from scipy.spatial.distance import cdist
from scipy.optimize import linear_sum_assignment
import numpy as np 

def compute_WED(pd_vertices, pd_edges, gt_vertices, gt_edges, cv=1.0, ce=1.0, normalized=True, squared=False):
    pd_vertices = np.array(pd_vertices)
    gt_vertices = np.array(gt_vertices)
    pd_edges = np.array(pd_edges)
    gt_edges = np.array(gt_edges)
    
    # Step 1: Bipartite Matching
    if squared:
        distances = cdist(pd_vertices, gt_vertices, metric='sqeuclidean')
    else:
        distances = cdist(pd_vertices, gt_vertices, metric='euclidean')

    row_ind, col_ind = linear_sum_assignment(distances)
    
    # Step 2: Vertex Translation
    
    if squared:
        translation_costs = cv * np.sqrt(np.sum(distances[row_ind, col_ind]))
    else:
        translation_costs = cv * np.sum(distances[row_ind, col_ind])
    
    # Additional: Vertex Deletion
    unmatched_pd_indices = set(range(len(pd_vertices))) - set(row_ind)
    deletion_costs = cv * len(unmatched_pd_indices)  # Assuming a fixed cost for vertex deletion
    
    # Step 3: Vertex Insertion
    unmatched_gt_indices = set(range(len(gt_vertices))) - set(col_ind)
    insertion_costs = cv * len(unmatched_gt_indices)  # Assuming a fixed cost for vertex insertion
    
    # Step 4: Edge Deletion and Insertion
    updated_pd_edges = [(row_ind[np.where(col_ind == edge[0])[0][0]], row_ind[np.where(col_ind == edge[1])[0][0]]) for edge in pd_edges if edge[0] in col_ind and edge[1] in col_ind]
    pd_edges_set = set(map(tuple, updated_pd_edges))
    gt_edges_set = set(map(tuple, gt_edges))
    
    # Delete edges not in ground truth
    edges_to_delete = pd_edges_set - gt_edges_set
    deletion_edge_costs = ce * sum(np.linalg.norm(pd_vertices[edge[0]] - pd_vertices[edge[1]]) for edge in edges_to_delete)
    
    # Insert missing edges from ground truth
    edges_to_insert = gt_edges_set - pd_edges_set
    insertion_edge_costs = ce * sum(np.linalg.norm(gt_vertices[edge[0]] - gt_vertices[edge[1]]) for edge in edges_to_insert) 
    
    # Step 5: Calculation of WED
    WED = translation_costs + deletion_costs + insertion_costs + deletion_edge_costs + insertion_edge_costs
    
    if normalized:
        total_length_of_gt_edges = np.linalg.norm((gt_vertices[gt_edges[:, 0]] - gt_vertices[gt_edges[:, 1]]), axis=1).sum()
        WED = WED / total_length_of_gt_edges
       
    return WED