#Directed Elimination Ordering



    # Initialize the best solution to a large value

    # Define a function to calculate the number of violated edges of a solution

    # Define a function to perform the branch-and-bound search
            # Use a heuristic function to order the elements
            # in the next level of the search tree

    # Perform the branch-and-bound search

    # Return the best solution


# Example usage


if __name__ == '__main__':
    import itertools
    def directed_elimination_ordering(elements, relations):
        best_violated = float('inf')
        best_solution = None
        def calculate_violated(solution):
            violated = 0
            for a, b in relations:
                if solution.index(a) > solution.index(b):
                    violated += 1
            return violated
        def search(elements, solution=[]):
            nonlocal best_violated, best_solution
            if not elements:
                violated = calculate_violated(solution)
                if violated < best_violated:
                    best_violated = violated
                    best_solution = solution
            else:
                heuristic = lambda e: sum(1 for a, b in relations if e == a and solution[-1] == b)
                for e in sorted(elements, key=heuristic):
                    search(elements - {e}, solution + [e])
        search(set(elements))
        return best_solution
    elements = [1, 2, 3, 4]
    relations = [(1, 2), (3, 4)]
    print(directed_elimination_ordering(elements, relations))
