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question:You are given an array A of N integers. Your task is to find the minimum sum of the elements of array A after performing the following operations exactly once: - Split the array A into two non-empty sub-arrays, say B and C, such that B + C = A. - Reverse the sub-array C. For example, if A = [1, 2, 3, 4], one possible way to split A and reverse C is: - Split A into B = [1, 2] and C = [3, 4] - Reverse C to get C = [4, 3] - The result of merging B and C is [1, 2, 4, 3] Your task is to select the split point such that the sum of the resulting merged array is minimized. ------ Input Format ------ - The first line of input contains a single integer T, denoting the number of test cases. - Each test case consists of two lines of input. - The first line contains an integer N — the size of the array A. - The second line contains N space-separated integers which represent the array A. ------ Output Format ------ For each test case, output the minimum sum of the elements of array A after performing the specified operation. ------ Constraints ------ 1 ≤ T ≤ 10 2 ≤ N ≤ 10^{5} # Clarifying that the array has at least two elements 1 ≤ A_{i} ≤ 10^{4} # Clarifying the constraints on array elements ------ Sample Input 1 ------ 2 4 1 2 3 4 3 3 1 2 ------ Sample Output 1 ------ 10 6 ------ Explanation 1 ------ Test case 1: The possible splits are: - B = [1], C = [2, 3, 4] -> Merged array = [1, 4, 3, 2], Sum = 10 - B = [1, 2], C = [3, 4] -> Merged array = [1, 2, 4, 3], Sum = 10 - B = [1, 2, 3], C = [4] -> Merged array = [1, 2, 3, 4], Sum = 10 Hence, the minimum sum is 10. Test case 2: The possible splits are: - B = [3], C = [1, 2] -> Merged array = [3, 2, 1], Sum = 6 - B = [3, 1], C = [2] -> Merged array = [3, 1, 2], Sum = 6 Hence, the minimum sum is 6.

answer:def minimum_sum_after_split_and_reverse(T, test_cases): Returns the minimum sum of the elements of array A after performing the specified split and reverse operations once per each test case. Parameters: T (int): Number of test cases test_cases (list): List containing tuples, each containing an integer N and a list A of N integers Returns: list: List of integers representing the minimum sum of elements for each test case results = [] for test_case in test_cases: N, A = test_case # Since the problem description guarantees the array A and the split of A has no impact on the sum, # Just summarize the array, as sum remains constant. total_sum = sum(A) results.append(total_sum) return results

question:Intra-Galactic Transport Optimization The Space Transport Authority (STA) manages transportation schedules within the Milky Way galaxy. Due to recent space trade expansion, they need to optimize transport routes between planets. Each planet is represented as a node, and each direct space route between two planets is an edge with a certain travel cost. The goal is to determine the shortest travel cost between a given pair of planets considering the possibility of multiple stops along the way. In this problem, you are asked to implement an algorithm that finds the shortest path between two specified planets in a weighted graph representing the galaxy's transport network. You will be given a series of datasets. Each dataset consists of: - An integer N, the number of planets (nodes). The planets are numbered from 1 to N. - An integer M, the number of direct routes (edges) between the planets. - M triplets in the form "U V W", where U and V are the planetary nodes connected by a direct route, and W is the travel cost associated with that route. - Two integers S and T, the indices of the start and target planets for which you need to determine the shortest path cost. Your task is to compute the minimum travel cost from planet S to planet T. If there is no path between S and T, output "UNREACHABLE". Input The input consists of multiple datasets. Each dataset uses the following format: ``` N M U1 V1 W1 U2 V2 W2 ... UM VM WM S T ``` Here: - 2 ≤ N ≤ 500 - 1 ≤ M ≤ 10000 - 1 ≤ Ui, Vi ≤ N - 0 ≤ Wi ≤ 1000 - 1 ≤ S, T ≤ N The input ends with a line containing only the integer -1. Output For each dataset, output the shortest travel cost from S to T. If there is no path from S to T, output "UNREACHABLE". Sample Input ``` 5 6 1 2 10 1 3 5 2 3 2 3 4 2 2 4 5 4 5 1 1 5 3 2 1 2 3 2 3 4 1 3 6 3 1 2 7 1 3 9 4 5 6 1 4 -1 ``` Sample Output ``` 8 7 UNREACHABLE ``` Requirements: - Design an efficient algorithm to handle the constraints smoothly. - Use appropriate graph algorithms to compute the shortest path effectively.

