https://x.com/cstominaga/status/1850700158981505122?s=61
https://x.com/cstominaga/status/1850700158981505122?s=61
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!s Dijkstra’s algorithm
Dijkstra's algorithm is a fundamental algorithm in computer science used to find the shortest paths between nodes in a graph, particularly from a single source node to all other nodes. It works with graphs that have non-negative edge weights.
**How It Works:**
1. **Initialization:** Start by assigning a tentative distance value to every node: set it to zero for the initial node and infinity for all other nodes. Set the initial node as current.
2. **Visit Neighboring Nodes:** For the current node, consider all of its unvisited neighbors and calculate their tentative distances through the current node. Compare the newly calculated tentative distance with the current assigned value and assign the smaller one.
3. **Mark as Visited:** After considering all of the neighbors of the current node, mark it as visited. A visited node will not be checked again.
4. **Select the Next Current Node:** Select the unvisited node with the smallest tentative distance and set it as the new current node.
5. **Repeat:** Repeat steps 2-4 until all nodes have been visited. The algorithm ends when the shortest paths to all nodes have been determined.
**Key Characteristics:**
- **Greedy Approach:** The algorithm always selects the node with the smallest known distance from the starting node.
- **Non-negative Weights:** It requires that all edge weights be non-negative; negative weights can lead to incorrect results.
- **Single-Source Shortest Path:** Primarily used to compute the shortest paths from one node to all other nodes in the graph.
**Applications:**
- **Navigation Systems:** Calculating the shortest route in mapping software.
- **Network Routing Protocols:** Determining the most efficient paths for data transmission.
- **Game Development:** Finding the shortest paths for characters or objects in a virtual environment.
Dijkstra's algorithm is valued for its efficiency and simplicity, making it a go-to choice for many shortest path problems in various domains.