feat: extracted repated functionality from split function

PYTHON/split/split_x_into_n_symmetrically.py

@@ -1,77 +1,58 @@
+def calculate_symmetric_weights(N, middle_weight, factors=None):
+    """
+    Calculate symmetric weights for both even and odd N.
+
+    N: Number in which to split.
+    middle_weight: The middle value for symmetry.
+    factors: If provided, controls the difference in weights (used for the `split_x_into_n_symmetrically` function).
+             Must have length N // 2 or N // 2 - 1 depending on N.
+    """
+    half_N = N // 2
+    weights_left = [middle_weight]
+
+    if factors:
+        for factor in factors:
+            next_weight = weights_left[-1] + factor
+            weights_left.append(next_weight)
+    else:
+        for i in range(half_N - 1):
+            weights_left.append(middle_weight - (i + 1))
+
+    if N % 2 == 0:
+        weights = weights_left[::-1] + weights_left
+    else:
+        weights = weights_left[::-1] + [middle_weight] + weights_left
+    
+    return weights
+
+def scale_to_total(X, weights):
+    """
+    Scale the weights so that their sum is proportional to X.
+    
+    X: Total value to distribute.
+    weights: The list of weights to be scaled.
+    """
+    total_weight = sum(weights)
+    base_unit = X / total_weight
+    distances = [base_unit * weight for weight in weights]
+    
+    return distances
+
 def split_x_into_n_symmetrically(X, N, factors):
     """
-    X: Total value to distribute
-    N: Number into which we split
-    factors: List controlling the difference in weights between consecutive days
-             Must have length of N // 2 (if N is odd) or (N // 2 - 1) (if N is even)
+    X: Total value to distribute.
+    N: Number in which we split.
+    factors: List controlling the difference in weights between consecutive days.
+             Must have length of N // 2 (if N is odd) or (N // 2 - 1) (if N is even).
     """
-    
-    # Calculate the mid-point index (for both even and odd N)
-    half_N = N // 2
-    
-    # Generate the base weights symmetrically around the middle
-    if N % 2 == 0:  # Even number of days
-        middle_weight = 1
-        weights_left = [middle_weight]
-        for factor in factors:
-            next_weight = weights_left[-1] + factor
-            weights_left.append(next_weight)
-        weights = weights_left[::-1] + weights_left
-    else:  # Odd number of days
-        middle_weight = 1
-        weights_left = [middle_weight]
-        for factor in factors:
-            next_weight = weights_left[-1] + factor
-            weights_left.append(next_weight)
-        weights = weights_left[::-1] + [middle_weight] + weights_left
-
-    total_weight = sum(weights)
-
-    # Calculate the base unit
-    base_unit = X / total_weight
-
-    # Calculate the distance for each day
-    distances = [base_unit * weight for weight in weights]
-
-    return distances
+    weights = calculate_symmetric_weights(N, middle_weight=1, factors=factors)
+    return scale_to_total(X, weights)
 
 def split_x_into_n_middle(X, N, middle_value):
     """
-    X: Total value to distribute
-    N: Number in which we split
-    middle_value: Value of the middle number (the biggest weight)
+    X: Total value to distribute.
+    N: Number in which we split.
+    middle_value: Value of the middle number (the biggest weight).
     """
-    
-    # Calculate the mid-point index
-    half_N = N // 2
-
-    # Initialize the weights list
-    weights = [0] * N
-
-    # Set the middle value
-    if N % 2 == 0:  # Even number of days
-        weights[half_N - 1] = middle_value
-        weights[half_N] = middle_value
-    else:  # Odd number of days
-        weights[half_N] = middle_value
-
-    # Fill in the decreasing values symmetrically
-    for i in range(half_N):
-        # Decrease the weight by 1 for each step toward the edges
-        if N % 2 == 0:
-            weights[half_N - 1 - i - 1] = middle_value - (i + 1)
-            weights[half_N + i + 1] = middle_value - (i + 1)
-        else:
-            weights[half_N - i - 1] = middle_value - (i + 1)
-            weights[half_N + i + 1] = middle_value - (i + 1)
-
-    # Sum the weights and calculate the base unit
-    total_weight = sum(weights)
-    
-    # Calculate the base unit
-    base_unit = X / total_weight
-
-    # Calculate the distance for each day
-    distances = [base_unit * weight for weight in weights]
-
-    return distances
+    weights = calculate_symmetric_weights(N, middle_weight=middle_value)
+    return scale_to_total(X, weights)