The shortest path problem is a classic problem in graph theory and network optimization. The goal is to find the shortest path between two specified nodes in a graph, where each edge has an associated numerical value called a weight or cost.
There are different variations of the shortest path problem, but the most common one involves finding the path with the minimum sum of edge weights. This problem is often solved using algorithms designed for graph traversal and optimization. The two most well-known algorithms for solving the shortest path problem are Dijkstra’s algorithm and the Bellman-Ford algorithm.
The shortest path problem has numerous applications, including route planning in transportation networks, network routing, and optimization in various fields.
Here’s a brief overview of each algorithm:
- Dijkstra’s Algorithm: This algorithm starts from the source node and explores the graph, iteratively selecting the node with the smallest tentative distance (sum of previously calculated distances and the edge weight) until it reaches the destination node. Dijkstra’s algorithm works well for graphs with non-negative edge weights. This works on greedy strategy.
- Bellman-Ford Algorithm: Unlike Dijkstra’s algorithm, Bellman-Ford can handle graphs with negative edge weights. It iteratively relaxes the edges, updating the shortest path estimates until convergence or the detection of a negative cycle. If a negative cycle is detected, it indicates that the problem doesn’t have a well-defined solution. Its works on dynamic programming approach [Click the following links to watch the video]
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