feat: added script for splitting a number symmetrically across another number

PYTHON/split/split_x_into_n_symmetrically.py

@@ -0,0 +1,77 @@
+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)
+    """
+    
+    # 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
+
+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)
+    """
+    
+    # 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