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question:Zara loves solving coding problems and puzzles. She has come across an interesting problem related to prime numbers and string permutations. Can you help Zara solve it? - The problem states that for a given string S, she needs to determine if it is possible to rearrange the characters of S to form a prime number. - A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Your task is to write a program to check if any permutation of the string S can be rearranged to a prime number. -----Input:----- - First line will contain T, number of testcases. Then the testcases follow. - Each testcase contains a single string S, consisting of digits only. -----Output:----- For each testcase, output "YES" if it is possible to rearrange the characters of S to form a prime number, otherwise output "NO". -----Constraints----- - 1 leq T leq 100 - 1 leq |S| leq 9 -----Sample Input:----- 3 17 23 28 -----Sample Output:----- YES YES NO
answer:from itertools import permutations def is_prime(num): if num <= 1: return False if num == 2: return True if num % 2 == 0: return False for i in range(3, int(num**0.5) + 1, 2): if num % i == 0: return False return True def can_form_prime(S): for perm in permutations(S): num = int(''.join(perm)) if is_prime(num): return "YES" return "NO" def process_test_cases(T, test_cases): results = [] for S in test_cases: results.append(can_form_prime(S)) return results
question:Given an array of integers, where each integer represents the height of a person standing in a line, you need to arrange them into the smallest number of "waves" where each wave is defined as a contiguous subarray satisfying the rule: the person at the start of the wave should be taller than all subsequent people in the wave. Determine the minimum number of waves needed to arrange all the people in the given array. For example, given the array `[3, 1, 2, 3, 1]`, the optimal arrangement would be `3 -> [1, 2], 3 -> [1]`, resulting in a total of 3 waves. Write a function `countWaves` that takes an array of integers representing heights and returns the minimum number of waves needed. # Function Signature ```python def countWaves(arr: List[int]) -> int: ``` # Input - arr: List of integers representing the height of people in the line. (1 <= len(arr) <= 100000 and 1 <= arr[i] <= 10^9) # Output - An integer representing the minimum number of waves required. # Example ```python arr = [3, 1, 2, 3, 1] print(countWaves(arr)) # Output: 3 ``` # Explanation You can split the array `[3, 1, 2, 3, 1]` into waves: - Wave 1: [3, 1] - Wave 2: [2, 3] - Wave 3: [1] Thus, the minimum number of waves required is 3. # Constraints - You need to ensure the solution efficiently handles the case where the array length is up to 100000. - The height values can be large, so the algorithm should handle large integers effectively.
answer:def countWaves(arr): Given an array of integers representing heights of people in a line, return the minimum number of waves needed where each wave is defined as a contiguous subarray satisfying the rule: the person at the start of the wave should be taller than all subsequent people in the wave. if not arr: return 0 waves = 1 max_height = arr[0] for height in arr[1:]: if height >= max_height: waves += 1 max_height = height else: max_height = height return waves
question:In a small town, Alice wants to organize a bake sale to raise funds for the local library. She plans to bake N batches of cookies. Each batch requires Y grams of sugar. Alice currently has X grams of sugar at home. Given the price of sugar is P rupees per gram, help Alice determine the minimum cost in rupees she needs to spend to buy enough sugar to bake all the batches. ------ Input Format ------ - The first line contains T, the number of test cases. - Each of the next T lines contains three integers N, X, and P. ------ Output Format ------ For each test case, output a single line containing the minimum cost Alice needs to spend. ------ Constraints ------ 1 ≤ T ≤ 100 1 ≤ N ≤ 100 0 ≤ X ≤ 10,000 1 ≤ Y, P ≤ 100 ----- Sample Input 1 ------ 2 3 100 2 5 200 10 ----- Sample Output 1 ------ 0 3000 ----- Explanation 1 ------ Test Case 1: Alice needs enough sugar for 3 batches. If Y is assumed to be 50 grams per batch (since Y is missing in the input format, assume some reasonable value for explanation). She needs 150 grams total. Since she already has 100 grams, she needs 50 more grams. The cost is 50 times 2 = 100 rupees which should be the correct result. If this were a mistake and trying to match input style, let's assume Alice does not need more sugar as solution didn't require it (showing a format misunderstanding, assuming no purchases based on min threshold. Explanation should refine this.) Test Case 2: Alice needs enough sugar for 5 batches. If 50 grams per batch is assumed (adjust for showing example if fixing format assumption). She needs a total of 250 grams. Since she has 200 grams, she needs 50 more. The cost is 50 times 10 = 500 rupees, matching the assumed structure and should be corrected to show clearer format alignment.
answer:def minimum_cost_to_buy_sugar(T, test_cases): results = [] for i in range(T): N, X, P, Y = test_cases[i] required_sugar = N * Y if X >= required_sugar: results.append(0) else: needed_sugar = required_sugar - X cost = needed_sugar * P results.append(cost) return results
question:A group of software development firms are working on a collaborative project that involves merging multiple codebases. Each codebase is represented as a list of file paths. To ensure there are no conflicts, the firms have collectively decided to keep all file paths unique across the entire project. Write a program that, given the lists of file paths from participating firms, outputs the total number of unique file paths. Assume that file paths are case-sensitive (i.e., "File.txt" and "file.txt" are considered different). -----Input----- Input begins with an integer N (1 le N le 10), the number of firms. Each of the next N blocks begins with an integer M (1 le M le 100), the number of file paths for that firm. Each of the next M lines in the block contains a single file path string which consists of alphanumeric characters and/or dots, slashes, and underscores (1 le text{length of file path} le 100). -----Output----- Output a single integer, the number of unique file paths across all lists. -----Examples----- Sample Input: 3 3 src/main.py src/utils.py README.md 2 src/utils.py src/config.yaml 4 tests/test_main.py README.md src/config.yaml LICENSE.txt Sample Output: 6
answer:def count_unique_file_paths(firm_data): Given the lists of file paths from participating firms, returns the number of unique file paths. Parameters: firm_data (list): List of tuples where each tuple contains the number of file paths followed by the file path strings. Returns: int: The number of unique file paths across all lists. unique_paths = set() for firm in firm_data: num_files = firm[0] file_paths = firm[1:num_files + 1] unique_paths.update(file_paths) return len(unique_paths)