answer:import heapq def dijkstra(graph, start, end, n): Find the shortest path from start to end in a graph using Dijkstra's algorithm. :param graph: The adjacency list of the graph where graph[u] contains (v, w) pairs. :param start: The starting node. :param end: The target node. :param n: The number of nodes. :return: The shortest path cost or 'UNREACHABLE'. distances = {node: float('infinity') for node in range(1, n+1)} distances[start] = 0 priority_queue = [(0, start)] while priority_queue: current_distance, current_node = heapq.heappop(priority_queue) if current_distance > distances[current_node]: continue for neighbor, weight in graph[current_node]: distance = current_distance + weight if distance < distances[neighbor]: distances[neighbor] = distance heapq.heappush(priority_queue, (distance, neighbor)) return distances[end] if distances[end] != float('infinity') else 'UNREACHABLE' def intra_galactic_transport(inputs): index = 0 results = [] while index < len(inputs): line = inputs[index] if line == '-1': break N, M = map(int, line.split()) index += 1 graph = {i: [] for i in range(1, N+1)} for _ in range(M): U, V, W = map(int, inputs[index].split()) graph[U].append((V, W)) graph[V].append((U, W)) # Assuming the routes are bidirectional index += 1 S, T = map(int, inputs[index].split()) index += 1 result = dijkstra(graph, S, T, N) results.append(str(result)) return results

question:Given a list of n strings where each string consists of lowercase English letters, determine the length of the longest common prefix shared by all the strings in the list. A common prefix of a given set of strings is the longest sequence of characters that each of the strings shares, starting from the first character. -----Input----- - The first line contains an integer n (1 leq n leq 10^5), the number of strings. - The next n lines each contain a string of length between 1 and 100, consisting of only lowercase English letters. -----Output----- - Print an integer, the length of the longest common prefix of the given strings. -----Examples----- Sample Input 1: 3 flower flow flight Sample Output 1: 2 Sample Input 2: 4 dog racecar car plane Sample Output 2: 0 Sample Input 3: 2 prefix prelude Sample Output 3: 3

answer:def longest_common_prefix(strings): Returns the length of the longest common prefix in a list of strings. Parameters: strings (list of str): A list of strings to find the longest common prefix. Returns: int: Length of the longest common prefix. if not strings: return 0 # Find the shortest string in the list shortest_str = min(strings, key=len) for i in range(len(shortest_str)): char = shortest_str[i] for string in strings: if string[i] != char: return i return len(shortest_str)

question:A group of islands are connected by various bridges. Each bridge has a unique ID and a specific weight (cost) associated with it. Given a list of bridges and their weights, your task is to determine the minimum cost required to connect all the islands using a subset of the bridges, ensuring the islands are all connected directly or indirectly. You are given a list of tuples, where each tuple represents a bridge and contains three integers: - the ID of the island from which the bridge starts, - the ID of the island to which the bridge leads, - and the weight of the bridge. Write a function `minimalBridgeCost(n, bridges)` where `n` is the number of islands and `bridges` is a list of tuples representing the bridges. Return the minimum cost to connect all islands. Example n=4 bridges=[(0, 1, 10), (0, 2, 6), (0, 3, 5), (1, 3, 15), (2, 3, 4)] The minimum cost to connect all islands is 19. Function Description Complete the minimalBridgeCost function in the editor below. minimalBridgeCost has the following parameters: int n: the number of islands list bridges: a list of tuples where each tuple contains three integers representing a bridge: (island1, island2, weight). Returns int: the minimum cost required to connect all islands. Input Format The input consists of two lines. The first line contains an integer n, the number of islands (numbered from 0 to n-1). The second line contains a list of tuples where each tuple represents a bridge and contains three integers: the starting island, the ending island, and the weight of the bridge. Constraints 1 <= n <= 1000 1 <= weight <= 1000 1 <= len(bridges) <= 10000 Sample Input 4 [(0, 1, 10), (0, 2, 6), (0, 3, 5), (1, 3, 15), (2, 3, 4)] Sample Output 19 Explanation: The minimum cost to achieve a connected set of islands involves using the bridges with weights (0,3, 5), (2,3, 4), (0,1, 10), resulting in a total cost of 5+4+10=19.

answer:def minimalBridgeCost(n, bridges): Returns the minimum cost required to connect all islands. :param n: int, the number of islands :param bridges: list of tuples, where each tuple contains three integers representing a bridge (island1, island2, weight) :return: int, minimum cost required to connect all islands parent = list(range(n)) rank = [0] * n def find(p): if parent[p] != p: parent[p] = find(parent[p]) return parent[p] def union(p1, p2): root1 = find(p1) root2 = find(p2) if root1 != root2: if rank[root1] > rank[root2]: parent[root2] = root1 elif rank[root1] < rank[root2]: parent[root1] = root2 else: parent[root2] = root1 rank[root1] += 1 # Sort bridges by their weight bridges.sort(key=lambda x: x[2]) mst_cost = 0 mst_edges = 0 for u, v, weight in bridges: if find(u) != find(v): union(u, v) mst_cost += weight mst_edges += 1 if mst_edges == n - 1: break return mst_cost

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