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question:Scarlet and Violet love solving puzzles together. One day, they came across a sequence puzzle where they have to decide the winner based on a special set of rules. The game consists of a sequence S of N positive integers. The players take turns, with Scarlet going first. In each turn, the player selects an integer from the sequence and removes it, trying to maximize their score. The game has a twist: There is a special number X. The players can choose to skip their turn only if the X-th multiple in the sequence has not been picked yet (where X is a 1-based index). If any player skips their turn, the other player gets back-to-back turns until the sequence is empty. Scarlet always tries to maximize her score such that she can end up with a higher score than Violet. The players can opt to skip their turn only using the given special rule, and they strategize optimally. If Scarlet wins by always adopting this strategy, you need to print "WIN"; otherwise, print "LOSE". -----Input----- - The first line contains a single integer T, the number of test cases. - The first line of each test case contains two space-separated integers N and X, the number of elements in the sequence and the special number X. - The second line contains N space-separated integers S_1, S_2, dots, S_N. -----Output----- For each test case, print a single line containing "WIN" if Scarlet can ensure her victory over Violet or "LOSE" otherwise. -----Constraints----- - 1 leq T leq 100 - 1 leq N leq 10,000 - 1 leq X leq N - 1 leq S_i leq 10,000 for each valid i -----Example Input----- 2 5 2 1 3 5 7 9 4 3 5 5 5 5 -----Example Output----- WIN LOSE -----Explanation----- Example Case 1: Scarlet can choose to strategically skip turns ensuring that she can always pick the higher values. Example Case 2: With an optimal strategy and considering the given constraints, Violet can tie or exceed Scarlet in points by equally leveraging the opportunity to skip turns at the right moment.

answer:def determine_winner(T, test_cases): results = [] for case in test_cases: N, X = case['N'], case['X'] S = case['S'] # Sort the sequence in descending order to prioritize larger values S.sort(reverse=True) # Split S into Scarlet's and Violet's picks assuming Scarlet starts first scarlet_score = sum(S[0::2]) violet_score = sum(S[1::2]) # Determine the winner if scarlet_score > violet_score: results.append("WIN") else: results.append("LOSE") return results # Helper function to parse input and process output def parse_input_and_process(input_str): lines = input_str.strip().split('n') T = int(lines[0]) test_cases = [] idx = 1 for _ in range(T): N, X = map(int, lines[idx].split()) S = list(map(int, lines[idx + 1].split())) test_cases.append({'N': N, 'X': X, 'S': S}) idx += 2 results = determine_winner(T, test_cases) return 'n'.join(results) # Main function to process the input with determination logic def determine_winner(T, test_cases): results = [] for case in test_cases: N, X = case['N'], case['X'] S = case['S'] # Sort the sequence in descending order to prioritize larger values S.sort(reverse=True) # Split S into Scarlet's and Violet's picks assuming Scarlet starts first scarlet_score = sum(S[0::2]) violet_score = sum(S[1::2]) # Determine the winner if scarlet_score > violet_score: results.append("WIN") else: results.append("LOSE") return results

question:Given an array of integers where each element appears three times except for one, which appears exactly once, find that single one. Example: Input: [2, 2, 3, 2] Output: 3 Input: [0, 1, 0, 1, 0, 1, 99] Output: 99

answer:def single_number(nums): Finds the number that appears exactly once in an array where every other number appears three times. :param nums: List[int] :return: int ones, twos = 0, 0 for num in nums: ones = (ones ^ num) & ~twos twos = (twos ^ num) & ~ones return ones

question:Given a string `s` that consists of only lowercase English letters, construct a string `t` by performing the following operations exactly once for each character in `s`: 1. Choose a character in `s` (denoted as `c_i`). 2. Move `c_i` to the front of `t`. Return the lexicographically smallest string `t` that can be constructed by the above operations. Example 1: Input: s = "cbacdcbc" Output: "acdb" Explanation: Let's reconstruct the string `t` starting with an empty string. By moving the characters as described: - Moving 'a' to the front gives us "a". - Moving 'b' to the front of "a" gives us "ba". - Moving 'c' to the front of "ba" and so on. The smallest lexicographical string we can get is "acdb". Example 2: Input: s = "bcabc" Output: "abc" Explanation: By moving the characters in the optimal way, the smallest lexicographical string we can get is "abc". Example 3: Input: s = "abacb" Output: "abc" Explanation: By optimally moving characters, the lexicographically smallest string is "abc". Constraints: - 1 <= s.length <= 10^4 - s consists of only lowercase English letters.

answer:def remove_duplicate_letters(s): Returns the lexicographically smallest string possible by moving the characters of `s` to the front one by one. stack = [] seen = set() last_occurrence = {char: idx for idx, char in enumerate(s)} for idx, char in enumerate(s): if char not in seen: while stack and char < stack[-1] and idx < last_occurrence[stack[-1]]: seen.remove(stack.pop()) stack.append(char) seen.add(char) return ''.join(stack)

question:You are given a string representing an arithmetic expression that contains only non-negative integers, '+', '-', '*', and '/' operators (where '/' represents integer division). Implement a function to evaluate the expression and return the result. The input string is valid and follows normal operator precedence rules. Assume the input does not contain any parentheses. Example: Input: "3+2*2" Output: 7 Explanation: Perform multiplication before addition: 2*2 = 4, then add 3. Example: Input: " 3/2 " Output: 1 Explanation: Perform integer division 3 / 2 = 1. Example: Input: " 3+5 / 2 " Output: 5 Explanation: First perform division 5 / 2 = 2, then add 3. Note: - You may assume that the given expression is always valid and contains only non-negative integers. - The function should handle whitespaces and ignore them as necessary. - You should aim to solve the problem in O(n) time complexity, where n is the length of the input string.

answer:def evaluate_expression(expression): Evaluates a string arithmetic expression containing non-negative integers and '+', '-', '*', and '/' operators with normal precedence rules. if not expression: return 0 num, stack, sign = 0, [], '+' expression = expression.replace(' ', '') for i, ch in enumerate(expression): if ch.isdigit(): num = num * 10 + int(ch) if ch in '+-*/' or i == len(expression) - 1: if sign == '+': stack.append(num) elif sign == '-': stack.append(-num) elif sign == '*': stack[-1] = stack[-1] * num elif sign == '/': stack[-1] = int(stack[-1] / num) # integer division num, sign = 0, ch return sum(stack)