Appearance
question:**Problem Statement** Alice loves playing games that involve finding patterns in numbers. Today, she found an interesting sequence and wants to determine certain properties about it. The sequence contains N integers, and Alice wants to find the longest subsequence within the given sequence such that all elements in the subsequence are strictly increasing. Given N and the sequence of N integers, help Alice find the length of the longest strictly increasing subsequence. Constraints: - 1 leq N leq 100 - 1 leq a_i leq 100 Input: Input is given from Standard Input in the following format: ``` N a_{0} a_{1} ... a_{N-1} ``` Output: Print a single integer representing the length of the longest strictly increasing subsequence. Examples: Input: ``` 5 2 1 5 3 7 ``` Output: ``` 3 ``` Input: ``` 6 1 3 2 4 3 5 ``` Output: ``` 4 ```
answer:def longest_increasing_subsequence_length(N, sequence): Returns the length of the longest strictly increasing subsequence. Parameters: N (int): The number of elements in the sequence. sequence (list of int): The sequence of integers. Returns: int: The length of the longest strictly increasing subsequence. if N == 0: return 0 # Initialize the LIS values for all indexes lis = [1] * N # Compute optimized LIS values in a bottom up manner for i in range(1, N): for j in range(0, i): if sequence[i] > sequence[j] and lis[i] < lis[j] + 1: lis[i] = lis[j] + 1 # Return the maximum value from the lis array return max(lis)
question:You are working on developing a simple game where players move around on a rectangular grid. Each player is represented by a unique number. Players can move up, down, left, or right, but they cannot move outside the boundaries of the grid. The movement is specified by a series of commands. You are required to write a function that simulates the players' movements and determines the final position of each player on the grid. Input - The first line of the input contains three integers N, M, P (1 ≤ N, M ≤ 10^3, 1 ≤ P ≤ 100), representing the number of rows and columns of the grid, and the number of players. - The next P lines contain two integers each, representing the initial positions of the players on the grid. The positions are given as (row, column), where 1 ≤ row ≤ N and 1 ≤ column ≤ M. - The next P lines contain a string of commands consisting of the characters 'U', 'D', 'L', 'R', representing the movements up, down, left, and right respectively. Each string has a length between 1 and 10^4. Output - Output P lines, where each line contains two integers representing the final position of the corresponding player after executing all their commands. Example Input 5 5 2 1 1 4 3 RRDD UULL Output 3 3 2 1 Note - In the first example, the first player starts at (1, 1) and moves 'RRDD', resulting in the final position (3, 3). - The second player starts at (4, 3) and moves 'UULL', resulting in the final position (2, 1). Boundary Constraints - Players cannot move outside the grid. If a movement command would result in a player moving outside the grid, that movement should be ignored. Your task is to implement the function that takes the initial positions and commands as inputs and outputs the final positions of the players.
answer:def simulate_movements(N, M, P, initial_positions, commands): Simulates the players' movements on the grid and determines their final positions. Args: N: int - number of rows in the grid M: int - number of columns in the grid P: int - number of players initial_positions: list of tuples - initial positions of the players commands: list of strings - commands for each player Returns: list of tuples - final positions of each player final_positions = [] for i in range(P): row, col = initial_positions[i] for command in commands[i]: if command == 'U' and row > 1: row -= 1 elif command == 'D' and row < N: row += 1 elif command == 'L' and col > 1: col -= 1 elif command == 'R' and col < M: col += 1 final_positions.append((row, col)) return final_positions
question:You are given an integer array a of length n, where 1 ≤ a[i] ≤ n for any valid i. You are asked to find the longest contiguous subarray that contains all elements from 1 to k exactly once, where 1 ≤ k ≤ n. If there are multiple valid subarrays, return the one with the smallest starting index. If no such subarray exists, return an empty array. Input The first line contains one integer n (1 ≤ n ≤ 10^5). The second line contains n integers a_1, a_2, ..., a_n. The third line contains one integer k (1 ≤ k ≤ n). Output Print k integers representing the longest contiguous subarray that contains all elements from 1 to k exactly once. If no such subarray exists, print an empty array. Examples Input 8 2 4 1 3 4 2 1 2 4 Output 2 4 1 3 Input 5 5 4 3 2 1 3 Output 3 2 1 Input 6 1 2 2 3 4 5 4 Output (empty array) Note In the first test case, the longest subarray that contains 1, 2, 3, and 4 exactly once is [2, 4, 1, 3]. In the second test case, the subarray that contains 1, 2, and 3 exactly once is [3, 2, 1]. Though it is the only valid subarray, it also happens to be the longest. In the third test case, there is no subarray that contains all elements from 1 to 4 exactly once, so the output is an empty array.
