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question:You are given a binary string S of length N. The binary string represents a sequence of zombies (denoted by '1') and empty spaces (denoted by '0'). Chef and his friend Munchy are playing a game where they take turns destroying zombies. The rules are as follows: 1. On each player’s turn, they must select and destroy exactly one contiguous block of zombies (a maximal substring of consecutive '1's). 2. The remaining zombies and empty spaces are concatenated together after removing the chosen block, maintaining their original order. 3. The game continues until no zombies are left to destroy. 4. The player who cannot make a move (because no zombies are left) loses the game. Chef always goes first. Given that both players play optimally, determine the winner of the game. ------ Input Format ------ - The first line of input contains a single integer T, the number of test cases. The description of T test cases follows. - For each test case, the first line contains a single integer N, the length of the binary string. - The second line contains the binary string S, which represents the initial state of zombies and empty spaces. ------ Output Format ------ For each test case, output a single line containing the string “CHEF” (without quotes) if Chef will be the winner, and “MUNCHY” otherwise. ------ Constraints ------ 1 ≤ T ≤ 10^{4} 1 ≤ N ≤ 10^{5} S is a binary string consisting of ‘0’ and ‘1’ only - The sum of N over all test cases will not exceed 10^{6} ------ Sample Input 1 ------ 3 6 110011 5 11111 4 1000 ------ Sample Output 1 ------ MUNCHY CHEF CHEF ------ Explanation 1 ------ Test case 1: There are three blocks of zombies: '11', '00', '11'. Chef and Munchy will alternately destroy blocks of zombies. Chef destroys a block of '11', then Munchy destroys the other block of '11'. Now, Chef cannot make a move and thus Munchy wins. Test case 2: There is only one block of zombies '11111' which Chef will destroy in the first move, leaving no zombies for Munchy to destroy, making Chef the winner. Test case 3: There is only one block of zombies '1', which Chef will destroy in the first move, leaving no zombies for Munchy to destroy, making Chef the winner.

answer:def find_game_winner(binary_string): Determines the winner of the game given a binary string. Chef wins if the number of contiguous blocks of '1's is odd. Munchy wins otherwise. Args: binary_string (str): The binary string representing zombies and empty spaces Returns: str: "CHEF" if Chef wins, "MUNCHY" if Munchy wins block_count = 0 in_block = False for char in binary_string: if char == '1': if not in_block: block_count += 1 in_block = True else: in_block = False return "CHEF" if block_count % 2 == 1 else "MUNCHY" def determine_winner_for_test_cases(T, test_cases): Determines the winner for each test case. Args: T (int): Number of test cases test_cases (list): List of tuples where each tuple contains (N, binary_string) Returns: list of str: List of results for each test case results = [] for _, binary_string in test_cases: result = find_game_winner(binary_string) results.append(result) return results

question:Tanya recently got into gardening and decided to grow some flowers in her backyard. She has N types of flower seeds, each of which has specific characteristics influencing how they grow. Each flower seed type i is characterized by two integers: Ai, which represents the amount of water needed per day for optimal growth, and Bi, which is the number of days it takes for that flower to fully blossom. Tanya aims to maximize the variety of flowers in her garden while adhering to the following rules: 1. Tanya can only water the flowers once per day, and each type i of flower must receive exactly Ai units of water every day. 2. She has a total of W units of water available per day. 3. The order of planting does not matter, but she can only start watering a new flower type after completing the full blossom period of any currently being watered type. Help Tanya determine the maximum number of different flower types she can grow in her garden under these constraints. # Input - The first line contains two integers, N and W, separated by a blank space, where N is the number of different types of flower seeds, and W is the total amount of water available per day. - The next N lines each contains two integers Ai and Bi separated by a blank space, representing the water requirement per day and the number of days to blossom for the i-th type of flower. # Output - Output a single integer representing the maximum number of different flower types Tanya can grow. # Example Input 1 ``` 4 10 4 2 3 3 5 4 2 1 ``` Output 1 ``` 3 ``` Input 2 ``` 3 5 6 5 4 3 2 2 ``` Output 2 ``` 1 ``` # Explanation In the first example, Tanya can choose flower types 1, 2, and 4, requiring no more than 10 units of water per day altogether. In the second example, Tanya can only choose the flower type 3 to maximize the number of different flower types she can grow. The goal is to implement an algorithm that efficiently determines the maximum number of flower types Tanya can plant based on her water constraints.

