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question:Alice is a hedge maze designer. She is currently working on a rectangular maze represented as a grid with `n` rows and `m` columns. Each cell in the grid is either empty (represented by '.') or contains a hedge (represented by '#'). Alice starts in the top-left cell of the maze and wants to reach the bottom-right cell. She can move up, down, left, or right, but not diagonally. Alice wonders if it is possible to drape a single uninterrupted path from the top-left to the bottom-right cell that only passes through empty cells. If there are multiple ways to reach the bottom-right cell, Alice is only interested if there exists such a path that covers all the empty cells in the maze exactly once. Write a program to determine if it is possible to create such a path. If it is possible, output "YES", otherwise output "NO". Input The first line contains two integers `n` and `m` (1 ≤ n, m ≤ 10) which are the dimensions of the maze. Each of the next `n` lines contains `m` characters (`.` or `#`) describing the maze. Output Output "YES" if there exists a path from the top-left to the bottom-right cell that passes through all empty cells exactly once. Otherwise, output "NO". Examples Input 3 4 .#.. ..#. #..# Output NO Input 2 2 .# #. Output NO Input 3 3 ... .#. ... Output YES
answer:def is_possible_single_path(n, m, maze): from collections import deque # Valid move directions (up, down, left, right) directions = [(-1, 0), (1, 0), (0, -1), (0, 1)] def is_valid(x, y): return 0 <= x < n and 0 <= y < m and maze[x][y] == '.' def bfs_and_count_empty_cells(start_x, start_y): queue = deque([(start_x, start_y)]) visited = set([(start_x, start_y)]) empty_cells_count = 1 while queue: x, y = queue.popleft() for dx, dy in directions: nx, ny = x + dx, y + dy if is_valid(nx, ny) and (nx, ny) not in visited: visited.add((nx, ny)) queue.append((nx, ny)) empty_cells_count += 1 return empty_cells_count, visited def count_total_empty_cells(): empty_count = sum(row.count('.') for row in maze) return empty_count # Check start and end cells if maze[0][0] == '#' or maze[n-1][m-1] == '#': return "NO" total_empty_cells = count_total_empty_cells() if total_empty_cells == 0: return "NO" cells_counted, visited_cells = bfs_and_count_empty_cells(0, 0) if cells_counted == total_empty_cells and (n-1, m-1) in visited_cells: return "YES" else: return "NO"
question:A group of botanists is studying different species of plants in a forest. They've tagged n plants and are recording their heights. They have noticed a pattern where some plants grow significantly slower than others. All the botanists want to analyze this data and find out the longest subsequence of plants that are growing in a strictly increasing height order. They need an algorithm to do this efficiently. Write a program to help the botanists find the length of the longest increasing subsequence of plant heights. Input The first line of input contains a single integer n, the number of plants being studied. The next line contains n space-separated integers representing the heights of the plants. Output Output a single integer which is the length of the longest increasing subsequence of plant heights. Constraints 1 <= n <= 1000 1 <= height <= 10000 for each plant Example Input: 6 10 22 9 33 21 50 Output: 4 Explanation: The longest increasing subsequence is 10, 22, 33, 50.
answer:def longest_increasing_subsequence_length(heights): This function takes a list of plant heights and returns the length of the longest increasing subsequence. if not heights: return 0 n = len(heights) lis = [1] * n # Initialize LIS values for all indexes # Compute optimized LIS values in bottom-up manner for i in range(1, n): for j in range(i): if heights[i] > heights[j] and lis[i] < lis[j] + 1: lis[i] = lis[j] + 1 # Find maximum of all LIS values return max(lis)
question:You are given a binary tree. Your task is to find the level order traversal of this tree, but each level should be printed from right to left. Input The input will contain multiple test cases. The first line will have an integer T, the number of test cases. For each test case, the first line will have an integer N, the number of nodes in the tree. The next line will have N space-separated integers representing the nodes of the tree in level order traversal where -1 denotes a null node. Output For each test case, output the level order traversal from right to left as an array of arrays. Each array will represent a level in the tree. Constraints 1 ≤ T ≤ 10 1 ≤ N ≤ 100 -1000 ≤ Tree Nodes ≤ 1000 -1 denotes a null node for tree representation Example Input: 2 7 1 2 3 -1 5 -1 4 3 10 20 -1 30 Output: [[1], [3, 2], [4, 5]] [[10], [20], [30]] Explanation In the first example, the level order traversal from right to left will be [[1], [3, 2], [4, 5]].
answer:from collections import deque class TreeNode: def __init__(self, x): self.val = x self.left = None self.right = None def build_tree(nodes): if not nodes or nodes[0] == -1: return None root = TreeNode(nodes[0]) queue = deque([root]) i = 1 n = len(nodes) while queue and i < n: current = queue.popleft() if nodes[i] != -1: current.left = TreeNode(nodes[i]) queue.append(current.left) i += 1 if i < n and nodes[i] != -1: current.right = TreeNode(nodes[i]) queue.append(current.right) i += 1 return root def level_order_right_to_left(root): if not root: return [] result = [] queue = deque([root]) while queue: level_size = len(queue) level_nodes = [] for _ in range(level_size): node = queue.popleft() level_nodes.append(node.val) if node.left: queue.append(node.left) if node.right: queue.append(node.right) result.append(level_nodes[::-1]) return result def process_test_cases(test_cases): results = [] for case in test_cases: n = case[0] nodes = case[1] root = build_tree(nodes) result = level_order_right_to_left(root) results.append(result) return results
question:Write a function `find_special_number_in_array` that takes an array of integers `arr` and returns the largest number in the array that is equal to the sum of three distinct elements of the array. If no such number exists, return -1. # Function Signature: ```python def find_special_number_in_array(arr: List[int]) -> int: pass ``` # Input: - An array `arr` of length (n) (1 ≤ ( n ) ≤ 50). # Output: - An integer representing the largest number in the array that is equal to the sum of three distinct elements, or -1 if no such number exists. # Example: ```python arr = [2, 4, 3, 6, 8, 1] Output: 8 ``` Explanation: - In the array [2, 4, 3, 6, 8, 1], the largest number that can be expressed as the sum of three distinct elements is `8` (2 + 3 + 3 = 8). # Example 2: ```python arr = [1, 1, 1, 1] Output: -1 ``` Explanation: - In the array [1, 1, 1, 1], no number can be expressed as the sum of three distinct elements.
answer:from typing import List def find_special_number_in_array(arr: List[int]) -> int: n = len(arr) arr_set = set(arr) max_special_number = -1 for i in range(n): for j in range(i + 1, n): for k in range(j + 1, n): sum_three = arr[i] + arr[j] + arr[k] if sum_three in arr_set: max_special_number = max(max_special_number, sum_three) return max_special_number