Question

Write a program that reads three numbers and prints "increasing" if they are in increasing order, "decreasing" if they are in decreasing order, and "ncither" otherwise. Here, "increasing" means "strictly increasing", with each value larger than its predecessor. The sequence 344 would not be considered increasing.

Short answer

Read three numbers, check order: print 'increasing', 'decreasing', or 'neither'.

Step-by-step solution

Understanding the Problem

We need to write a program that reads three integers and determines their order. The program should output 'increasing' if the numbers form a strictly increasing sequence, 'decreasing' if they form a strictly decreasing sequence, or 'neither' if they are neither.

Input Three Numbers

We start by writing code that takes three inputs from the user. In most programming languages, this can be done using a function like `input()` to read and convert the inputs into integers.

Check for Strictly Increasing Order

Compare the three numbers to see if the first number is less than the second, and the second number is less than the third. If so, print 'increasing'.

Check for Strictly Decreasing Order

If the numbers are not increasing, check if the first number is greater than the second, and the second is greater than the third. If this condition is true, print 'decreasing'.

Default to 'Neither'

If neither the conditions for increasing nor decreasing are satisfied, print 'neither' to indicate that the numbers do not form a strictly ordered sequence.

Test the Program

Run the program with different sets of numbers to ensure it correctly identifies the order. For instance, test with (1, 2, 3), (3, 2, 1), and (1, 1, 2) to check all outcomes.

Key concepts

Understanding Increasing Sequences

When we say a sequence is "increasing," particularly in programming logic, it implies that each successive number in the sequence is larger than the one before. This concept is central to determining the order of numbers. For a sequence to be strictly increasing, like the one required by the exercise, no two numbers can be equal. For instance, the sequence 1, 2, 3 is strictly increasing because 1 is less than 2, and 2 is less than 3.

Why is this important? Checking sequences in programming helps in sorting, searching, and organizing data effectively. In computer science, this concept helps identify patterns and trends within datasets. When coding a solution to identify increasing order, you would compare consecutive numbers using conditional statements to ensure each is greater than its predecessor. This can be done using simple comparisons such as if a < b < c to determine the sequence behavior.

Understanding Decreasing Sequences

A decreasing sequence in programming refers to a sequence where each number is smaller than the one before it. Similar to increasing sequences, being strictly decreasing means that each number in the series must be different from its predecessor, specifically, each must be smaller.

For example, the sequence 3, 2, 1 is strictly decreasing because 3 is greater than 2, and 2 is greater than 1. This property is crucial, especially when it's necessary to organize or process data in descending order. Such sequences can simplify tasks involving ranking or removing items from sorted lists.

In programming, you can check for a decreasing sequence using a condition such as if a > b > c. This line of logic is often used in algorithms that need to identify maximum values or process data backward.

Utilizing Conditional Statements

Conditional statements are the backbone of decision-making in programming. These statements allow the program to choose a path or an outcome based on certain criteria. Typical conditional statements involve keywords like if, else if, and else, which help branch logic in the code.

For the problem of determining ascending or descending order among three numbers, conditional statements are used to test each possible sequence:

• First, the program checks if the numbers are in an increasing order using a condition like if a < b < c.
• If this condition is not met, the program checks if the numbers are in a decreasing order using another condition like else if a > b > c.
• If neither condition is true, the sequence is neither increasing nor decreasing, leading to the else statement.

By setting up these conditional statements, you enable the program to make logical decisions on its own, managing multiple outcomes efficiently. Proper use of conditional statements ensures your program can adapt to various inputs and execute the correct block of code based on the data it receives.