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question:A small town has recently started its own public transportation system consisting of several bus routes. Each bus route runs on a specific schedule and covers certain stops. The i-th bus route starts at stop ai, ends at stop bi, and can transport pi passengers at a time. The town also has several bus stops where passengers wait. Each bus stop can have a different number of passengers waiting to board the bus. Specifically, there are n bus stops, and the j-th bus stop has qj passengers waiting. Your task is to determine the most efficient bus route to accommodate the largest number of passengers. The efficiency of a bus route is defined as the minimum between the number of passengers the bus can carry and the number of passengers waiting at the busiest stop within its range. The goal is to find the bus route that maximizes this efficiency. If multiple routes yield the same efficiency, you can choose any of them. The first line contains two integers n (1 ≤ n ≤ 100 000) — the number of bus stops, and r (1 ≤ r ≤ 100) — the number of bus routes. Each of the following n lines contains one integer qj (0 ≤ qj ≤ 100 000) — the number of passengers waiting at the j-th bus stop. Each of the following r lines contains three integers ai, bi, pi (1 ≤ ai ≤ bi ≤ n, 1 ≤ pi ≤ 100 000) — representing the start and end stops of the corresponding bus route, and the number of passengers the bus can carry. Print an integer representing the maximum possible efficiency. If it's not possible to board any passengers, print zero. In the first sample, the most efficient bus route is the third one, which can accommodate a minimum of 7 passengers either due to its capacity or due to the busiest stop within its range. The efficiency in this case is 7. In the second sample, none of the bus routes overlap with any bus stops that have waiting passengers, so the answer is zero.

answer:def find_most_efficient_bus_route(n, r, passengers_waiting, bus_routes): max_efficiency = 0 for a, b, p in bus_routes: max_passengers_waiting = max(passengers_waiting[a - 1:b]) efficiency = min(max_passengers_waiting, p) if efficiency > max_efficiency: max_efficiency = efficiency return max_efficiency # Example usage: n = 5 r = 3 passengers_waiting = [2, 5, 6, 3, 7] bus_routes = [(1, 3, 5), (2, 4, 6), (3, 5, 8)] print(find_most_efficient_bus_route(n, r, passengers_waiting, bus_routes)) # Output: 7

question:A newly opened zoo has just set up its Automated Ticketing System (ATS). The ATS issues tickets with a unique ticket number represented by a string of uppercase English letters. The ticket numbers are generated in such a way that each alphabet can be used infinite number of times independent of others. The zoo managers have recognized that tickets that contain certain substrings are considered lucky. Thus, if a tourist's ticket number contains any of these lucky substrings, they are considered VIP guests and will receive special treatment. The format of each input is a unique string of uppercase letters representing the ticket number. Write a function `find_lucky_substrings(ticket: str, lucky_substrings: List[str]) -> List[str]` that takes two arguments: - `ticket` which is the unique ticket number (1 <= len(ticket) <= 1000) - `lucky_substrings` which is a list of strings representing the lucky substrings (1 <= len(lucky_substrings) <= 100, 1 <= len(lucky_substrings[i]) <= 10). The function should return a list of all lucky substrings that are found within the ticket number. If no lucky substrings are found, return an empty list. **Example** Input: ``` ticket = "ZOOLOGIST" lucky_substrings = ["ZOO", "LOG", "CAT", "STI"] ``` Output: ``` ["ZOO", "LOG"] ``` **Explanation** In the given example, only "ZOO" and "LOG" are found as substrings in the ticket number "ZOOLOGIST". The substrings "CAT" and "STI" are not found in the ticket number. **Note** The returned list should contain the matching lucky substrings in the order they appear in the `lucky_substrings` list.