answer:def find_longest_k_subarray(a, n, k): def is_valid_subarray(subarray, k): return sorted(subarray) == list(range(1, k+1)) longest_subarray = [] for i in range(n): for j in range(i + k - 1, n): subarray = a[i:j+1] if is_valid_subarray(subarray, k): if len(subarray) > len(longest_subarray): longest_subarray = subarray break # No need to go further as we need the longest one return longest_subarray # Test cases as per examples print(find_longest_k_subarray([2, 4, 1, 3, 4, 2, 1, 2], 8, 4)) # Expected output: [2, 4, 1, 3] print(find_longest_k_subarray([5, 4, 3, 2, 1], 5, 3)) # Expected output: [3, 2, 1] print(find_longest_k_subarray([1, 2, 2, 3, 4, 5], 6, 4)) # Expected output: []
question:# Hiker's Path Problem A group of hikers is on a trail that can be represented as a 2D grid. Each cell in the grid either has an elevation or is a water body. The hikers can move up, down, left, or right, but cannot move into a cell that contains water or off the grid. The goal is to find the highest elevation they can reach starting from any given starting point on the grid. Write a program that determines the maximum elevation reachable from a starting position on the grid. Input: - The first line contains two integers `n` and `m` (1 ≤ n, m ≤ 100) - the dimensions of the grid. - The next `n` lines each contain `m` integers. Each integer represents the elevation of the cell or `-1` if the cell contains water (elevations are non-negative integers ≤ 10^4). - The last line contains two integers `x` and `y` (0 ≤ x < n, 0 ≤ y < m) - the starting position in the grid. Output: - Print a single integer - the highest elevation reachable from the starting position `(x, y)`. Examples: # Input: ``` 3 3 1 2 3 4 5 6 7 -1 8 1 1 ``` # Output: ``` 8 ``` # Input: ``` 4 5 0 1 2 3 4 5 -1 6 7 8 9 10 11 -1 12 13 14 15 16 17 2 0 ``` # Output: ``` 17 ``` Explanation: In the first example, starting from position (1, 1) with elevation 5, the hiker can move to a maximum elevation of 8 at position (2, 2). In the second example, starting from position (2, 0) with elevation 9, the highest reachable elevation is 17 at position (3, 4).
answer:def max_elevation_reachable(n, m, grid, start_x, start_y): Finds the highest elevation reachable from the starting position on the grid. The grid is represented as a 2D array where -1 represents water and non-negative integers represent elevations. def is_valid_move(x, y): return 0 <= x < n and 0 <= y < m and grid[x][y] != -1 def dfs(x, y): stack = [(x, y)] visited = set(stack) max_elevation = grid[x][y] while stack: cx, cy = stack.pop() current_elevation = grid[cx][cy] max_elevation = max(max_elevation, current_elevation) for dx, dy in [(-1, 0), (1, 0), (0, -1), (0, 1)]: nx, ny = cx + dx, cy + dy if is_valid_move(nx, ny) and (nx, ny) not in visited: stack.append((nx, ny)) visited.add((nx, ny)) return max_elevation if not is_valid_move(start_x, start_y): return -1 return dfs(start_x, start_y)