#Comparative vector inequalities

from itertools import product

def check_vector_inequalities(vectors, inequalities):
    n = len(vectors)
    m = len(inequalities)

    # Generate all possible assignments of vectors to subsets
    for assignment in product([0, 1], repeat=n):
        subset1 = []
        subset2 = []

        # Assign vectors to subsets based on the assignment
        for i in range(n):
            if assignment[i] == 0:
                subset1.append(vectors[i])
            else:
                subset2.append(vectors[i])

        # Check if all inequalities hold
        for inequality in inequalities:
            i, j = inequality[0], inequality[1]
            operator = inequality[2]

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

    # No valid assignment found
    return False

def compare_vectors(vector1, vector2):
    # 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
    return vector1 > vector2

# Example usage
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)

