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Master-Level Programming Assignment Question 1
Question: Implement Dijkstra’s shortest-path algorithm in Python for a weighted graph and return the shortest distance from a selected source vertex to every other vertex.
Expert Solution:
import heapq def dijkstra(graph, source): distances = {node: float('inf') for node in graph} distances[source] = 0 queue = [(0, source)] while queue: current_dist, node = heapq.heappop(queue) if current_dist > distances[node]: continue for neighbor, weight in graph[node]: distance = current_dist + weight if distance < distances[neighbor]: distances[neighbor] = distance heapq.heappush(queue, (distance, neighbor)) return distances
This implementation uses a priority queue to efficiently select the next vertex with the minimum tentative distance. Its time complexity is O((V + E) log V) when a binary heap is used.
Master-Level Programming Assignment Question 2
Question: Write a C++ function that determines whether a directed graph contains a cycle using depth-first search.
Expert Solution:
bool hasCycle(int node, vector<vector<int>>& graph, vector<bool>& visited, vector<bool>& active) { visited[node] = true; active[node] = true; for (int next : graph[node]) { if (!visited[next] && hasCycle(next, graph, visited, active)) return true; if (active[next]) return true; } active[node] = false; return false; }
The active array tracks vertices currently present in the DFS recursion stack. Finding an edge to an active vertex indicates a directed cycle. This approach runs in O(V + E) time.
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A strong programming assignment requires more than code that simply executes. Solutions should be logically structured, readable, appropriately documented, and tested against relevant cases. Professional assistance can help students address complicated programming tasks while maintaining academic requirements.
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