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question:You are given a string of length n, consisting of lowercase English letters. We define the cost of a substring as the number of distinct letters present in that substring. Your task is to find a substring of the given string such that its cost is the maximum among all substrings of the given string with a length of k. If there are multiple substrings with the same maximum cost, return the lexicographically smallest substring. Input The first line of input contains two integers n and k (1 ≤ k ≤ n ≤ 105). The second line contains a string s of length n. Output Print the substring with the maximum cost. If there are multiple such substrings, print the lexicographically smallest one. Example Input 7 3 abcabc Output abc Input 5 2 aabbc Output ab
answer:def max_cost_substring(n, k, s): max_cost = 0 max_cost_substrings = [] for i in range(n - k + 1): substring = s[i:i + k] cost = len(set(substring)) if cost > max_cost: max_cost = cost max_cost_substrings = [substring] elif cost == max_cost: max_cost_substrings.append(substring) return min(max_cost_substrings)
question:# Problem: Shared Network Paths You and your friends are working on a distributed application. The application consists of multiple nodes connected in a network, and each node can communicate only with a specific set of nodes. To facilitate efficient resource sharing, you have designed the network such that it forms a binary tree. Each node in the tree can have at most two children: a left child and a right child. The goal is to navigate through this network to ensure connectivity from any node to the root node. Given the binary tree representation of the network, determine if a given list of nodes (identified by their unique indices) connects to the root node. The nodes are identified in a way that roots are at index 0, the left child of the root is at index 1, the right child of the root is at index 2, and so forth. # Input The input consists of: 1. An integer `n` (1 ≤ n ≤ 1000) representing the number of nodes in the network. 2. An integer `m` (1 ≤ m ≤ 1000) representing the number of nodes to be checked. 3. An array of `m` integers representing the indices of the nodes to be checked. # Output Output "YES" if all given nodes can connect to the root node, otherwise, output "NO". # Example Input: ``` 7 3 3 0 5 ``` Output: ``` YES ``` Explanation: The binary tree with 7 nodes looks like this: ``` 0 / 1 2 / / 3 4 5 6 ``` All nodes 3, 0, and 5 are either the root or have a path to the root, so the answer is "YES". Input: ``` 7 3 7 8 9 ``` Output: ``` NO ``` Explanation: Nodes 7, 8, and 9 do not exist in the binary tree of 7 nodes, so the answer is "NO". # Note Ensure to check if each node exists in the binary tree and has a path to the root node. Nodes are indexed starting from 0 up to `n-1`, and the tree structure ensures every node in the given tree can be traced back to the root.
answer:def check_nodes_connectivity(n, m, nodes_to_check): Returns "YES" if all given nodes can connect to the root node, otherwise returns "NO". # The nodes should be in the range from 0 to n - 1 for node in nodes_to_check: if node >= n: return "NO" return "YES"
question:You are given a sequence of integers. You need to process multiple queries on this sequence. Each query will ask you to find the minimum integer in a specified range of the sequence. The sequence contains n integers, and there are q queries. Each query is defined by two integers l and r, asking for the minimum integer in the sequence between the l-th and the r-th positions (1-based indexing, inclusive). Input The first line contains two integers n and q (1 ≤ n, q ≤ 100,000) — the number of elements in the sequence and the number of queries. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 10^9) — the elements of the sequence. The next q lines each contain two integers l and r (1 ≤ l ≤ r ≤ n) — the 1-based range for the corresponding query. Output For each query, output the minimum integer in the specified range in the sequence. Example Input 8 3 1 3 2 7 9 11 3 5 1 4 2 6 3 8 Output 1 2 2 Explanation In the first query, the minimum integer in the range [1, 4] is 1. In the second query, the minimum integer in the range [2, 6] is 2. In the third query, the minimum integer in the range [3, 8] is 2.
answer:def process_queries(n, q, sequence, queries): For each query, find the minimum integer in the specified range of the sequence. Parameters: n (int): Number of elements in the sequence q (int): Number of queries sequence (list of int): The sequence of integers queries (list of tuple): List of queries where each query is a tuple (l, r) Returns: list of int: The results of the queries results = [] for l, r in queries: # Convert 1-based indexing to 0-based indexing l -= 1 r -= 1 # Find the minimum in the range min_value = min(sequence[l:r+1]) results.append(min_value) return results
question:You are given a positive integer array A of length N. You need to process Q queries of the following types. Each query is represented by three integers T_i, L_i, and R_i. * T_i=1: Add 1 to each element in the subarray A[L_i…R_i]. * T_i=2: Find the maximum element in the subarray A[L_i…R_i]. Note: - Updates and queries start from indices 1 to N inclusive. Constraints * 1 ≤ N ≤ 10^5 * 1 ≤ A_i ≤ 10^9 * 1 ≤ Q ≤ 10^5 * 1 ≤ T_i ≤ 2 * 1 ≤ L_i ≤ R_i ≤ N * All input values are integers. Input Input is given from Standard Input in the following format: ``` N Q A_1 A_2 ... A_N T_1 L_1 R_1 T_2 L_2 R_2 ... T_Q L_Q R_Q ``` Output For each query with T_i=2, print the answer in a new line. Example Input ``` 5 4 1 3 2 6 4 2 1 3 1 2 4 2 2 5 2 1 5 ``` Output ``` 3 7 7 ```
answer:def process_queries(N, Q, A, queries): Process the given queries on the array A. Args: N : int : Length of the array A Q : int : Number of queries A : list : The array on which queries are performed queries: list : List of queries where each query is represented by [T_i, L_i, R_i] Returns: list : The results of the maximum element queries (T_i=2) result = [] for query in queries: T_i, L_i, R_i = query if T_i == 1: for j in range(L_i - 1, R_i): # Convert to 0-indexed A[j] += 1 elif T_i == 2: max_value = max(A[L_i - 1:R_i]) # Convert to 0-indexed result.append(max_value) return result