optimize computational efficiency

Implement memoization and guard clauses to eliminate redundant computations and improve algorithmic performance. Many algorithms can be significantly optimized by caching intermediate results and avoiding unnecessary work.

Key optimization strategies:

1. Use memoization for recursive functions - Cache results of expensive recursive calls to avoid recalculating the same values multiple times
2. Add guard clauses for conditional processing - Check if work is needed before performing expensive operations
3. Choose efficient iteration patterns - Use lazy evaluation techniques like islice instead of creating full intermediate collections
4. Ensure proper memoization scope - Create memo objects at the appropriate scope to maximize reuse

Example of proper memoization implementation:

# Before: Redundant recursive calculations
def recursive_will_execute(prompt, outputs, node_id):
    # Expensive recursive computation repeated many times
    return calculate_dependencies(prompt, outputs, node_id)

# After: Memoized version with proper scope
memo = {}  # Create memo outside the sorting algorithm
output_node_id = min(to_execute, key=lambda a: len(recursive_will_execute(prompt, outputs, a, memo)))

Example of guard clause optimization:

# Before: Always processes string replacements
def compute_vars(input, image_width, image_height):
    input = input.replace("%width%", str(image_width))
    input = input.replace("%height%", str(image_height))
    return input

# After: Skip processing if no variables present
def compute_vars(input, image_width, image_height):
    if '%' not in input:
        return input  # Guard clause avoids unnecessary work
    input = input.replace("%width%", str(image_width))
    input = input.replace("%height%", str(image_height))
    return input

These optimizations can dramatically improve performance, especially in algorithms that process large datasets or perform repeated calculations.