Fibonacci Series In Dart

The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. It is important in various fields, including mathematics, computer science, and even nature, where it can describe patterns of growth. Understanding the Fibonacci series helps in algorithm development, recursive programming, and even in solving complex problems.

What is Fibonacci Series?

The Fibonacci series is defined as follows:

• ✅ The first two numbers in the series are 0 and 1.
• ✅ Each subsequent number is the sum of the previous two numbers.

For example, the series starts as 0, 1, 1, 2, 3, 5, 8, 13, and continues indefinitely. It is used in algorithms for dynamic programming, data structures, and in modeling natural phenomena such as the branching of trees, the arrangement of leaves on a stem, and the fruit sprouts of a pineapple.

Syntax

// Function to generate Fibonacci series up to n terms
List<int> fibonacci(int n) {
  List<int> series = [0, 1]; // Initialize the series with the first two numbers
  for (int i = 2; i < n; i++) { // Start from the third number
    series.add(series[i - 1] + series[i - 2]); // Add the last two numbers
  }
  return series; // Return the complete series
}

How It Works

1. We start by initializing a list to store the Fibonacci series with the first two numbers, 0 and 1.
2. We then use a loop to calculate the next numbers in the series.
3. In each iteration, we add the last two numbers of the list to get the next number, which we append to the list.
4. Finally, we return the complete list containing the Fibonacci series.

Example 1: Basic Usage

Example
Copy
void main() {
  int n = 10; // Number of terms to generate
  List<int> fibSeries = fibonacci(n); // Call the fibonacci function
  print(fibSeries); // Print the Fibonacci series
}

List<int> fibonacci(int n) {
  List<int> series = [0, 1]; // Start the series
  for (int i = 2; i < n; i++) {
    series.add(series[i - 1] + series[i - 2]); // Calculate next term
  }
  return series; // Return the series
}
Try it Yourself

Output:

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

Explanation: This code generates the first 10 terms of the Fibonacci series and prints them.

Example 2: Intermediate Usage with Variations

void main() {
  int n = 15; // Generate 15 terms
  List<int> fibSeries = fibonacci(n); // Get Fibonacci series
  print("Fibonacci Series of $n terms: $fibSeries"); // Print with message
}

List<int> fibonacci(int n) {
  if (n <= 0) return []; // Return empty if n is 0 or less
  List<int> series = [0]; // Start with the first term
  if (n > 1) series.add(1); // Add second term if n is more than 1
  for (int i = 2; i < n; i++) {
    series.add(series[i - 1] + series[i - 2]); // Compute next term
  }
  return series; // Return the series
}

Output:

Fibonacci Series of 15 terms: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

Explanation: This example shows how to handle cases where the input is less than or equal to zero, and prints a formatted output message.

Example 3: Real-World Application

void main() {
  int n = 20; // Number of Fibonacci numbers to generate
  List<int> fibSeries = fibonacci(n); // Generate series
  print("The Fibonacci series can be used in algorithms: $fibSeries");
}

List<int> fibonacci(int n) {
  List<int> series = [0, 1]; // Start the list
  for (int i = 2; i < n; i++) {
    series.add(series[i - 1] + series[i - 2]); // Calculate next number
  }
  return series; // Return the result
}

Output:

The Fibonacci series can be used in algorithms: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]

Explanation: This example highlights the usefulness of the Fibonacci series in algorithm design and problem-solving.

When to Use Fibonacci Series in Dart

Key Points

This tutorial provides a comprehensive understanding of the Fibonacci series in Dart, demonstrating its implementation and practical applications through multiple examples.