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question:def total_length_of_roads_to_be_removed(n: int, m: int, roads: List[Tuple[int, int, int]], q: int, removals: List[Tuple[int, int]]) -> int: Calculate the total length of the existing roads that will be removed to improve transportation efficiency among a list of cities and roads. Parameters: n (int): number of cities m (int): number of roads roads (List[Tuple[int, int, int]]): list of roads, where each road connects two cities and has a specific length q (int): number of existing roads to be removed removals (List[Tuple[int, int]]): list of roads to be removed, where each road is represented by the two cities it connects Returns: int: the total length of the roads to be removed Example: n = 5 m = 6 roads = [ (1, 2, 4), (1, 3, 3), (2, 4, 2), (3, 4, 1), (3, 5, 7), (4, 5, 6) ] q = 3 removals = [ (1, 3), (3, 4), (4, 5) ] total_length_of_roads_to_be_removed(n, m, roads, q, removals) # Should return 10 import pytest from typing import List, Tuple def test_example_case(): n = 5 m = 6 roads = [ (1, 2, 4), (1, 3, 3), (2, 4, 2), (3, 4, 1), (3, 5, 7), (4, 5, 6) ] q = 3 removals = [ (1, 3), (3, 4), (4, 5) ] assert total_length_of_roads_to_be_removed(n, m, roads, q, removals) == 10 def test_no_removals(): n = 5 m = 6 roads = [ (1, 2, 4), (1, 3, 3), (2, 4, 2), (3, 4, 1), (3, 5, 7), (4, 5, 6) ] q = 0 removals = [] assert total_length_of_roads_to_be_removed(n, m, roads, q, removals) == 0 def test_all_removals(): n = 3 m = 3 roads = [ (1, 2, 3), (2, 3, 4), (1, 3, 5) ] q = 3 removals = [ (1, 2), (2, 3), (1, 3) ] assert total_length_of_roads_to_be_removed(n, m, roads, q, removals) == 12 def test_duplicate_roads(): n = 5 m = 6 roads = [ (1, 2, 4), (1, 3, 3), (2, 4, 2), (3, 4, 1), (3, 5, 7), (4, 5, 6) ] q = 6 removals = [ (1, 3), (3, 4), (4, 5), (1, 3), (3, 4), (4, 5) ] assert total_length_of_roads_to_be_removed(n, m, roads, q, removals) == 20

answer:def total_length_of_roads_to_be_removed(n, m, roads, q, removals): # Create a dictionary to store the roads and their lengths road_dict = {} for u, v, w in roads: road_dict[(u, v)] = w road_dict[(v, u)] = w # Calculate the total length of the roads to be removed total_length_removed = 0 for a, b in removals: total_length_removed += road_dict.get((a, b), 0) return total_length_removed # Example usage: n = 5 m = 6 roads = [ (1, 2, 4), (1, 3, 3), (2, 4, 2), (3, 4, 1), (3, 5, 7), (4, 5, 6) ] q = 3 removals = [ (1, 3), (3, 4), (4, 5) ] print(total_length_of_roads_to_be_removed(n, m, roads, q, removals)) # Output should be 10

question:from typing import List def min_diff_to_target(n: int, target: int, skill_levels: List[int]) -> int: Determine the minimum possible absolute difference between the target value and the sum of the skill levels within any team formed. >>> min_diff_to_target(5, 10, [1, 2, 3, 4, 5]) 0 >>> min_diff_to_target(6, 20, [5, 5, 5, 5, 5, 5]) 5 # Test Cases def test_exact_match(): assert min_diff_to_target(5, 10, [1, 2, 3, 4, 5]) == 0 def test_no_exact_match(): assert min_diff_to_target(6, 20, [5, 5, 5, 5, 5, 5]) == 5 def test_large_numbers(): assert min_diff_to_target(6, 10000, [5000, 5000, 5000, 5000, 5000, 5000]) == 5000 def test_all_same(): assert min_diff_to_target(6, 15, [5, 5, 5, 5, 5, 5]) == 0 def test_high_variety(): assert min_diff_to_target(7, 17, [1, 2, 3, 4, 5, 6, 7]) == 0 def test_smallest_possible_input(): assert min_diff_to_target(3, 10, [1, 2, 8]) == 1 def test_large_skills(): assert min_diff_to_target(4, 12000, [3000, 4000, 3500, 4500]) == 0

