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question:def is_valid_route(M, N, x, y, movements): Determine if the route for the truck is valid based on the given conditions. Args: M : int : number of streets (grid rows) N : int : number of avenues (grid columns) x : int : starting x-coordinate y : int : starting y-coordinate movements : str : movement directions as string consisting of 'U', 'D', 'L', 'R' Returns: str : "Valid" if the route does not exceed grid boundaries or revisit intersections, else "Invalid" >>> is_valid_route(5, 5, 2, 2, 'UURRDDL') "Valid" >>> is_valid_route(5, 5, 1, 1, 'RRUULL') "Invalid" pass def determine_routes(test_cases): Determine if the routes for multiple test cases are valid. Args: test_cases : List of tuples, each containing: M : int : number of streets (grid rows) N : int : number of avenues (grid columns) routes : List of tuples, each containing: x : int : starting x-coordinate y : int : starting y-coordinate movements : str : movement directions as string consisting of 'U', 'D', 'L', 'R' Returns: List[str] : "Valid" or "Invalid" for each route >>> determine_routes([(5, 5, [(2, 2, 'UURRDDL'), (1, 1, 'RRUULL')])]) ["Valid", "Invalid"] pass def process_input(input_data): Parse input data to extract test cases. Args: input_data : str : raw input data as string Returns: List[tuple] : parsed test cases >>> input_data = "1n5 5n2n3 3 UURRDDLn2 2 RRUULLn" >>> process_input(input_data) [(5, 5, [(2, 2, 'UURRDDL'), (1, 1, 'RRUULL')])] pass

answer:def is_valid_route(M, N, x, y, movements): visited = set() visited.add((x, y)) for move in movements: if move == 'U': x -= 1 elif move == 'D': x += 1 elif move == 'L': y -= 1 elif move == 'R': y += 1 if x < 0 or x >= M or y < 0 or y >= N or (x, y) in visited: return "Invalid" visited.add((x, y)) return "Valid" def determine_routes(test_cases): results = [] for M, N, routes in test_cases: for x, y, movements in routes: results.append(is_valid_route(M, N, x, y, movements)) return results # Function to read input data def process_input(input_data): input_lines = input_data.strip().split('n') T = int(input_lines[0].strip()) index = 1 test_cases = [] for _ in range(T): M, N = map(int, input_lines[index].strip().split()) K = int(input_lines[index+1].strip()) routes = [] for i in range(K): x, y, movements = input_lines[index + 2 + i].strip().split(maxsplit=2) x = int(x) - 1 y = int(y) - 1 routes.append((x, y, movements)) test_cases.append((M, N, routes)) index += 2 + K return test_cases

question:def sum_of_subarray_minimums(T: int, test_cases: List[Tuple[int, List[int]]]) -> List[int]: John loves programming and enjoys solving mathematical problems. One day, he encountered a challenge where he needs to calculate the sum of all subarray minimums for a given array. John seeks your help to solve this problem efficiently. Given an array A of N integers, find the sum of the minimum value of every subarray of A. Parameters: T (int): The number of test cases. test_cases (List[Tuple[int, List[int]]]): List of tuples, each containing an integer N and a list of N integers representing the array. Returns: List[int]: For each test case, the sum of the minimum values of every subarray of A modulo 10^9 + 7. Example: >>> sum_of_subarray_minimums(2, [(3, [1, 2, 3]), (4, [4, 3, 2, 1])]) [10, 20] >>> sum_of_subarray_minimums(1, [(4, [2, 4, 3, 1])]) [20] pass

answer:def sum_of_subarray_minimums(T, test_cases): MOD = 10**9 + 7 def calculate_subarray_mins(arr): n = len(arr) left = [0] * n right = [0] * n stack = [] # Finding previous less element for i in range(n): while stack and arr[stack[-1]] >= arr[i]: stack.pop() if stack: left[i] = stack[-1] else: left[i] = -1 stack.append(i) stack = [] # Finding next less element for i in range(n - 1, -1, -1): while stack and arr[stack[-1]] > arr[i]: stack.pop() if stack: right[i] = stack[-1] else: right[i] = n stack.append(i) result = 0 for i in range(n): result += arr[i] * (i - left[i]) * (right[i] - i) result %= MOD return result results = [] for t in range(T): N = test_cases[t][0] A = test_cases[t][1] results.append(calculate_subarray_mins(A)) return results

question:def is_valid_parentheses(s: str) -> bool: Determines whether an input string of parentheses is valid. A string is considered valid if: 1. Every open parenthesis '(' has a corresponding close parenthesis ')'. 2. Open parentheses must be closed in the correct order. Args: s (str): The input string containing only '(' and ')'. Returns: bool: True if the string is valid, False otherwise. Examples: >>> is_valid_parentheses("()") True >>> is_valid_parentheses("(())") True >>> is_valid_parentheses("()()") True >>> is_valid_parentheses("(()())()") True >>> is_valid_parentheses(")(") False >>> is_valid_parentheses("())") False >>> is_valid_parentheses("()(") False >>> is_valid_parentheses("(") False >>> is_valid_parentheses(")") False >>> is_valid_parentheses("") True

answer:def is_valid_parentheses(s): Determines whether an input string of parentheses is valid. Args: s (str): The input string containing only '(' and ')'. Returns: bool: True if the string is valid, False otherwise. stack = [] for char in s: if char == '(': stack.append(char) elif char == ')': if not stack: return False stack.pop() return not stack

question:def smallest_string_by_reversing_substring(t: int, test_cases: List[str]) -> List[str]: For each input string, return the lexicographically smallest string by reversing exactly one substring. Parameters: t (int): number of test cases. test_cases (list of str): list of strings to process. Returns: list of str: list of results for each test case. >>> smallest_string_by_reversing_substring(3, ["acb", "aab", "bab"]) ["abc", "aab", "abb"] >>> smallest_string_by_reversing_substring(1, ["aaa"]) ["aaa"]

answer:def smallest_string_by_reversing_substring(t, test_cases): For each input string, return the lexicographically smallest string by reversing exactly one substring. Parameters: t (int): number of test cases. test_cases (list of str): list of strings to process. Returns: list of str: list of results for each test case. results = [] for s in test_cases: n = len(s) smallest = s for i in range(n): for j in range(i+1, n+1): reversed_substring = s[:i] + s[i:j][::-1] + s[j:] if reversed_substring < smallest: smallest = reversed_substring results.append(smallest) return results