Unexpected Results When Implementing Dijkstra's Algorithm in C++ with Priority Queue
I'm working on a project and hit a roadblock. I've been struggling with this for a few days now and could really use some help... I'm trying to implement Dijkstra's algorithm in C++ to find the shortest path in a weighted graph, but I'm encountering unexpected results. I’m using a priority queue for the vertex selection, and I thought my implementation would be efficient, but I'm getting incorrect distances for some nodes. Here's a simplified version of my code: ```cpp #include <iostream> #include <vector> #include <queue> #include <limits> using namespace std; const int INF = numeric_limits<int>::max(); void dijkstra(int start, const vector<vector<pair<int, int>>>& graph) { vector<int> distance(graph.size(), INF); priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq; distance[start] = 0; pq.push({0, start}); while (!pq.empty()) { int dist = pq.top().first; int u = pq.top().second; pq.pop(); if (dist > distance[u]) continue; // This line is crucial for (const auto& neighbor : graph[u]) { int v = neighbor.first; int weight = neighbor.second; if (distance[u] + weight < distance[v]) { distance[v] = distance[u] + weight; pq.push({distance[v], v}); } } } for (int i = 0; i < distance.size(); ++i) { cout << "Distance to " << i << ": " << distance[i] << '\n'; } } ``` The graph is represented as an adjacency list, where each entry has pairs of (neighbor vertex, edge weight). However, when I run this code with a test graph, the distances seem to jump to some arbitrary high values instead of correctly reflecting the shortest paths. I’ve verified that the graph is initialized correctly and contains no negative weights. Also, I noticed that the line `if (dist > distance[u]) continue;` seems to be causing problems. When I comment it out, the distances are more accurate but still not correct. Could there be an issue with how I'm managing the priority queue or the distance updates? Any insights on how I might fix this or improve the implementation would be greatly appreciated. I'm working on a web app that needs to handle this. Any help would be greatly appreciated! This is part of a larger service I'm building. Thanks in advance!