answer:from typing import List def find_lucky_substrings(ticket: str, lucky_substrings: List[str]) -> List[str]: Returns a list of lucky substrings that are found within the ticket number. found_substrings = [substring for substring in lucky_substrings if substring in ticket] return found_substrings

question:You are given a forest consisting of n trees. The forest is represented as an undirected graph with n vertices and k edges. Your task is to determine whether the forest can be turned into a single connected tree by adding exactly one edge. A tree is a connected undirected graph consisting of n vertices and n-1 edges. A forest is a collection of one or more trees. The first line of the input contains two integers n and k — the number of vertices and the number of edges in the undirected graph (1 ≤ n ≤ 100, 0 ≤ k ≤ n-1). Each of the following k lines contains a pair of integers u and v, indicating the existence of an edge between vertices u and v (1 ≤ u, v ≤ n, u ≠ v). Each pair of vertices will have at most one edge between them, and no edge connects a vertex to itself. Print "YES" if it's possible to turn the forest into a single tree by adding exactly one edge. Otherwise, print "NO". Example: Input: 5 3 1 2 2 3 4 5 Output: YES Explanation: You can connect vertex 3 and vertex 4 to form a single tree.

answer:def can_form_single_tree(n, k, edges): Determines if a forest can be turned into a single tree by adding exactly one edge. :param n: int, number of vertices :param k: int, number of edges :param edges: List of tuples where each tuple is a pair of connected vertices. :return: str, "YES" if possible, otherwise "NO" if k != n - 2: return "NO" parent = list(range(n)) def find(x): if parent[x] != x: parent[x] = find(parent[x]) return parent[x] def union(x, y): rootX = find(x) rootY = find(y) if rootX != rootY: parent[rootY] = rootX for u, v in edges: union(u-1, v-1) root_count = len(set(find(i) for i in range(n))) return "YES" if root_count == 2 else "NO"

question:In a land called Codevalley, there are `n` towns connected by `m` bidirectional roads. The governor of Codevalley, Ada, wants to install security cameras on some of the towns. Each camera can monitor the town it is installed in as well as all neighboring towns directly connected by a road. Ada wants to minimize the number of cameras installed but still ensure that all towns are monitored. You are provided with the following information: - The number of towns `n` and the number of roads `m` (1 ≤ n, m ≤ 100). - A list of `m` pairs of integers, each pair representing a road connecting two towns. Your task is to determine the minimum number of cameras needed and the towns where the cameras should be installed. The input starts with two integers `n` and `m`, representing the number of towns and roads, respectively. This is followed by `m` pairs of integers where each pair `(u, v)` indicates that there is a road between town `u` and town `v`. Output the minimum number of cameras needed. If multiple solutions exist, output any one of them. In the first line, output a single integer, the number of cameras installed. In the second line, output the towns where the cameras should be installed, separated by spaces. Example input: ``` 5 4 1 2 2 3 3 4 4 5 ``` Example output: ``` 2 2 4 ``` In this example, installing cameras in towns 2 and 4 would be sufficient to monitor all the towns.

answer:def find_minimum_cameras(n, m, roads): # Build the adjacency list representation of the graph from collections import defaultdict adj = defaultdict(list) for u, v in roads: adj[u].append(v) adj[v].append(u) # Visited array to track nodes that are monitored monitored = [False] * (n + 1) # Greedily choose nodes with maximum degree, this works well for dense graphs degree = {i: len(adj[i]) for i in range(1, n + 1)} sorted_nodes = sorted(degree, key=degree.get, reverse=True) cameras = [] for node in sorted_nodes: if not monitored[node]: # Place a camera in this town cameras.append(node) monitored[node] = True for neighbor in adj[node]: monitored[neighbor] = True return len(cameras), cameras # Function to parse input and return as needed def parse_input(input_str): input_lines = input_str.strip().split('n') n, m = map(int, input_lines[0].split()) roads = [tuple(map(int, line.split())) for line in input_lines[1:]] return n, m, roads # Function to convert output to required format def output_result(cameras): count, towns = cameras result_str = f"{count}n" + " ".join(map(str, towns)) return result_str