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question:In a distant land called Algorithmia, there is a prestigious sword-fighting school where students are trained to become elite fighters. Every student has a skill level, and in order to become a master, a student must participate in a series of duals with other students. Each day, the instructor pairs up students to fight in duals. Each dual consists of two students whose combined skill level doesn't exceed a maximum threshold m. Most importantly, every student can only participate in one dual per day. Your task is to determine the maximum number of duals that can take place each day for a given list of students' skill levels and a skill threshold m. Input: The first line of input contains two integers n and m (1 ≤ n ≤ 100, 1 ≤ m ≤ 100), where n is the number of students and m is the maximum allowed combined skill level for a dual. The second line contains n integers s1, s2, ..., sn (1 ≤ si ≤ 100), where si is the skill level of the i-th student. Output: Output a single integer denoting the maximum number of duals that can take place each day. Examples: Input: 4 5 1 2 3 4 Output: 2 Input: 5 8 3 3 3 3 3 Output: 2 Input: 3 10 1 2 3 Output: 1 Note: In the first sample, students can be paired as follows: (1, 4) and (2, 3), resulting in 2 duals. In the second sample, pairs can be (3, 3), and another pair of (3, 3), resulting in 2 duals. In the third sample, the only possible pairs are (1, 2) and 3 remains without a pair, resulting in 1 dual.

answer:def max_duals(n, m, skills): # Sort the skill levels in ascending order skills.sort() # Initialize pointers to the start and end of the list left = 0 right = n - 1 duals_count = 0 # Use a two-pointer approach to pair students while left < right: # Check if the current pair is valid if skills[left] + skills[right] <= m: # If so, it forms a valid dual duals_count += 1 # Move both pointers inward left += 1 right -= 1 else: # Otherwise, move the right pointer to a lower value right -= 1 return duals_count

question:You are given an endless stream of integers and a sliding window of size `k`. Your task is to write a function that processes the stream to continuously find the maximum integer in the current window of size `k`, and output this maximum value each time the window moves by one position. If the window reaches the end of the stream, the function should terminate. For example, if the stream is [1, 3, -1, -3, 5, 3, 6, 7] and k = 3, then the function should output: 3, 3, 5, 5, 6, 7. Input - The first line contains integer k (1 ≤ k ≤ 105), the size of the sliding window. - The second line should continuously read the integers a[1], a[2], ..., a[n] from the stream, where the size of n is unknown and the values can be between -109 and 109. Output Continuously print the maximum integer in the current sliding window of size k each time it moves by one position, until there are no more integers left in the stream. Example Input 3 1 3 -1 -3 5 3 6 7 Output 3 3 5 5 6 7 Additional notes: The function should maintain efficiency and process the stream in an optimal manner, ensuring it continuously reads and processes new integers without unnecessary delays. The result should be updated and printed for each position of the sliding window, demonstrating real-time processing of the data stream.

answer:from collections import deque import sys def sliding_window_maximum(k, stream): Processes the stream to continuously find the maximum integer in the current window of size k. q = deque() # Will store indices of potential max elements result = [] # Store the results for testing purposes for i, num in enumerate(stream): # Remove the elements indices from deque which are out of bound for the window if q and q[0] == i - k: q.popleft() # Remove elements from deque which are less than current element while q and stream[q[-1]] < num: q.pop() q.append(i) # Record the maximum values from current window if i >= k - 1: result.append(stream[q[0]]) print(stream[q[0]]) # Print max in the sliding window return result

question:Implement a function `min_operations_to_transpose(matrix)` that calculates the minimum number of operations required to convert a given square matrix into its transpose. An operation is defined as swapping any two elements in the matrix. # Funciton Signature: ```python def min_operations_to_transpose(matrix: List[List[int]]) -> int: pass ``` # Input - `matrix` : `List[List[int]]` (a list of lists of integers), representing an `n x n` square matrix (1 <= n <= 1000, 0 <= matrix[i][j] <= 1000) # Output - An integer which is the minimum number of operations to make `matrix` equal to its transpose # Example ```python matrix = [ [1, 3, 5], [3, 2, 8], [5, 8, 6] ] print(min_operations_to_transpose(matrix)) # Output: 0 matrix = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] print(min_operations_to_transpose(matrix)) # Output: 3 ``` # Constraints - When matrix is already a transpose of itself, the output should be 0. - Each operation can swap any two elements in the matrix.

answer:from typing import List def min_operations_to_transpose(matrix: List[List[int]]) -> int: n = len(matrix) ops = 0 for i in range(n): for j in range(i + 1, n): if matrix[i][j] != matrix[j][i]: ops += 1 return ops

question:Given an array of N integers, define a "wavy" array as an array where each element is either greater than or less than both of its neighbors. Your task is to determine if an array is "wavy" or not. Input: The first line contains a single integer N. The second line contains N space-separated integers a1, a2, ..., aN. Output: Output "Yes" if the array is "wavy", otherwise output "No". Constraints: 2 ≤ N ≤ 10^3 1 ≤ ai ≤ 10^6 where i=1, 2, 3 ... N SAMPLE INPUT 5 1 3 2 4 3 SAMPLE OUTPUT Yes Explanation: The array [1, 3, 2, 4, 3] is "wavy" because: - 3 > 1 and 3 > 2 - 2 < 3 and 2 < 4 - 4 > 2 and 4 > 3

answer:def is_wavy(arr): Returns "Yes" if the array is wavy, otherwise returns "No". n = len(arr) for i in range(1, n - 1): if not ((arr[i] > arr[i - 1] and arr[i] > arr[i + 1]) or (arr[i] < arr[i - 1] and arr[i] < arr[i + 1])): return "No" return "Yes"