#Directed Optimal Linear Arrangement



    # Initialize the best solution to a large value

    # Define a function to calculate the cost of a solution

    # Define a function to check if a solution is valid

    # Define a function to perform the branch-and-bound search

    # Perform the branch-and-bound search

    # Return the best solution


# Example usage


if __name__ == '__main__':
    import itertools
    def directed_optimal_linear_arrangement(elements, relations, cost_matrix):
        best_cost = float('inf')
        best_solution = None
        def calculate_cost(solution):
            cost = 0
            for i in range(len(solution)):
                for j in range(i + 1, len(solution)):
                    cost += cost_matrix[solution[i]][solution[j]]
            return cost
        def is_valid(solution):
            for a, b in relations:
                if solution.index(a) > solution.index(b):
                    return False
            return True
        def search(elements, solution=[]):
            nonlocal best_cost, best_solution
            if not elements:
                if is_valid(solution):
                    cost = calculate_cost(solution)
                    if cost < best_cost:
                        best_cost = cost
                        best_solution = solution
            else:
                for e in elements:
                    search(elements - {e}, solution + [e])
        search(set(elements))
        return best_solution
    elements = [1, 2, 3, 4]
    relations = [(1, 2), (3, 4)]
    cost_matrix = [[0, 10, 15, 20],
                   [10, 0, 35, 25],
                   [15, 35, 0, 30],
                   [20, 25, 30, 0]]
    print(directed_optimal_linear_arrangement(elements, relations, cost_matrix))
