# Discovering Odd Palindrome Numbers in Python: A Range-Based Approach

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π‘ Problem Formulation: Finding odd palindrome numbers within a specific number range involves identifying numbers that are the same forwards and backwards (palindromes) and are not divisible by two (odd). For instance, if our range is 100 to 200, the output should be a list of numbers like [101, 111, 121, 131, 141, 151, 161, 171, 181, 191] that meet the criteria.

## Method 1: Brute-Force Iteration

This method iterates over each number in the range, checking firstly if it’s odd, and secondly, if the string representation is the same forwards and backwards. It’s straightforward and easy to understand, but not the most efficient for large ranges.

Here’s an example:

```def find_odd_palindromes(start, end):
odd_palindromes = []
for num in range(start, end + 1):
if num % 2 != 0 and str(num) == str(num)[::-1]:
odd_palindromes.append(num)
return odd_palindromes

print(find_odd_palindromes(100, 200))
```

Output: [101, 111, 121, 131, 141, 151, 161, 171, 181, 191]

This code defines a function `find_odd_palindromes()` that takes a start and end number and returns a list of all odd palindromes within that range. The function uses a for loop and Python’s slicing syntax to check for the palindromes.

## Method 2: Using List Comprehension

List comprehension offers a more concise way to achieve the same iteration by encapsulating the logic into a single line of code. Itβs elegant and Pythonic, suitable for scripting and smaller ranges.

Here’s an example:

```def find_odd_palindromes(start, end):
return [num for num in range(start, end + 1) if num % 2 != 0 and str(num) == str(num)[::-1]]

print(find_odd_palindromes(100, 200))
```

Output: [101, 111, 121, 131, 141, 151, 161, 171, 181, 191]

The `find_odd_palindromes()` function is now a single line using list comprehension, which checks for odd numbers and palindromes, effectively condensing the logic used in Method 1.

## Method 3: Utilizing Functions and Filter

Incorporating Python’s `filter()` function, this method applies a filter object to process each number, which can be more readable and separates concerns. It leverages built-in functions and is ideal for users preferring functional programming paradigms.

Here’s an example:

```def is_odd_palindrome(num):
return num % 2 != 0 and str(num) == str(num)[::-1]

def find_odd_palindromes(start, end):
return list(filter(is_odd_palindrome, range(start, end + 1)))

print(find_odd_palindromes(100, 200))
```

Output: [101, 111, 121, 131, 141, 151, 161, 171, 181, 191]

The `find_odd_palindromes()` function in this method uses `filter()` to apply a separate `is_odd_palindrome()` function to each number in the range. It cleanly separates the checking logic from the iteration logic.

## Method 4: Generator Expressions

A generator expression is similar to list comprehension but more memory-efficient, as it generates values on the fly rather than storing them all at once. This can be especially useful for very large ranges where memory is a consideration.

Here’s an example:

```def find_odd_palindromes(start, end):
return (num for num in range(start, end + 1) if num % 2 != 0 and str(num) == str(num)[::-1])

print(list(find_odd_palindromes(100, 200)))
```

Output: [101, 111, 121, 131, 141, 151, 161, 171, 181, 191]

The code replaces the list from list comprehension with parentheses to create a generator expression in function `find_odd_palindromes()`, yielding odd palindromes as they are computed.

## Bonus One-Liner Method 5: Lambda Function and Filter

A lambda function provides an inline, anonymous function to be used with `filter()`. This one-liner is compact and blends the functionality of previous methods into an elegant one-liner, ideal for functional programming enthusiasts.

Here’s an example:

```print(list(filter(lambda num: num % 2 != 0 and str(num) == str(num)[::-1], range(100, 200))))
```

Output: [101, 111, 121, 131, 141, 151, 161, 171, 181, 191]

This uses an anonymous lambda function within the `filter()` call to identify odd palindromes in a one-liner code snippet, avoiding the need for separate function definitions.

## Summary/Discussion

• Method 1: Brute-Force Iteration. Simple and direct approach. Can be inefficient for large ranges.
• Method 2: Using List Comprehension. Condensed and Pythonic. Still not memory-efficient for large ranges.
• Method 3: Utilizing Functions and Filter. More readable, encourages functional programming. May have slight overhead due to function calls.
• Method 4: Generator Expressions. Memory-efficient, suitable for huge ranges. Requires additional syntax comprehension.
• Method 5: Lambda Function and Filter. Elegant one-liner. Readability can be a concern for those not familiar with lambdas.