array, it asks, 'Is this number greater than the current maximum?

A real-life analogy could be, when you're trying to find the heaviest book in your bag, you'll compare the weight of each book one by one against the heaviest you've found so far. Similarly, the algorithm maintains a 'maximum' variable, and for each new number it encounters during the traversal process, it uses a comparison operation to see if the new number should replace the 'maximum' as the new highest value found. If you think of the 'maximum' value as the champion of a tournament, each new number is a challenger trying to take the title.

Looping Constructs

Looping constructs are what make computers powerful tools for automation. They allow a piece of code to be executed repeatedly without the need to write the code multiple times. In our algorithm to find the largest number in an array, we use a loop to perform array traversal and comparison operations on each element. Think of a loop as a racetrack, where the same route is followed for several laps. The loop begins after considering the first element as the initial 'maximum' and continues until every element has been compared.

Different loops are available depending on the programming language being used, including 'for', 'while', and 'do-while' loops. The choice of loop often depends on the specific task and personal preference. A 'for' loop, for example, is often used when the number of iterations is known in advance—as it is when traversing an array. The steps of comparison and potential re-assignment of the 'maximum' variable happen inside this loop with each iteration, effectively allowing the algorithm to scale regardless of the array's size.