class DijkstraStats:
    def __init__(self):
        self.extract_min_calls = 0
        self.relax_attempts = 0
        self.relax_success = 0
        # self.decrease_key_calls = 0
        # self.add_calls = 0

def heap_dijkstra(nodes, adj, heap, start, end):
    INF = float('inf')
    dist = [INF] * nodes
    visited = [False] * nodes
    stats = DijkstraStats()

    dist[start] = 0

    for v in range(nodes):
        heap.add(v, dist[v])
        # stats.add_calls += 1
    
    while True:
        res = heap.extract_min()
        stats.extract_min_calls += 1
        if res is None:
            break
        cur, cur_dist = res

        if cur_dist == INF:
            break

        if cur == end:
            break

        for nxt, d in adj[cur]:
            stats.relax_attempts += 1
            if visited[nxt]:
                continue
            new = cur_dist + d
            if new < dist[nxt]:
                stats.relax_success += 1
                dist[nxt] = new
                heap.decrease_key(nxt, new)
        
        visited[cur] = True
    
    return dist[end], stats