answer:def max_flower_types(N, W, flower_data): Determine the maximum number of flower types Tanya can grow. Args: N : int : The number of different types of flower seeds. W : int : The total amount of water available per day. flower_data : list of tuples : Each tuple containing (Ai, Bi), representing the water requirement per day and the number of days to blossom for each type of flower. Returns: int : The maximum number of flower types Tanya can grow. # Sort flowers by their water requirement (Ai) flower_data.sort() current_water = 0 flower_count = 0 for Ai, Bi in flower_data: if current_water + Ai <= W: current_water += Ai flower_count += 1 else: break return flower_count

question:Alice is a linguist working with a large corpus of text samples. As part of her analysis, she needs to determine whether a given text sample can be segmented into exactly n words, such that each word appears at least once in a given dictionary of valid words. Write a function to help Alice decide if this segmentation is possible. -----Input----- The first line of input contains a string text containing lowercase English letters (1 ≤ |text| ≤ 1000). The second line contains an integer n (1 ≤ n ≤ 1000). The third line contains a list of words representing the dictionary. You may assume that all words in the dictionary and the text are composed of lowercase English letters and each word is unique. -----Output----- Print "YES" (without quotes) if it's possible to segment the text into exactly n words that each appear in the dictionary. Otherwise, print "NO" (without quotes). -----Examples----- Input thisisaword 4 this is a word Output YES Input appleorangebanana 2 apple orange banana Output NO -----Note----- In the first sample, "thisisaword" can be segmented into "this", "is", "a", and "word", each of which appears in the given dictionary. In the second sample, "appleorangebanana" can potentially be segmented into "apple", "orange", and "banana", but that's 3 words, not 2. Therefore, the answer is "NO".

answer:def can_segment(text, n, dictionary): Function that determines if text can be segmented into exactly n words from the given dictionary. :param text: str, the input text to be segmented :param n: int, the number of segments required :param dictionary: list, list of valid words :return: str, "YES" or "NO" if the segmentation is possible or not word_set = set(dictionary) text_len = len(text) # dp[i] will be a list of tuples (length, count), where length is the length of the word, and count is the # number of segments up to index i that forms a valid segmentation with 'n' words. Example (4, 2) means # using 4 letter words formed valid segmentation up to index 'i' with 2 words. dp = [None] * (text_len + 1) dp[0] = (0, 0) # Starting condition: zero length, zero words for i in range(1, text_len + 1): for j in range(i): word = text[j:i] if word in word_set: if dp[j] is not None: length_so_far, word_count_so_far = dp[j] if word_count_so_far + 1 <= n: if dp[i] is None or (dp[i][1] > word_count_so_far + 1): dp[i] = (length_so_far + len(word), word_count_so_far + 1) # Check if we can split the text into exactly 'n' words if dp[-1] is not None and dp[-1][1] == n: return "YES" else: return "NO"

question:A group of friends is planning a road trip. They need to determine the optimal route to visit a certain number of cities. Each city is connected to at least one other city by a direct road, and each road has a fixed travel cost associated with it. The goal is to find the minimum total travel cost necessary to visit each city at least once. You need to write a program that calculates this minimum travel cost given the list of cities and roads. -----Input----- - The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. - The first line of each test case contains two integers N and M where N is the number of cities and M is the number of roads. - The next M lines each contain three integers u, v, and w, representing a road between city u and city v with a cost w. -----Output----- For each test case, print a single line containing the minimum total travel cost to visit each city at least once. If it is not possible to visit all cities, print "impossible". -----Constraints----- - 1 le T le 10 - 1 le N le 1000 - 1 le M le 10,000 - 1 le u, v le N - 1 le w le 10,000 -----Example Input----- 2 4 4 1 2 4 2 3 2 3 4 1 4 1 5 3 3 1 2 6 2 3 8 3 1 5 -----Example Output----- 7 11

answer:class UnionFind: def __init__(self, size): self.root = list(range(size)) self.rank = [1] * size def find(self, u): if u != self.root[u]: self.root[u] = self.find(self.root[u]) return self.root[u] def union(self, u, v): root_u = self.find(u) root_v = self.find(v) if root_u != root_v: if self.rank[root_u] > self.rank[root_v]: self.root[root_v] = root_u elif self.rank[root_u] < self.rank[root_v]: self.root[root_u] = root_v else: self.root[root_v] = root_u self.rank[root_u] += 1 def minimum_travel_cost(T, test_cases): results = [] for case in test_cases: N, M, edges = case uf = UnionFind(N) edges.sort(key=lambda x: x[2]) mst_cost = 0 edges_used = 0 for u, v, w in edges: if uf.find(u - 1) != uf.find(v - 1): uf.union(u - 1, v - 1) mst_cost += w edges_used += 1 if edges_used == N - 1: break if edges_used != N - 1: results.append("impossible") else: results.append(str(mst_cost)) return results def process_input(input_string): data = input_string.strip().split('n') T = int(data[0]) idx = 1 test_cases = [] for _ in range(T): N, M = map(int, data[idx].split()) edges = [tuple(map(int, data[idx + i + 1].split())) for i in range(M)] test_cases.append((N, M, edges)) idx += M + 1 return T, test_cases def process_output(results): return 'n'.join(results) def main(input_string): T, test_cases = process_input(input_string) results = minimum_travel_cost(T, test_cases) return process_output(results)