answer:def max_beauty(n, beauties): Returns the maximum sum of the beauty values of any contiguous subsegment of the parade route, and the length of the subsegment that produces this sum. If the maximum sum is zero, return the shortest length of the subsegment producing this sum. Parameters: n (int): The number of segments in the parade route. beauties (list of int): The beauty values of the segments. Returns: tuple of (int, int): The maximum sum and the length of the subsegment. max_sum = -float('inf') current_sum = 0 start_index = 0 min_length = float('inf') best_start = 0 best_end = 0 for end, value in enumerate(beauties): if current_sum <= 0: start_index = end current_sum = value else: current_sum += value if current_sum > max_sum or (current_sum == max_sum and (end - start_index + 1 < min_length)): max_sum = current_sum min_length = end - start_index + 1 best_start = start_index best_end = end if max_sum == 0: # find the shortest subsegment with zero sum min_zero_length = float('inf') for start in range(n): current_sum = 0 for end in range(start, n): current_sum += beauties[end] if current_sum == 0 and (end - start + 1 < min_zero_length): min_zero_length = end - start + 1 return (0, min_zero_length) return (max_sum, min_length)

answer:def max_subarray_sum(nums): Finds the maximum possible sum of elements in any contiguous subarray of the given array nums. If the array contains only negative numbers, returns the single largest number from it. Uses Kadane's algorithm. if not nums: return 0 max_current = max_global = nums[0] for num in nums[1:]: max_current = max(num, max_current + num) if max_current > max_global: max_global = max_current return max_global

answer:def max_connected_components(M, N, grid): Determines the maximum number of connected components of colored cells in a grid after performing optimal toggle operations. Args: M : int : number of rows in the grid N : int : number of columns in the grid grid : list of list of str : the initial configuration of the grid Returns: int : the maximum number of connected components # The maximum number of connected components is achieved by coloring each cell such that # no two adjacent cells are both colored. max_components = (M * N + 1) // 2 return max_components

answer:from collections import deque def min_moves_to_reach_end(n, board): directions = [(1, 0), (0, 1), (-1, 0), (0, -1)] visited = [[False] * n for _ in range(n)] queue = deque([(0, 0, 0)]) # (row, col, distance) visited[0][0] = True while queue: r, c, dist = queue.popleft() if (r, c) == (n-1, n-1): return dist for dr, dc in directions: nr, nc = r + dr, c + dc if 0 <= nr < n and 0 <= nc < n and not visited[nr][nc] and board[nr][nc] == '.': visited[nr][nc] = True queue.append((nr, nc, dist + 1)) return -1 # If reaching (n-1, n-1) is not possible