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question:You are given an array of `n` integers which you can rotate to the right any number of times. A right rotation operation moves the last element of the array to the beginning. Your task is to find the maximum possible value of the array after exactly `k` rotations. A valid solution should consider the impact of each rotation and find the optimal state after k rotations. ------ Input Format ------ - The first line contains two integers, n (the length of the array) and k (the number of rotations you can perform). - The second line contains n space-separated integers representing the elements of the array. ------ Output Format ------ - Print the maximum possible value of the array as an integer after exactly `k` rotations. ------ Constraints ------ 1 ≤ n ≤ 10^5 0 ≤ k ≤ 10^9 -10^9 ≤ array[i] ≤ 10^9 ------ Sample Input 1 ------ 5 2 1 2 3 4 5 ------ Sample Output 1 ------ 5 ------ Explanation 1 ------ After one rotation: [5, 1, 2, 3, 4] After two rotations: [4, 5, 1, 2, 3] The maximum possible value in the array after 2 rotations is 5. ------ Sample Input 2 ------ 3 4 3 9 7 ------ Sample Output 2 ------ 9 ------ Explanation 2 ------ Since `k ≥ n`, we can simplify the problem as the array would end up in the same state as after performing `k % n` rotations. Rotation operations: Original: [3, 9, 7] After one rotation: [7, 3, 9] After two rotations: [9, 7, 3] After three rotations: [3, 9, 7] After four rotations (which is same as one rotation): [7, 3, 9] Thus, the maximum possible value in the array after 4 rotations is 9.
answer:def max_after_k_rotations(n, k, array): Returns the maximum possible value of the array after exactly k rotations to the right. Parameters: n (int): The length of the array. k (int): The number of rotations. array (list): The array of integers. Returns: int: The maximum possible value in the array after exactly k rotations. # Since the array will repeat its state after n rotations, # we only need to consider k % n rotations k = k % n rotated_array = array[-k:] + array[:-k] return max(rotated_array)
question:Write a function that takes an integer `n` and returns the `n-th` Fibonacci number. The function should be efficient, utilizing memoization to cache intermediate results and avoid redundant calculations. The Fibonacci sequence is defined as follows: - `Fib(0) = 0` - `Fib(1) = 1` - For `n > 1, Fib(n) = Fib(n-1) + Fib(n-2)` The function should handle large values of `n` efficiently (up to 10,000). # Examples ``` Input: n = 5 Output: 5 Input: n = 10 Output: 55 ```
answer:def fibonacci(n, memo={}): Returns the n-th Fibonacci number using memoization. if n in memo: return memo[n] if n <= 0: return 0 elif n == 1: return 1 else: memo[n] = fibonacci(n-1, memo) + fibonacci(n-2, memo) return memo[n]
question:A group of friends are organizing a potluck dinner. Each friend will bring one or more dishes, but no dish should be duplicated among the group's contributions. The goal is to compile a list of unique dishes each friend will bring without any duplication. Write a program to generate the final list of dishes specifying the friend and their unique dishes. # Input The input is a list of dictionaries. Each dictionary contains: - `name` - a string representing the friend's name - `dishes` - a list of strings representing the dishes they are planning to bring # Output The output should be a list of dictionaries. Each dictionary contains: - `name` - a string representing the friend's name - `dishes` - a list of strings representing the unique dishes brought by the friend # Examples ```python def potluck_dinner(input_list): # your code here potluck_dinner([ {'name': 'Alice', 'dishes': ['Salad', 'Pizza']} ]) # Output: [{'name': 'Alice', 'dishes': ['Salad', 'Pizza']}] potluck_dinner([ {'name': 'Alice', 'dishes': ['Salad', 'Pizza']}, {'name': 'Bob', 'dishes': ['Pizza', 'Cake']} ]) # Output: [{'name': 'Alice', 'dishes': ['Salad']}, # {'name': 'Bob', 'dishes': ['Cake']}] potluck_dinner([ {'name': 'Alice', 'dishes': ['Salad', 'Pizza']}, {'name': 'Bob', 'dishes': ['Cake']}, {'name': 'Charlie', 'dishes': ['Salad', 'Cake']} ]) # Output: [{'name': 'Alice', 'dishes': ['Pizza']}, # {'name': 'Bob', 'dishes': []}, # {'name': 'Charlie', 'dishes': []}] potluck_dinner([ {'name': 'Alice', 'dishes': ['Salad']}, {'name': 'Bob', 'dishes': ['Cake']}, {'name': 'Charlie', 'dishes': ['Sandwich']} ]) # Output: [{'name': 'Alice', 'dishes': ['Salad']}, # {'name': 'Bob', 'dishes': ['Cake']}, # {'name': 'Charlie', 'dishes': ['Sandwich']}] ```
answer:def potluck_dinner(input_list): Compiles a list of unique dishes each friend will bring without any duplication among the group's contributions. Parameters: input_list (list): List of dictionaries each containing `name` (string) and `dishes` (list of strings) Returns: list: A list of dictionaries each containing `name` (string) and their unique `dishes` (list of strings) all_dishes = {} for entry in input_list: for dish in entry['dishes']: if dish in all_dishes: all_dishes[dish].append(entry['name']) else: all_dishes[dish] = [entry['name']] result = [] for entry in input_list: unique_dishes = [dish for dish in entry['dishes'] if len(all_dishes[dish]) == 1] result.append({'name': entry['name'], 'dishes': unique_dishes}) return result
question:Write a function `longest_substring_with_k_distinct` that, given a string `s` and an integer `k`, returns the length of the longest substring that contains exactly `k` distinct characters. If no such substring exists, return 0. # Input - A string `s` with length `n` where 1 leq n leq 2 times 10^5. - An integer `k` where 1 leq k leq 26. # Output - An integer representing the length of the longest substring with exactly `k` distinct characters. # Examples Example 1: ```plaintext Input: s = "eceba" k = 2 Output: 3 Explanation: The longest substring with exactly 2 distinct characters is "ece". ``` Example 2: ```plaintext Input: s = "aa" k = 1 Output: 2 Explanation: The longest substring with exactly 1 distinct character is "aa". ``` Example 3: ```plaintext Input: s = "abc" k = 4 Output: 0 Explanation: There are no substrings with exactly 4 distinct characters since the string itself only has 3 distinct characters. ```
answer:def longest_substring_with_k_distinct(s, k): if k == 0 or not s: return 0 char_map = {} left = 0 max_length = 0 for right in range(len(s)): char_map[s[right]] = char_map.get(s[right], 0) + 1 while len(char_map) > k: char_map[s[left]] -= 1 if char_map[s[left]] == 0: del char_map[s[left]] left += 1 if len(char_map) == k: max_length = max(max_length, right - left + 1) return max_length