import matplotlib.pyplot as plt
import numpy as np


def plot_linear_functions(list1, list2, list3, b, x_range=(0, 10)):
    """
    Plots linear functions y = Cx + D where:
    C = b - k (k elements removed)
    D = sum of remaining elements
    k ranges from 0 to b.
    """
    datasets = [list1, list2, list3]
    # Distinct colors for the 3 sets
    colors = ['#E63946', '#457B9D', '#1D3557']
    labels = ['List 1', 'List 2', 'List 3']

    plt.figure(figsize=(12, 8))
    x = np.linspace(x_range[0], x_range[1], 100)

    for i, current_list in enumerate(datasets):
        # Sort descending so the first k elements are the 'top k'
        sorted_list = sorted(current_list, reverse=True)

        for k in range(len(sorted_list) + 1):
            # C is the fixed number b minus the number of elements removed
            C = k-b

            # Remove top k elements (if k > list length, remaining is empty)
            remaining = sorted_list[k:] if k < len(sorted_list) else []

            # D is the sum of the remaining elements
            D = sum(remaining)

            y = C * x + D

            # Plot the line; label only once per list for a clean legend
            line_label = labels[i] if k == 0 else ""
            if C == 0:
                plt.plot(x, y, color=colors[i], alpha=1,
                         label=line_label, linestyle='-')
            else:
                plt.plot(x, y, color=colors[i], alpha=0.6,
                         label=line_label, linestyle='--')

    plt.title(
        f"2D Linear Functions: $y = (b-k)x + sum(rem)$ for $0 ≤ k ≤ b$ ($b={b}$)")
    plt.xlabel("x")
    plt.ylabel("y")
    plt.grid(True, linestyle='--', alpha=0.7)
    plt.legend()
    plt.savefig('linear_plot.png')
    plt.show()


# --- Example Usage ---
# Replace these with your actual lists and b value
L1 = [45, 14, 7, 7, 4, 2]
L2 = [20, 15, 10, 5, 4, 2]
L3 = [5, 5, 5, 5, 5, 5]
fixed_b = 2

plot_linear_functions(L1, L2, L3, fixed_b)