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question:A palindrome is a word or phrase that reads the same backward as forward. For example, "radar" is a palindrome because it reads the same from left to right and from right to left. Write a function that takes a string as input and returns "YES" if the string is a palindrome and "NO" otherwise. The input string consists of lowercase Latin letters. The string is not empty and its length does not exceed 100 symbols. Function signature: `def is_palindrome(s: str) -> str:` Examples: - `is_palindrome("radar")` should return "YES" - `is_palindrome("hello")` should return "NO"
answer:def is_palindrome(s: str) -> str: Returns 'YES' if the string is a palindrome and 'NO' otherwise. if s == s[::-1]: return "YES" return "NO"
question:The company you work for has decided to host an internal hackathon to boost employee engagement and innovation. As part of the competition, one of the challenges presented is to solve the "magic square" problem. A "magic square" is a 3x3 grid filled with distinct integers from 1 to 9 such that the sum of the numbers in each row, column, and both main diagonals are the same. Given a partially filled 3x3 grid, complete the grid with distinct integers from 1 to 9 such that it forms a magic square. If it is possible to complete the grid to form a magic square, print the completed grid. If there is no possible way to complete the grid into a magic square, print "Impossible". The input consists of nine integers, each representing a cell in the 3x3 grid. The integer 0 represents an empty cell. The integers are provided in a single line with spaces separating them, read in a row-wise manner. Sample Input 1: 8 1 6 3 5 0 4 9 0 Sample Output 1: 8 1 6 3 5 7 4 9 2 Sample Input 2: 5 3 4 1 0 0 0 0 0 Sample Output 2: Impossible Ensure to follow these steps for solving the problem: 1. Check the partially filled grid for any constraints that make it impossible to complete. 2. Try to determine the empty cells and find the appropriate integers to fill in while maintaining the magic square property. 3. Validate whether the completed grid fulfills the magic square conditions.
answer:def is_magic_square(grid): Check if a 3x3 grid is a magic square. s = sum(grid[0]) for i in range(3): if sum(grid[i]) != s or sum(grid[j][i] for j in range(3)) != s: return False if sum(grid[i][i] for i in range(3)) != s or sum(grid[i][2-i] for i in range(3)) != s: return False return True def find_magic_square(grid): from itertools import permutations all_numbers = set(range(1, 10)) filled_numbers_set = set() for row in grid: for num in row: if num != 0: filled_numbers_set.add(num) empty_positions = [(i, j) for i in range(3) for j in range(3) if grid[i][j] == 0] available_numbers = list(all_numbers - filled_numbers_set) for perm in permutations(available_numbers): for idx, (i, j) in enumerate(empty_positions): grid[i][j] = perm[idx] if is_magic_square(grid): return grid for i, j in empty_positions: grid[i][j] = 0 return "Impossible" def solve_magic_square(input): nums = list(map(int, input.split())) grid = [nums[i*3:(i+1)*3] for i in range(3)] result = find_magic_square(grid) if result == "Impossible": print("Impossible") else: for row in result: print(" ".join(map(str, row))) # To call the function you would need to replace input_string with actual input # input_string = "8 1 6 3 5 0 4 9 0" # solve_magic_square(input_string)
question:You are given an array consisting of non-negative integers. Your task is to modify the array as follows: replace each element with the greatest element among the elements to its right, and replace the last element with -1. Write a function `replaceElements(arr)` that takes an array `arr` and performs the above modifications. The function should update the array in-place and does not need to return anything. **Example:** ``` Input: arr = [17, 18, 5, 4, 6, 1] Output: arr = [18, 6, 6, 6, 1, -1] ``` Constraints: - `arr` will have at least one element. - The elements of `arr` are non-negative. - `arr` can have up to 10,000 elements.
answer:def replaceElements(arr): Modify the array so that each element is replaced by the greatest element among the elements to its right, and the last element is replaced with -1. # Edge case: if array is empty or has one element if not arr: return if len(arr) == 1: arr[0] = -1 return n = len(arr) max_right = -1 for i in range(n-1, -1, -1): new_val = max_right if arr[i] > max_right: max_right = arr[i] arr[i] = new_val
question:Consider a scenario where you have a grid of integers and your task is to find the largest possible sum of numbers in any subgrid of a given size. The subgrid is defined as a contiguous block within the grid. Your task is to implement a function that receives a 2D list (a grid) and the dimensions of the subgrid (rows and columns) and returns the largest sum of elements within any such subgrid. # Function Signature ```python def largest_subgrid_sum(grid: List[List[int]], subgrid_rows: int, subgrid_cols: int) -> int: ``` # Input Format - **grid**: A 2D list of integers. - **subgrid_rows**: An integer representing the number of rows in the subgrid. - **subgrid_cols**: An integer representing the number of columns in the subgrid. # Constraints - `1 ≤ len(grid) ≤ 1000` - `1 ≤ len(grid[0]) ≤ 1000` - `1 ≤ subgrid_rows ≤ len(grid)` - `1 ≤ subgrid_cols ≤ len(grid[0])` # Output Format Return an integer representing the largest sum of any subgrid with the given dimensions. # Example ```python grid = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] subgrid_rows = 2 subgrid_cols = 2 result = largest_subgrid_sum(grid, subgrid_rows, subgrid_cols) print(result) # Output should be 28 ``` # Explanation In the example, the subgrid with the largest sum is: ``` 5 6 8 9 ``` Which sums to 28. # Notes - You should aim for an efficient solution as the grid can be large. - Consider pre-computing sums to avoid repeated calculations if necessary.
answer:from typing import List def largest_subgrid_sum(grid: List[List[int]], subgrid_rows: int, subgrid_cols: int) -> int: def calculate_prefix_sum(matrix): rows = len(matrix) cols = len(matrix[0]) prefix_sum = [[0] * (cols + 1) for _ in range(rows + 1)] for r in range(1, rows + 1): for c in range(1, cols + 1): prefix_sum[r][c] = matrix[r-1][c-1] + prefix_sum[r-1][c] + prefix_sum[r][c-1] - prefix_sum[r-1][c-1] return prefix_sum rows = len(grid) cols = len(grid[0]) prefix_sum = calculate_prefix_sum(grid) max_sum = float('-inf') for r in range(subgrid_rows, rows + 1): for c in range(subgrid_cols, cols + 1): total = prefix_sum[r][c] - prefix_sum[r - subgrid_rows][c] - prefix_sum[r][c - subgrid_cols] + prefix_sum[r - subgrid_rows][c - subgrid_cols] if total > max_sum: max_sum = total return max_sum