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question:You are organizing a competition for which you need to arrange several games in such a way that there is no overlapping. You will be given a list of games, each with a start time and an end time. A game can be described as a pair (start, end), indicating that the game starts at `start` and ends at `end`. Two games are considered non-overlapping if for any two distinct games (a, b) and (c, d), either b <= c or d <= a. Your task is to find the maximum number of non-overlapping games that you can schedule. Input: - The first line contains an integer `n` (1 le n le 10^5), the number of games. - The next `n` lines each contain two integers `start` and `end` (0 le start < end le 10^9), the start and end times of the games. Output: - A single integer, the maximum number of non-overlapping games you can schedule. Example: ``` Input: 3 1 2 2 3 3 4 Output: 3 ``` ``` Input: 4 1 3 2 4 3 5 0 6 Output: 2 ``` Note: - In the first example, all games can be scheduled without overlapping. - In the second example, the optimal way to schedule the games is to select the games (1,3) and (3,5) or (2,4) and (0,6).
answer:def max_non_overlapping_games(n, games): Given a number of games with their start and end times, this function returns the maximum number of non-overlapping games. Parameters: n (int): The number of games. games (list of tuples): Each tuple (start, end) represents a game's start and end time. Returns: int: The maximum number of non-overlapping games that can be scheduled. # Sort the games based on their end times. games.sort(key=lambda x: x[1]) # Initialize the count of non-overlapping games max_games = 0 last_end_time = 0 # Iterate through the sorted games and choose the non-overlapping ones for start, end in games: if start >= last_end_time: max_games += 1 last_end_time = end return max_games
question:You are given a list of integers. Your task is to determine if the list can be partitioned into two non-empty subsets such that the sum of the elements in both subsets is equal. If such a partition is possible, output "YES". Otherwise, output "NO". # Input The first line of input contains a single integer T (1 leq T leq 10) which denotes the number of test cases. The first line of each test case contains an integer n (2 leq n leq 1000) — the number of elements in the list. The second line of each test case contains n space-separated integers a_1, a_2, ..., a_n (1 leq a_i leq 10000) — the elements of the list. # Output For each test case, print "YES" if the list can be partitioned into two non-empty subsets with equal sum, otherwise print "NO". # Example Input ``` 2 4 1 5 11 5 3 1 1 3 ``` Output ``` YES NO ``` # Explanation In the first test case, the list `[1, 5, 11, 5]` can be partitioned into `[1, 5, 5]` and `[11]`, both subsets having equal sum of 11. In the second test case, the list `[1, 1, 3]` cannot be partitioned into two subsets with equal sum.
answer:def can_partition(nums): total_sum = sum(nums) if total_sum % 2 != 0: return "NO" target = total_sum // 2 n = len(nums) dp = [False] * (target + 1) dp[0] = True for num in nums: for t in range(target, num - 1, -1): dp[t] = dp[t] or dp[t - num] return "YES" if dp[target] else "NO" def solve_partition_problem(test_cases): results = [] for nums in test_cases: results.append(can_partition(nums)) return results
question:Alice has a collection of paintings displayed in an art gallery. The paintings are arranged in a single row, and each painting is given a beauty value represented by an integer array p. Alice wants to select exactly k consecutive paintings in such a way that the sum of their beauty values is maximized. You are given an integer n (1 le n le 10^5) representing the number of paintings and an integer k (1 le k le n) representing the number of consecutive paintings Alice must select. You are also given an integer array p of length n, where p[i] represents the beauty value of the i-th painting. Find the maximum sum of beauty values of any k consecutive paintings. The first line contains the integer n and the integer k. The second line contains the integer array p, where p[i] ( 1 le p[i] le 10^9 ) is the beauty value of the i-th painting. # Input - The first line of input contains two integers n and k. - The second line contains n integers representing the array p. # Output Print a single integer representing the maximum sum of beauty values of any k consecutive paintings. Example Input: ``` 5 2 1 2 3 4 5 ``` Output: ``` 9 ``` Explanation: - The maximum sum is obtained by selecting the last two consecutive paintings with beauty values 4 and 5, their sum is 9.
answer:def max_beauty_sum(n, k, p): Finds the maximum sum of beauty values of any k consecutive paintings. Parameters: n (int): The number of paintings. k (int): The number of consecutive paintings to select. p (list): List of integers representing the beauty value of each painting. Returns: int: The maximum sum of beauty values of any k consecutive paintings. current_sum = sum(p[:k]) # Sum of the first k elements max_sum = current_sum # Slide the window across the array for i in range(1, n - k + 1): current_sum = current_sum - p[i - 1] + p[i + k - 1] if current_sum > max_sum: max_sum = current_sum return max_sum
question:You are given an n-digit integer and k transformations. The transformation consists of choosing a digit in the integer and swapping it with any other digit of the integer to form a new integer. The goal is to obtain the smallest possible integer after exactly k transformations. If multiple smallest integers can be obtained, choose the lexicographically smallest one. The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 100) - the number of test cases. Each test case consists of a single line containing two integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ 100), followed by a string s of n digits representing the integer. For each test case, print the smallest possible integer that can be obtained after exactly k transformations. # Example Input 3 5 1 54321 5 2 43215 2 0 21 Output 14325 12345 21 In the first test case, you can swap '5' with any other digit to get the smallest possible integer '14325'. In the second test case, you need two transformations to obtain the smallest possible integer '12345'. In the third test case, no transformations are needed.
answer:def smallest_integer_after_transformations(n, k, s): Returns the smallest possible integer after k transformations. Parameters: n (int): length of the integer string k (int): number of transformations s (str): the integer in string format Returns: str: the smallest possible integer after k transformations s = list(s) for i in range(n): if k == 0: break min_digit = s[i] min_index = i # Find the smallest digit in the remaining array for j in range(i + 1, n): if s[j] < min_digit: min_digit = s[j] min_index = j # If the smallest digit is not in the current position if min_index != i: s[i], s[min_index] = s[min_index], s[i] k -= 1 return ''.join(s)