answer:from itertools import combinations def min_diff_to_target(n, target, skill_levels): min_diff = float('inf') for team in combinations(skill_levels, 3): team_sum = sum(team) diff = abs(team_sum - target) min_diff = min(min_diff, diff) return min_diff

question:from typing import List def minimal_number_of_rounds(n: int, a: List[int]) -> int: Determine the minimal number of rounds needed for all players to have played at least one card. Args: n (int): The number of players. a (List[int]): List where a[i] indicates the number of rounds player i must skip after playing a card. Returns: int: The minimal number of rounds required for all players to have played at least one card. ***Examples*** >>> minimal_number_of_rounds(3, [2, 1, 2]) 3 >>> minimal_number_of_rounds(4, [1, 1, 1, 1]) 2 >>> minimal_number_of_rounds(4, [3, 4, 2, 5]) 61 >>> minimal_number_of_rounds(5, [3, 3, 3, 3, 3]) 4 >>> minimal_number_of_rounds(3, [1000, 1000, 1000]) 1001

answer:import math from functools import reduce def minimal_number_of_rounds(n, a): Return the minimal number of rounds required for all players to have played at least one card. Args: n (int): Number of players. a (list of int): List of integers where a[i] indicates the number of rounds player i must skip after playing a card. Returns: int: The minimal number of rounds required. def lcm(x, y): return x * y // math.gcd(x, y) return reduce(lcm, a) + 1 # Example usage: # n = 3 # a = [2, 1, 2] # print(minimal_number_of_rounds(n, a)) # Should output 3

question:def find_unsorted_subarray(arr): Finds the smallest length subarray that, when sorted, makes the entire array sorted. Parameters: arr (list): List of integers Returns: tuple: (l, r) - the zero-based indices of the left and right boundaries Examples: >>> find_unsorted_subarray([1, 2, 3, 4, 5]) (-1, -1) >>> find_unsorted_subarray([1, 3, 2, 2, 2]) (1, 4) >>> find_unsorted_subarray([1, 2, 3, 5, 4]) (3, 4) >>> find_unsorted_subarray([1, 5, 3, 4, 6]) (1, 3) >>> find_unsorted_subarray([6, 5, 4, 3, 2, 1]) (0, 5) >>> find_unsorted_subarray([1, 3, 5, 2, 4, 6, 7, 8, 9, 10]) (1, 4) >>> find_unsorted_subarray([1, 2, 8, 4, 5, 6, 7, 3, 9, 10]) (2, 7)

answer:def find_unsorted_subarray(arr): Finds the smallest length subarray that, when sorted, makes the entire array sorted. Parameters: arr (list): List of integers Returns: tuple: (l, r) - the zero-based indices of the left and right boundaries n = len(arr) if n <= 1: # An array with 0 or 1 element is always sorted return -1, -1 # Step 1: Find the first element which is out of order from the left left = 0 while left < n - 1 and arr[left] <= arr[left + 1]: left += 1 if left == n - 1: # The array is already sorted return -1, -1 # Step 2: Find the first element which is out of order from the right right = n - 1 while right > 0 and arr[right] >= arr[right - 1]: right -= 1 # Step 3: Find the min and max in the unsorted subarray min_unsorted = min(arr[left:right+1]) max_unsorted = max(arr[left:right+1]) # Step 4: Extend the left boundary to include any elements greater than the min_unsorted while left > 0 and arr[left - 1] > min_unsorted: left -= 1 # Step 5: Extend the right boundary to include any elements less than the max_unsorted while right < n - 1 and arr[right + 1] < max_unsorted: right += 1 return (left, right)