#Minimum Cut Linear Arrangement



    # Initialize the best solution to a large value

    # Define a function to calculate the number of cuts 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 minimum_cut_linear_arrangement(elements, relations, cost_matrix):
        best_cuts = float('inf')
        best_solution = None
        def calculate_cuts(solution):
            cuts = 0
            for a, b in relations:
                if solution.index(a) > solution.index(b):
                    cuts += 1
            return cuts
        def search(elements, solution=[]):
            nonlocal best_cuts, best_solution
            if not elements:
                cuts = calculate_cuts(solution)
                if cuts < best_cuts:
                    best_cuts = cuts
                    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)]
    cost_matrix = [[0, 10, 15, 20],
                   [10, 0, 35, 25],
                   [15, 35, 0, 30],
                   [20, 25, 30, 0]]
    print(minimum_cut_linear_arrangement(elements, relations, cost_matrix))
