answer:def submatrix_sum(matrix, upper_left, lower_right): Returns the sum of all elements in the specified submatrix. Parameters: - matrix: list of lists of integers representing the n x m matrix. - upper_left: tuple of integers representing the upper-left corner of submatrix (row, column). - lower_right: tuple of integers representing the lower-right corner of submatrix (row, column). Returns: - Sum of all elements in the specified submatrix. sum_elements = 0 start_row, start_col = upper_left end_row, end_col = lower_right for i in range(start_row, end_row + 1): for j in range(start_col, end_col + 1): sum_elements += matrix[i][j] return sum_elements

answer:def can_schedule_games(N, M, restricted_pairs): Determines whether it is possible to create a valid schedule given the limitations. Parameters: N (int): The number of players. M (int): The number of restricted pairs. restricted_pairs (list of tuples): List of pairs which indicate restricted matches. Returns: str: "YES" if a valid schedule can be created, otherwise "NO". from collections import defaultdict, deque # Create a graph adjacency list graph = defaultdict(list) for u, v in restricted_pairs: graph[u].append(v) graph[v].append(u) # Use coloring to determine if the graph is bipartite. color = {} def bfs(start): queue = deque([start]) color[start] = 0 while queue: node = queue.popleft() current_color = color[node] for neighbor in graph[node]: if neighbor not in color: color[neighbor] = 1 - current_color queue.append(neighbor) elif color[neighbor] == current_color: return False return True # Check for each component in the graph for player in range(1, N + 1): if player not in color: if not bfs(player): return "NO" return "YES"

answer:def minimum_remaining_element(arr): Returns the minimum possible value of the remaining element after performing n-1 operations. return sum(arr)

answer:def process_commands(commands): Processes a list of commands on a grid and returns the state of light bulbs for each query command. Parameters: commands (List[str]): List of command strings in the format 'L x y', 'T x y', 'Q x y' Returns: List[str]: List of results for each query in the order they appeared, each one being "ON" or "OFF" grid = {} results = [] for command in commands: parts = command.split() cmd = parts[0] x, y = int(parts[1]), int(parts[2]) key = (x, y) if cmd == 'L': grid[key] = True elif cmd == 'T': if key in grid and grid[key] == True: grid[key] = False else: grid[key] = True elif cmd == 'Q': if key in grid and grid[key] == True: results.append("ON") else: results.append("OFF") return results