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question:def final_position_and_orientation(instructions: str) -> tuple: Determines the robot's final position and orientation after executing the given instructions. >>> final_position_and_orientation("GGRLLGG") (-2, 2, "West") >>> final_position_and_orientation("GGGGR") (0, 4, "East") >>> final_position_and_orientation("GLGLGLGL") (0, 0, "North") >>> final_position_and_orientation("GRGRGRGR") (0, 0, "North") >>> final_position_and_orientation("G") (0, 1, "North") >>> final_position_and_orientation("L") (0, 0, "West") >>> final_position_and_orientation("R") (0, 0, "East") >>> final_position_and_orientation("G"*10000) (0, 10000, "North") >>> final_position_and_orientation("GLGLGLGLG"*1000) (0, 1000, "North") >>> final_position_and_orientation("GL") (0, 1, "West") >>> final_position_and_orientation("GR") (0, 1, "East") >>> final_position_and_orientation("GGLL") (0, 2, "South") >>> final_position_and_orientation("GRR") (0, 1, "South") >>> final_position_and_orientation("GLR") (0, 1, "North")
answer:def final_position_and_orientation(instructions): Determines the robot's final position and orientation after executing the given instructions. Parameters: instructions (str): A string of instructions containing only 'G', 'L', and 'R'. Returns: tuple: Final coordinates (x, y) of the robot and its orientation as a string ("North", "East", "South", "West"). # Initial position and direction x, y = 0, 0 directions = ['North', 'East', 'South', 'West'] current_direction = 0 # Start facing North # Direction vectors for North, East, South, West respectively direction_vectors = [(0, 1), (1, 0), (0, -1), (-1, 0)] for instruction in instructions: if instruction == 'G': dx, dy = direction_vectors[current_direction] x += dx y += dy elif instruction == 'L': current_direction = (current_direction - 1) % 4 elif instruction == 'R': current_direction = (current_direction + 1) % 4 return (x, y, directions[current_direction])
question:def can_fulfill_deliveries(warehouses, deliveries): Determines if the total supply in the warehouses can fulfill the total demand from the deliveries. Args: warehouses (list of int): A list of integers representing the number of items in each warehouse. deliveries (list of int): A list of integers representing the number of items required for each delivery. Returns: bool: True if total supply of items in warehouses is greater than or equal to the total demand from deliveries, False otherwise. # Your implementation here # Test cases def test_example_1(): warehouses = [10, 20, 30] deliveries = [15, 25] assert can_fulfill_deliveries(warehouses, deliveries) == True def test_example_2(): warehouses = [5, 5] deliveries = [3, 4, 4] assert can_fulfill_deliveries(warehouses, deliveries) == False def test_exact_match(): warehouses = [10, 20, 30] deliveries = [10, 20, 30] assert can_fulfill_deliveries(warehouses, deliveries) == True def test_more_supply_than_demand(): warehouses = [50, 50] deliveries = [30, 20, 10, 10] assert can_fulfill_deliveries(warehouses, deliveries) == True def test_more_demand_than_supply(): warehouses = [10, 10] deliveries = [10, 10, 1] assert can_fulfill_deliveries(warehouses, deliveries) == False def test_no_warehouses(): warehouses = [] deliveries = [1] assert can_fulfill_deliveries(warehouses, deliveries) == False def test_no_deliveries(): warehouses = [1, 1, 1] deliveries = [] assert can_fulfill_deliveries(warehouses, deliveries) == True
answer:def can_fulfill_deliveries(warehouses, deliveries): Determines if the total supply in the warehouses can fulfill the total demand from the deliveries. Args: warehouses (list of int): A list of integers representing the number of items in each warehouse. deliveries (list of int): A list of integers representing the number of items required for each delivery. Returns: bool: True if total supply of items in warehouses is greater than or equal to the total demand from deliveries, False otherwise. total_supply = sum(warehouses) total_demand = sum(deliveries) return total_supply >= total_demand
question:def process_operations(n, initial_scores, m, operations): Process a series of operations to update and retrieve scores of posts. Args: n (int): The number of posts. initial_scores (List[int]): The initial scores of the posts. m (int): The number of operations. operations (List[Tuple[int]]): The operations to process. Returns: List[int]: The results of each "retrieve" operation. Example: >>> process_operations(3, [10, 20, 30], 5, [(1, 1, 5), (2, 2, 3), (3, 1), (1, 3, 10), (3, 2)]) [15, 17]
answer:def process_operations(n, initial_scores, m, operations): scores = initial_scores[:] results = [] for operation in operations: if operation[0] == 1: # Increment score of post with ID x by y x, y = operation[1], operation[2] scores[x-1] += y elif operation[0] == 2: # Decrement score of post with ID x by y x, y = operation[1], operation[2] scores[x-1] -= y elif operation[0] == 3: # Retrieve current score of post with ID x x = operation[1] results.append(scores[x-1]) return results
question:def min_additional_routes(N: int, M: int, edges: List[Tuple[int, int]]) -> int: Determine the minimum number of additional hyperspace routes needed to ensure there is a path between every pair of planets. Parameters: N (int): The number of planets. M (int): The number of hyperspace routes. edges (list of tuples): Each tuple contains two integers u and v indicating a direct route between planet u and planet v. Returns: int: The minimum number of additional hyperspace routes required. Unit Test: from solution import min_additional_routes def test_example_1(): N = 5 M = 3 edges = [(1, 2), (2, 3), (4, 5)] assert min_additional_routes(N, M, edges) == 1 def test_example_2(): N = 4 M = 4 edges = [(1, 2), (2, 3), (3, 4), (4, 1)] assert min_additional_routes(N, M, edges) == 0 def test_single_component(): N = 3 M = 2 edges = [(1, 2), (2, 3)] assert min_additional_routes(N, M, edges) == 0 def test_no_edges(): N = 4 M = 0 edges = [] assert min_additional_routes(N, M, edges) == 3 # 4 planets need 3 edges to connect all def test_two_components(): N = 6 M = 3 edges = [(1, 2), (2, 3), (4, 5)] assert min_additional_routes(N, M, edges) == 2 # Needs two edges to fully connect the graph
answer:def min_additional_routes(N, M, edges): Determine the minimum number of additional hyperspace routes needed to ensure there is a path between every pair of planets. Parameters: N (int): The number of planets. M (int): The number of hyperspace routes. edges (list of tuples): Each tuple contains two integers u and v indicating a direct route between planet u and planet v. Returns: int: The minimum number of additional hyperspace routes required. from collections import defaultdict, deque # Construct the graph as an adjacency list graph = defaultdict(list) for u, v in edges: graph[u].append(v) graph[v].append(u) def bfs(start, visited): queue = deque([start]) visited[start] = True while queue: node = queue.popleft() for neighbor in graph[node]: if not visited[neighbor]: visited[neighbor] = True queue.append(neighbor) # Count the number of connected components visited = [False] * (N + 1) connected_components = 0 for i in range(1, N + 1): if not visited[i]: bfs(i, visited) connected_components += 1 # The number of additional routes needed to connect all components is (connected_components - 1) return connected_components - 1