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question:Simon lives in a town with a grid layout. The town has `n` intersections, each identified by a pair of coordinates `(xi, yi)`. Simon wants to place traffic lights at some of these intersections. However, he wants to ensure that no two intersections in a horizontal or vertical line both have traffic lights. Your task is to help him find the maximum number of intersections where he can place traffic lights without violating the above condition. The first line of input contains a single integer n (1 ≤ n ≤ 100) — the number of intersections. Each of the following n lines contains two integers xi and yi (1 ≤ xi, yi ≤ 1000) — the coordinates of the i-th intersection. All intersections' locations are distinct. Output a single integer representing the maximum number of intersections where Simon can place traffic lights. Example: Input: 5 1 1 2 2 3 3 4 4 5 5 Output: 5 Explanation: In the given sample, no two intersections fall on the same horizontal or vertical line, so traffic lights can be placed at all intersections.
answer:def max_traffic_lights(n, intersections): Find the maximum number of intersections where Simon can place traffic lights without violating the condition that no two intersections in a horizontal or vertical line both have traffic lights. Args: n (int): the number of intersections intersections (List[Tuple[int, int]]): list of intersections coordinates Returns: int: the maximum number of intersections where traffic lights can be placed rows = set() cols = set() for x, y in intersections: rows.add(x) cols.add(y) return min(len(rows), len(cols))
question:You are a risk assessment manager for an insurance company. Your company's policies are based on evaluating the potential risk scores of insured properties. Each property has a certain risk level associated with it and is characterized by a unique identification number. You are given a list of properties, each with its unique identification number and its risk score. Additionally, you are given the intervals of risk scores that correspond to different risk categories, such as low, medium, and high risk. To aid you in the evaluation, you need to write a function that processes this data and categorizes each property based on its risk score. # Input: - The first line contains three integers, `n`, `m`, and `k`: - `n` (1 ≤ n ≤ 10⁵): the number of properties. - `m` (1 ≤ m ≤ 10³): the number of unique risk categories. - `k` (1 ≤ k ≤ 10⁵): the number of category intervals. - The next line contains `n` integers, each representing the risk scores of the properties. - The following `n` lines contain two integers each: - The unique identification number of the property. - Its corresponding risk score. - The last `m` lines contain three values each: - A string describing the risk category (e.g., "Low" or "Medium" or "High"). - Two integers representing the inclusive range of risk scores for that category. - `k` integers representing the intervals within which the properties fall for that given range. Your task is to categorize each property into one of the risk categories based on its risk score and the provided intervals. # Output: - Print the unique identification number of each property followed by its respective risk category. # Example: Input: ``` 5 3 4 150 300 450 600 750 1001 150 1002 300 1003 450 1004 600 1005 750 Low 100 299 100 199 250 Medium 300 599 300 399 450 High 600 899 600 799 50 ``` Output: ``` 1001 Low 1002 Medium 1003 Medium 1004 High 1005 High ``` # Notes: - Each property will have a distinct identification number. - Each risk category will have a unique range of risk scores. - The intervals provided will cover all the risk scores without overlap, but all properties will have their scores falling into exactly one of the k partitions of the stated intervals. Write an efficient algorithm to determine the appropriate risk category for each property based on their risk score and the intervals provided for each range.
answer:def categorize_properties(n, m, k, risk_scores, properties, categories): # Create a dictionary to map property id to its risk score property_dict = {pid: score for pid, score in properties} # Initialize result list to store the final categories of properties result = [] # Iterate over each property to determine its category for pid, score in properties: for category in categories: category_name = category[0] lower_bound = category[1] upper_bound = category[2] if lower_bound <= score <= upper_bound: result.append(f"{pid} {category_name}") break # Return the result as a list of strings return result
question:The festival organizers are planning a musical event across several stages, and they want to ensure that the performances on different stages do not overlap as much as possible, so attendees can enjoy multiple performances. Each stage has its list of performances, and each performance has a start and end time. The goal is to determine the maximum number of performances a single attendee can watch if they can move from one stage to another without any travel time. Each performance is represented by a tuple (stage, start_time, end_time), where - stage is a string identifying the stage where the performance is happening, - start_time and end_time are integers (in minutes past midnight) representing when the performance begins and ends, respectively. Given a list of performances, write a program to find the maximum number of non-overlapping performances an attendee can watch. Input: - The first line contains an integer N (1 ≤ N ≤ 1000) representing the number of performances. - The next N lines each contain a string and two integers, `stage`, `start_time`, and `end_time`, separated by spaces. Output: - Print the maximum number of non-overlapping performances an attendee can watch. Example: Input: 5 MainStage 0 30 MainStage 35 45 Stage1 0 15 Stage1 20 30 MainStage 50 70 Output: 4 Explanation: One possible way to watch the maximum number of performances is: Watch performance 1 (MainStage: 0-30) Move to Stage1 and watch performance 3 (Stage1: 0-15) Watch performance 4 (Stage1: 20-30) Go back to MainStage and watch performance 5 (MainStage: 50-70)
answer:def max_non_overlapping_performances(performances): Finds the maximum number of non-overlapping performances an attendee can watch. Args: performances: list of tuples, where each tuple contains a performance identified by (stage, start_time, end_time) Returns: int: maximum number of non-overlapping performances # Sort performances by end time performances.sort(key=lambda x: x[2]) max_count = 0 last_end_time = -1 # Loop through the sorted performances and count non-overlapping ones for stage, start_time, end_time in performances: if start_time >= last_end_time: max_count += 1 last_end_time = end_time return max_count # Example usage: N = 5 performances = [ ('MainStage', 0, 30), ('MainStage', 35, 45), ('Stage1', 0, 15), ('Stage1', 20, 30), ('MainStage', 50, 70) ] print(max_non_overlapping_performances(performances)) # Output: 4
question:Given two strings, you are to determine if they are isomorphic. Two strings are isomorphic if the characters in one string can be replaced to get the other string, preserving the order of characters. More formally, the strings 'egg' and 'add' are isomorphic because 'e' can be replaced with 'a' and 'g' can be replaced with 'd'. However, 'foo' and 'bar' are not isomorphic because 'f' mapping to 'b' and 'o' mapping to both 'a' and 'r' results in a contradiction. Write a function to determine if two strings are isomorphic. The function should return true if the strings are isomorphic, and false otherwise. The input consists of two lines: - The first line contains a string s of length n (1 le n le 100,000). - The second line contains a string t of length m (1 le m le 100,000). Print "yes" if the strings are isomorphic, and "no" otherwise. # Example Input ``` egg add ``` # Example Output ``` yes ``` # Example Input ``` foo bar ``` # Example Output ``` no ``` # Example Input ``` ab aa ``` # Example Output ``` no ```
answer:def is_isomorphic(s, t): Determines if two strings s and t are isomorphic. Args: s (str): First string. t (str): Second string. Returns: str: "yes" if the strings are isomorphic, "no" otherwise. if len(s) != len(t): return "no" s_to_t = {} t_to_s = {} for c1, c2 in zip(s, t): if c1 in s_to_t and s_to_t[c1] != c2: return "no" if c2 in t_to_s and t_to_s[c2] != c1: return "no" s_to_t[c1] = c2 t_to_s[c2] = c1 return "yes"