Java Program to Check Geometric Progression

Problem Statement

Write a Java program that determines whether a grid number sequence forms a geometric progression (GP). A geometric progression is defined as a sequence in which each joint after the first joint is obtained by multiplying the preceding joint by a constant. The program should:

1. Accept a sequence of integers as input.
2. Validate the input and ensure it contains at least two elements.
3. Calculates the common ratio between consecutive terms in a sequence.
4. Verify if the ratio remains consistent throughout the sequence.
5. Handle edge cases, such as sequences containing zeros or negative numbers, and return appropriate results.

Geometric Progressions (GP)

Geometric progression (GP) is a numerical sequence in which each lead after the first lead is created by multiplying by a fixed non-zero number that is the common ratio of the previous leads. Mathematically, a sequence is represented by GP, where the first term is the common ratio.

The common ratio can be determined by dividing any term. in a sequence with a preceding term. GP is ubiquitous in mathematical and real-world applications. including exponential growth Population study Financial Modeling and Physics Understanding how to test whether a sequence of numbers forms a GP is a fundamental concept in mathematics and programming.

Examples

Input:

• Sequence: [2, 6, 18, 54]
• Output: "The sequence is a geometric progression."

Explanation

Common ratio = Ratios between terms are consistent (3).

Input:

Sequence: [1, 2, 4, 8, 16]

Output: "The sequence is a geometric progression."

Explanation

Common ratio = Ratios between terms are consistent (2).

Input:

Sequence: [5, 15, 45, 100]

Output: "The sequence is NOT a geometric progression."

Explanation

Ratios: The ratio changes, so the sequence is not a GP.

Steps to Check for Geometric Progression

Follow these steps to check if a given sequence is a geometric progression.

1. Input validation: Make sure there are at least two numbers in the sequence. Otherwise the concept of progress is meaningless.
2. Common Ratio Calculation: Calculates the ratio between consecutive terms in a sequence.
3. Proportion check: Verifies that the proportions of all terms in a sequence are consistent.
4. Handle Edge Cases: Consider special cases, such as when a sequence contains zeros or negative numbers.

File Name: GeometricProgressionChecker.java

Output:

 Enter the number of elements in the sequence: 4 Enter the elements of the sequence: 2 6 18 54 The sequence is a geometric progression. 

Explanation

The program begins by defining a method isGeometricProgression(), which takes an array of integers as input. The method first checks whether the sequence has fewer than two terms, returning false in such cases since a GP requires at least two numbers.

Next, the program calculates the common ratio using the first two terms of the sequence. It then iterates through the sequence, checking whether the ratio between consecutive terms matches the common ratio. If a mismatch is found or if a term results in division by zero, the method returns false.

The main() method handles user input, prompting the user to enter the sequence's length and elements. After collecting the input, it calls the isGeometricProgression() method and prints whether the sequence is a GP.

Complexity Analysis

1. Time Complexity:
   
   • The isGeometricProgression() method iterates through the sequence once to check the common ratio for all terms. Therefore, the time complexity is O(n), where is the number of elements in the sequence.
   • Reading the input in the main() method also takes, but this does not add to the overall asymptotic complexity since the operations are sequential.
   • Overall, the time complexity of the program is O(n).
2. Space Complexity:
   
   • The program uses an integer array to store the sequence, which requires space.
   • Other variables (for example, commonRatio, currentRatio) require a constant amount of space, .
   • Therefore, the space complexity is O(n).

Conclusion

This Java program efficiently checks whether a sequence of numbers forms a geometric progression. The implementation covers edge cases like zero and negative numbers while ensuring accurate calculations through type casting.

By understanding the underlying logic and code, you can adapt this program for various applications, such as validating sequences in mathematical computations, simulating real-world scenarios, or enhancing educational tools.