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question:You are given two arrays representing the inventory of two different warehouses, each containing unique item IDs (positive integers). You want to merge the two inventories in a specific way and then answer queries about the resulting inventory. Specifically, you need to count the number of times a specific item ID appears in the merged inventory only if it appears in both original inventories. Write a function `merged_inventory_queries(arr1: List[int], arr2: List[int], queries: List[int]) -> List[int]` that takes in three inputs: - `arr1`: a list of unique integers representing the first warehouse's inventory - `arr2`: a list of unique integers representing the second warehouse's inventory - `queries`: a list of integers representing the item IDs we want to query The function should return a list of integers where each element is the count of the corresponding item ID in the merged inventory if it appears in both original arrays, otherwise it should be `0`. # Example ```python def merged_inventory_queries(arr1, arr2, queries): # Your code here # Example input arr1 = [1, 2, 3, 4, 5] arr2 = [3, 4, 5, 6, 7] queries = [1, 4, 5, 6] # Function call print(merged_inventory_queries(arr1, arr2, queries)) ``` # Example Output ```python [0, 1, 1, 0] ``` # Constraints - Length of `arr1` and `arr2` will be between 1 and 100, inclusive. - Length of `queries` will be between 1 and 100, inclusive. - Each element in `arr1`, `arr2`, and `queries` will be a positive integer less than or equal to `10^9`.
answer:from typing import List def merged_inventory_queries(arr1: List[int], arr2: List[int], queries: List[int]) -> List[int]: Returns the count of each query item if it appears in both original inventories, otherwise 0. # Convert both arrays into sets for faster intersection and membership checking set1 = set(arr1) set2 = set(arr2) # Find the intersection of the two sets common_items = set1 & set2 # Create a dictionary for quick query result lookup result_dict = {item: 1 for item in common_items} # Process each query and determine its result result = [result_dict.get(query, 0) for query in queries] return result
question:A popular tactical board game, JG Chess, involves a complex grid and multiple different types of pieces each with unique movements. You’ve been tasked in creating a feature to determine the optimal path for a rook from one point to another. In this game, the rook can only move horizontally (left/right) or vertically (up/down) any number of cells. The 8x8 grid, representing the board, is numbered from (1,1) to (8,8). Write a function to calculate and output the minimum number of moves required for a rook to move from a given start position to a given end position on an 8x8 grid. # Input: The first line of input contains four integers x1, y1, x2, y2 (1 ≤ x1, y1, x2, y2 ≤ 8), representing the starting position (x1, y1) and the end position (x2, y2) respectively. # Output: Print a single integer — the minimum number of moves required for the rook to go from the starting position to the end position. # Example: Input: 2 3 2 7 Output: 1 Input: 4 4 7 8 Output: 2 # Note: In the first example, the rook can move directly from (2,3) to (2,7) in one vertical move. In the second example, the rook needs to move either horizontally or vertically from (4,4) to (7,4) and then vertically or horizontally from (7,4) to (7,8), which totals two moves. Your task is to determine the minimum number of moves for any given positions.
answer:def rook_moves(x1, y1, x2, y2): Returns the minimum moves needed for a rook to move from (x1, y1) to (x2, y2) on an 8x8 grid. if x1 == x2 or y1 == y2: return 1 else: return 2
question:You are given an array of integers. You need to determine if it is possible to divide the array into two non-empty parts such that the sum of the elements in each part is equal. Write a function `can_partition(arr)` that takes in an array of integers and returns a boolean value indicating whether such a division is possible. # Input - An array `arr` of length n (1 ≤ n ≤ 50) containing integers where each element is between -100 and 100. # Output - Return `True` if the array can be partitioned into two parts with equal sum, otherwise return `False`. # Example ```python print(can_partition([1, 5, 11, 5])) # Output: True print(can_partition([1, 2, 3, 5])) # Output: False ``` # Note - The two parts must be non-empty. Hence, there must be at least one element in each part after the partition. - The sum of elements in both parts after partition must be the same.
answer:def can_partition(arr): Determines if it is possible to divide the array into two non-empty parts such that the sum of the elements in each part is equal. total_sum = sum(arr) if total_sum % 2 != 0: return False target = total_sum // 2 n = len(arr) # Using a subset sum problem approach with dynamic programming dp = [[False] * (target + 1) for _ in range(n + 1)] for i in range(n + 1): dp[i][0] = True for i in range(1, n + 1): for j in range(1, target + 1): if arr[i-1] <= j: dp[i][j] = dp[i-1][j] or dp[i-1][j-arr[i-1]] else: dp[i][j] = dp[i-1][j] return dp[n][target]
question:You are given an array of n integers. Your task is to find the minimum number of operations required to make all elements of the array equal. In one operation, you can pick any two adjacent elements and change both elements to the maximum of the two. The first line of input contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. The first line of each test case contains an integer n (2 ≤ n ≤ 100000), the number of elements in the array. The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 10^9), representing the elements of the array. For each test case, print one integer — the minimum number of operations required to make all elements of the array equal. Example: Input: ``` 3 4 4 2 3 1 3 5 5 5 5 1 3 2 5 4 ``` Output: ``` 3 0 4 ``` Explanation: 1. In the first test case, you can perform the following operations: - Change 4 and 2 to 4. The array becomes [4, 4, 3, 1]. - Change 3 and 1 to 3. The array becomes [4, 4, 4, 3]. - Change 4 and 3 to 4. The array becomes [4, 4, 4, 4]. 2. In the second test case, all elements are already equal, so no operations are required. 3. In the third test case, you can perform the following operations: - Change 1 and 3 to 3. The array becomes [3, 3, 2, 5, 4]. - Change 3 and 2 to 3. The array becomes [3, 3, 3, 5, 4]. - Change 3 and 5 to 5. The array becomes [3, 3, 3, 5, 5]. - Change 3 and 5 to 5. The array becomes [5, 5, 5, 5, 5].
answer:def min_operations_to_make_equal(test_cases): results = [] for a in test_cases: a.sort() max_element = a[-1] operations = 0 i = len(a) - 2 while i >= 0: if a[i] != max_element: operations += 1 i -= 1 results.append(operations) return results def process_input(input_data): lines = input_data.strip().split('n') t = int(lines[0]) test_cases = [] index = 1 for _ in range(t): n = int(lines[index]) array = list(map(int, lines[index + 1].split())) test_cases.append(array) index += 2 return test_cases