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question:Jane is planning her schedule for the next n days. She has a list of m tasks that she needs to complete during this period, and each task i has a specific day si on which she can start working on the task and a deadline di by which the task must be completed. Each task requires a certain number of consecutive days ti to complete. Jane can only work on one task each day, and she can only start working on a task on or after its start day and must finish it on or before its deadline. Write a program to help Jane determine if it's possible to complete all her tasks within the given constraints. Input The first line contains two integers n and m (1 ≤ n, m ≤ 100) — the number of days Jane has and the number of tasks. Each of the next m lines contains three integers si, di, ti (1 ≤ si ≤ di ≤ n, 1 ≤ ti ≤ 50) — the start day, deadline day, and the number of days required to complete the i-th task, respectively. Output Output "YES" if Jane can complete all the tasks within the given constraints. Otherwise, output "NO". Examples Input 10 3 1 5 3 2 9 4 6 10 2 Output YES Input 5 2 1 3 3 2 5 3 Output NO
answer:def can_complete_tasks(n, m, tasks): Determines if Jane can complete all tasks within the given period and constraints. :param n: Number of days available :param m: Number of tasks :param tasks: List of tuples where each tuple is (si, di, ti) representing start day, deadline day, and number of days required to complete the task :return: "YES" if all tasks can be completed, otherwise "NO" # Sort tasks based on the deadline day di tasks.sort(key=lambda x: x[1]) days = [0] * (n + 1) # Track the schedule on each day for si, di, ti in tasks: # Try to schedule the task between its si and di days_needed = ti for day in range(si, di + 1): if days[day] == 0: days[day] = 1 days_needed -= 1 if days_needed == 0: break # If unable to find the required number of days, return NO if days_needed > 0: return "NO" return "YES"
question:A tic-tac-toe game is represented by a 3x3 grid of characters, 'X', 'O', or '.', where 'X' and 'O' represent the marks placed by two players, and '.' represents an empty cell. Write a program to determine the state of the game by printing: - "X wins" if player 'X' has won, - "O wins" if player 'O' has won, - "Draw" if the board is full and no player has won, - "Game continues" if the board is not full and no player has won yet. A player wins if they have three of their marks in a horizontal, vertical, or diagonal row. # Constraints The input grid will always be a 3x3 character grid with 'X', 'O', and '.' only. # Input The input is given as three lines, each containing three characters, representing each row of the tic-tac-toe board. ``` r1c1 r1c2 r1c3 r2c1 r2c2 r2c3 r3c1 r3c2 r3c3 ``` Where `ri` and `ci` denote row and column indices of the cell respectively. # Output Print one of the following four strings: - "X wins" - "O wins" - "Draw" - "Game continues" # Examples Example 1 Input ``` X.O OXX OXO ``` Output ``` X wins ``` Example 2 Input ``` XOX OXO XOX ``` Output ``` Draw ``` Example 3 Input ``` XOX OO. XOX ``` Output ``` Game continues ```
answer:def check_tic_tac_toe(board): Determines the state of a tic-tac-toe game. Args: board (list of list of str): 3x3 tic-tac-toe board. Returns: str: "X wins", "O wins", "Draw", or "Game continues". def check_winner(c): # Check horizontal for row in board: if row == [c] * 3: return True # Check vertical for col in range(3): if all(board[row][col] == c for row in range(3)): return True # Check diagonal if all(board[i][i] == c for i in range(3)) or all(board[i][2-i] == c for i in range(3)): return True return False if check_winner('X'): return "X wins" if check_winner('O'): return "O wins" for row in board: if '.' in row: return "Game continues" return "Draw"
question:A social media platform has a feature where users can create and attend events. The system keeps track of the list of events each user attends. Due to a system update, some event attendance records were corrupted. The platform's admin wants to determine if each user's attendance history follows a chronological order based on the event IDs. More specifically, each event has a unique positive integer identifier, and the events must be attended in strictly increasing order by each user. If a user attends events with IDs 3, 5, and 7, they must appear in exactly this order in the records. Given a list of attendance records consisting of pairs of user IDs and event IDs, determine if the records for each user respect the chronological order of event IDs. Input The first line of the input contains an integer n (1 ≤ n ≤ 105) — the number of attendance records. Each of the following n lines contains two integers separated by a space: u and e (1 ≤ u ≤ 105; 1 ≤ e ≤ 105), indicating that user u attended event e. Output A single line of the output should contain "VALID" if all users' attendance records respect the chronological order of event IDs, and "INVALID" otherwise. Examples Input 3 1 3 1 5 1 7 Output VALID Input 4 1 3 1 7 1 5 2 1 Output INVALID Input 5 1 3 2 1 2 2 1 4 1 5 Output VALID
answer:def validate_event_attendance(records): from collections import defaultdict user_events = defaultdict(list) for u, e in records: user_events[u].append(e) for events in user_events.values(): if events != sorted(events): return "INVALID" return "VALID"
question:Given a list of N integers, determine if there exists a subsequence of these integers whose sum is equal to a given number S. A subsequence is defined as a sequence derived from the original list by deleting some or none of the elements without changing the order of the remaining elements. Constraints - All values in input are integers. - 1 leq N leq 20 - -10^5 leq each integer in the list leq 10^5 - -10^6 leq S leq 10^6 Input Input is given from Standard Input in the following format: N S a_1 a_2 ... a_N Output Print "Yes" if such a subsequence exists, otherwise print "No". Examples Input 5 9 1 2 3 4 5 Output Yes Input 3 10 1 2 3 Output No Input 4 0 -1 1 -2 2 Output Yes
answer:def subsequence_sum_exists(N, S, arr): Determines if there exists a subsequence of the list whose sum is equal to S. Args: - N: integer, the number of elements in the list - S: integer, the target sum - arr: list of N integers Returns: - 'Yes' if such a subsequence exists, otherwise 'No' from itertools import combinations for i in range(N+1): for comb in combinations(arr, i): if sum(comb) == S: return "Yes" return "No" # Example usage: # print(subsequence_sum_exists(5, 9, [1, 2, 3, 4, 5])) # Output: Yes # print(subsequence_sum_exists(3, 10, [1, 2, 3])) # Output: No # print(subsequence_sum_exists(4, 0, [-1, 1, -2, 2])) # Output: Yes