#Decision Tree



    # Initialize the dynamic programming table

    # Build the decision tree using dynamic programming

    # Reconstruct the decision tree





    # Reconstruct the decision tree using backtracking


# Example usage
    # Example instance

    # Solve the "Decision Tree" problem

    # Print the decision tree



if __name__ == '__main__':
    class Node:
        def __init__(self, attribute=None, left=None, right=None):
            self.attribute = attribute
            self.left = left
            self.right = right
    def decision_tree(X, T, K):
        n = len(X)  # Number of objects
        m = len(T)  # Number of tests
        dp = [[float('inf')] * (K + 1) for _ in range(n + 1)]
        dp[0][0] = 0
        for i in range(1, n + 1):
            for k in range(K + 1):
                for j in range(m):
                    if satisfies_test(X[i - 1], T[j]):
                        left_length = min(k, dp[i - 1][k] + 1)
                        right_length = min(k - 1, dp[i - 1][k - 1] + 1)
                        dp[i][k] = min(dp[i][k], max(left_length, right_length))
        root = reconstruct_tree(X, T, dp, K)
        return root
    def satisfies_test(x, test):
        for i in range(len(x)):
            if test[i] != 'x' and test[i] != x[i]:
                return False
        return True
    def reconstruct_tree(X, T, dp, K):
        n = len(X)  # Number of objects
        m = len(T)  # Number of tests
        root = Node()
        for i in range(n, 0, -1):
            for j in range(m):
                if satisfies_test(X[i - 1], T[j]):
                    left_length = min(K, dp[i - 1][K])
                    right_length = min(K - 1, dp[i - 1][K - 1])
                    if max(left_length, right_length) == dp[i][K]:
                        root.attribute = T[j]
                        root.left = reconstruct_tree(X[:i - 1], T, dp, left_length)
                        root.right = reconstruct_tree(X[:i - 1], T, dp, right_length)
                        return root
        return root
    if __name__ == '__main__':
        X = ['A', 'B', 'C', 'D']
        T = [['0', 'x', '1', '0'], ['x', '1', '0', '1']]
        K = 3
        root = decision_tree(X, T, K)
        print("Decision Tree:")
        print_tree(root)
    def print_tree(node, indent=''):
        if node.attribute is None:
            print(indent + "Leaf: " + str(node.label))
        else:
            print(indent + "Attribute: " + str(node.attribute))
            print(indent + "Left:")
            print_tree(node.left, indent + "  ")
            print(indent + "Right:")
            print_tree(node.right, indent + "  ")
