Generating Sequences
Advanced Sequence Generation Techniques
Mathematical Sequence Generation
Arithmetic Progressions
def arithmetic_sequence(start, step, length):
return [start + i * step for i in range(length)]
## Example: Generate arithmetic sequence
arithmetic_seq = arithmetic_sequence(1, 3, 6)
## Result: [1, 4, 7, 10, 13, 16]
Geometric Progressions
def geometric_sequence(start, ratio, length):
return [start * (ratio ** i) for i in range(length)]
## Example: Generate geometric sequence
geometric_seq = geometric_sequence(2, 2, 5)
## Result: [2, 4, 8, 16, 32]
Sequence Generation Strategies
Strategy |
Method |
Pros |
Cons |
Range-based |
range() |
Memory efficient |
Limited to integers |
Comprehension |
List comprehension |
Flexible |
Memory intensive |
Generator |
Generator expression |
Lazy evaluation |
Less readable |
Advanced Generation Techniques
Fibonacci Sequence
def fibonacci_sequence(n):
sequence = [0, 1]
while len(sequence) < n:
sequence.append(sequence[-1] + sequence[-2])
return sequence
fib_seq = fibonacci_sequence(8)
## Result: [0, 1, 1, 2, 3, 5, 8, 13]
Prime Number Sequence
def prime_sequence(limit):
def is_prime(num):
return num > 1 and all(num % i != 0 for i in range(2, int(num**0.5) + 1))
return [num for num in range(2, limit) if is_prime(num)]
prime_nums = prime_sequence(20)
## Result: [2, 3, 5, 7, 11, 13, 17, 19]
Sequence Generation Workflow
graph TD
A[Start] --> B{Sequence Type}
B --> |Mathematical| C[Define Mathematical Rule]
B --> |Complex| D[Use Generator Functions]
C --> E[Generate Sequence]
D --> E
E --> F[Process/Manipulate Sequence]
Random Sequence Generation
import random
def random_sequence(start, end, length):
return [random.randint(start, end) for _ in range(length)]
random_seq = random_sequence(1, 100, 5)
## Result: Random sequence of 5 integers between 1-100
- Use generators for large sequences
- Implement caching for repetitive sequences
- Choose appropriate generation method based on use case
Key Techniques
- Mathematical sequence generation
- Comprehension-based creation
- Generator-based approaches
- Random sequence generation