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question:You are given a list of students, each with their respective scores in three subjects: Math, Science, and English. The goal is to determine the overall ranking of students based on their average scores. The student with the highest average score should be ranked first. In case of a tie in average scores, rank the tied students by their Math scores. If there is still a tie, rank them alphabetically by their names. Write a function `rank_students` that takes in a list of dictionaries, where each dictionary contains a student's name and their scores in Math, Science, and English. The function should return a list of student names sorted by their rank. # Example: Input: ``` [ {"name": "John", "Math": 80, "Science": 90, "English": 85}, {"name": "Doe", "Math": 90, "Science": 70, "English": 80}, {"name": "Jane", "Math": 85, "Science": 80, "English": 80}, {"name": "Smith", "Math": 90, "Science": 85, "English": 90} ] ``` Output: ``` ["Smith", "John", "Jane", "Doe"] ``` Explanation: - Smith's average score is 88.33, John’s average score is 85, Jane's average score is 81.66, and Doe’s average score is 80. - Smith is ranked first based on the highest average score. - John is next with an average score of 85. - Jane is ranked third with an average score of 81.66. - Doe is ranked fourth with an average score of 80. # Notes: - The input list will always contain valid data. - You may assume there are no duplicated names and all names are unique. - Scores are integers and the average can be a float with up to 2 decimal places.

answer:def rank_students(students): Ranks students based on average scores. Ties are broken by Math scores, then by names alphabetically. Args: students (list of dict): A list of dictionaries, where each dictionary contains a student's name and their scores in Math, Science, and English. Returns: list of str: A list of student names sorted by their rank. # Calculate the average score for each student and store it in a tuple students_with_avg = [] for student in students: avg_score = (student["Math"] + student["Science"] + student["English"]) / 3 students_with_avg.append((student["name"], avg_score, student["Math"])) # Sort primarily by average score (descending), then by Math score (descending), then by name (alphabetically) students_with_avg.sort(key=lambda x: (-x[1], -x[2], x[0])) # Extract the sorted student names sorted_students = [student[0] for student in students_with_avg] return sorted_students

question:Write functions to evaluate simple mathematical expressions given as strings. The expressions will consist of integers and the operators +, -, *, and /. The operators must follow the standard precedence rules: * and / have higher precedence than + and -, and operations of the same precedence are performed from left to right. You must also handle parentheses to override the standard precedence rules. To simplify the implementation, you can assume that: - The input expression is always valid. - There are no spaces in the input string. - The integer values are non-negative. -----Input----- The input is a single string representing a valid mathematical expression as defined above. The string's length will be at least 1 and at most 100 characters. -----Output----- The output should be a single integer result of evaluating the given expression. -----Examples----- Sample Input 1: 3+5*2 Sample Output 1: 13 Sample Input 2: (2+3)*(5-2) Sample Output 2: 15 Sample Input 3: 20/(4+1) Sample Output 3: 4

answer:def evaluate_expression(expr): def evaluate(tokens): stack = [] num = 0 sign = '+' while tokens: token = tokens.pop(0) if token.isdigit(): num = num * 10 + int(token) if token == '(': num = evaluate(tokens) if (not token.isdigit() and token != ' ') or not tokens: if sign == '+': stack.append(num) elif sign == '-': stack.append(-num) elif sign == '*': stack[-1] *= num elif sign == '/': stack[-1] = int(stack[-1] / float(num)) sign = token num = 0 if token == ')': break return sum(stack) return evaluate(list(expr))

question:You are given an array of integers. Your task is to determine the maximum product of three distinct elements in this array. If the array contains fewer than three elements, return -1. The function should take an array of integers as input and output a single integer representing the maximum possible product of three distinct elements, or -1 if it's not feasible. -----Input----- The input consists of a single line containing a space-separated list of integers a (−10^4 ≤ a[i] ≤ 10^4, 1 ≤ |a| ≤ 3 * 10^4) — the elements of the array. -----Output----- Output a single integer — the maximum possible product of three distinct elements, or -1 if the array contains fewer than three elements. -----Examples----- Input 4 1 3 2 Output 24 Input -1 -2 -3 -4 Output -6 Input 1 2 Output -1 -----Note----- In the first sample, you can choose the elements 4, 3, and 2 to get the product 4 * 3 * 2 = 24. In the second sample, although all elements are negative, the maximum product of three distinct elements is -1 * -2 * -3 = -6. In the third sample, there are fewer than three elements in the array, so the output is -1.

answer:def maximum_product_of_three(arr): Determine the maximum product of three distinct elements in the list. If the list contains fewer than three elements, return -1. Args: arr (list of int): The input list of integers. Returns: int: The maximum product of three distinct elements or -1 if not feasible. if len(arr) < 3: return -1 arr.sort() # Maximum product can be from either: # 1. The product of the three largest numbers # 2. The product of the two smallest numbers (which might be negative) and the largest number max_product = max(arr[-1] * arr[-2] * arr[-3], arr[0] * arr[1] * arr[-1]) return max_product

question:A new tech company is setting up its office with N servers to handle large volumes of data. These servers need to be connected in a way such that any server can communicate with any other server either directly or indirectly. The administration plans to connect these servers using network cables, and each cable can directly connect two servers. Your task is to determine the minimum number of cables required to connect all N servers in such a way that every server is reachable from any other server. Input: First line will contain integer T - number of test cases. Next T lines each will contain a single integer N - number of servers. Output: Print the minimum number of cables required for each test case in a new line. Constraints: 1 ≤ T ≤ 10000 1 ≤ N ≤ 1000000000 (10^9) SAMPLE INPUT: 3 4 5 1 SAMPLE OUTPUT: 3 4 0 Explanation: For 4 servers, you need a minimum of 3 cables to connect them in a linear fashion. For 5 servers, you need a minimum of 4 cables. If there is only 1 server, no cables are required.

answer:def min_cables(N): This function calculates the minimum number of cables required to connect N servers in such a way that they are all reachable from each other. return max(0, N - 1)