#Comparative vector inequalities



    # Generate all possible assignments of vectors to subsets

        # Assign vectors to subsets based on the assignment

        # Check if all inequalities hold

            # Compare the i-th and j-th vectors based on the operator
            # All inequalities hold for this assignment

    # No valid assignment found

    # Compare vectors based on a specific criterion
    # Modify this function according to your problem's criteria
    # Return True if vector1 satisfies the criterion compared to vector2, False otherwise

# Example usage



if __name__ == '__main__':
    from itertools import product
    def check_vector_inequalities(vectors, inequalities):
        n = len(vectors)
        m = len(inequalities)
        for assignment in product([0, 1], repeat=n):
            subset1 = []
            subset2 = []
            for i in range(n):
                if assignment[i] == 0:
                    subset1.append(vectors[i])
                else:
                    subset2.append(vectors[i])
            for inequality in inequalities:
                i, j = inequality[0], inequality[1]
                operator = inequality[2]
                if operator == "<":
                    if not compare_vectors(subset1[i], subset2[j]):
                        break
                elif operator == ">":
                    if not compare_vectors(subset2[j], subset1[i]):
                        break
                elif operator == "=":
                    if not compare_vectors(subset1[i], subset2[j]) or not compare_vectors(subset2[j], subset1[i]):
                        break
            else:
                return True
        return False
    def compare_vectors(vector1, vector2):
        return vector1 > vector2
    vectors = [(2, 3, 5), (1, 4, 6), (3, 2, 4)]
    inequalities = [(0, 1, "<"), (2, 1, ">")]
    is_valid_assignment = check_vector_inequalities(vectors, inequalities)
    print("Is there a valid assignment?", is_valid_assignment)
