Content:<\/h2>\n\n- What is Dijkstra’s Shortest Path Algorithm?<\/a><\/li>\n
- How does Dijkstra’s Algorithm Work?<\/a><\/li>\n
- Step by Step explanation of Dijkstra’s Algorithm:<\/a><\/li>\n
- Implementation of Dijkstra’s Algorithm – minHeap<\/a><\/a><\/li>\n
- Implementation of Dijkstra’s Algorithm – array<\/a><\/li>\n
- An interesting information – Shared by the man himself<\/a><\/li>\n<\/ol>\n<\/div>\n
How does Dijkstra’s Algorithm Work?<\/h2>\n
Dijkstra’s algorithm works by maintaining a set of unexplored nodes and a tentative distance for each node. Initially, all nodes have a tentative distance of infinity, except for the starting node which has a tentative distance of zero. The algorithm then selects the node with the smallest tentative distance and explores all its neighbors. For each neighbor, the algorithm updates its tentative distance if the new distance is smaller than the current tentative distance. This process continues until the destination node is explored or all nodes have been explored.<\/p>\n
![\"Dijkstras](\"https:\/\/vmlogger.com\/algorithms\/wp-content\/uploads\/sites\/15\/2023\/04\/Dijkstra_Animation.gif\")
Dijkstras Algorithm Animation (Source: Wiki)<\/p><\/div>\n
Step by Step explanation of Dijkstra’s Algorithm:<\/h2>\n\n\n- Create a set of visited nodes.<\/li>\n
- Assign a tentative distance of infinity to all nodes.<\/li>\n
- Set the start node distance to zero [0].<\/li>\n
- Set the starting node as the current node.<\/li>\n
- Traverse all its neighbors and update their tentative distances if necessary.<\/li>\n
- Mark the node as visited and move to the next non-visited node.<\/li>\n
- Select the node with the smallest tentative distance and set it as the new current node. If all nodes have been visited, stop.<\/li>\n
- Repeat steps 4 to 6 until the destination node is visited.<\/li>\n
- The algorithm can be optimized by using a priority queue [minHeap<\/a>] to select the node with the smallest tentative distance instead of scanning all unexplored nodes.<\/li>\n<\/ol>\n<\/div>\n
Implementation of Dijkstra’s Algorithm<\/h2>\n
The algorithm can be implemented using a variety of data structures, but the most common implementation uses a priority queue to keep track of unexplored nodes sorted by their tentative distances. The algorithm can also be implemented using an array.
\nHere is an implementation of Dijkstra’s algorithm using Python in both data structures – minHeap<\/a> and Array.<\/p>\nDijkstra’s Algorithm implementation using minHeap<\/code><\/h2>\n
How does Dijkstra’s Algorithm Work?<\/h2>\n
Dijkstra’s algorithm works by maintaining a set of unexplored nodes and a tentative distance for each node. Initially, all nodes have a tentative distance of infinity, except for the starting node which has a tentative distance of zero. The algorithm then selects the node with the smallest tentative distance and explores all its neighbors. For each neighbor, the algorithm updates its tentative distance if the new distance is smaller than the current tentative distance. This process continues until the destination node is explored or all nodes have been explored.<\/p>\n
Dijkstras Algorithm Animation (Source: Wiki)<\/p><\/div>\n
Step by Step explanation of Dijkstra’s Algorithm:<\/h2>\n\n\n- Create a set of visited nodes.<\/li>\n
- Assign a tentative distance of infinity to all nodes.<\/li>\n
- Set the start node distance to zero [0].<\/li>\n
- Set the starting node as the current node.<\/li>\n
- Traverse all its neighbors and update their tentative distances if necessary.<\/li>\n
- Mark the node as visited and move to the next non-visited node.<\/li>\n
- Select the node with the smallest tentative distance and set it as the new current node. If all nodes have been visited, stop.<\/li>\n
- Repeat steps 4 to 6 until the destination node is visited.<\/li>\n
- The algorithm can be optimized by using a priority queue [minHeap<\/a>] to select the node with the smallest tentative distance instead of scanning all unexplored nodes.<\/li>\n<\/ol>\n<\/div>\n
Implementation of Dijkstra’s Algorithm<\/h2>\n
The algorithm can be implemented using a variety of data structures, but the most common implementation uses a priority queue to keep track of unexplored nodes sorted by their tentative distances. The algorithm can also be implemented using an array.
\nHere is an implementation of Dijkstra’s algorithm using Python in both data structures – minHeap<\/a> and Array.<\/p>\nDijkstra’s Algorithm implementation using minHeap<\/code><\/h2>\n
- \n
- Create a set of visited nodes.<\/li>\n
- Assign a tentative distance of infinity to all nodes.<\/li>\n
- Set the start node distance to zero [0].<\/li>\n
- Set the starting node as the current node.<\/li>\n
- Traverse all its neighbors and update their tentative distances if necessary.<\/li>\n
- Mark the node as visited and move to the next non-visited node.<\/li>\n
- Select the node with the smallest tentative distance and set it as the new current node. If all nodes have been visited, stop.<\/li>\n
- Repeat steps 4 to 6 until the destination node is visited.<\/li>\n
- The algorithm can be optimized by using a priority queue [minHeap<\/a>] to select the node with the smallest tentative distance instead of scanning all unexplored nodes.<\/li>\n<\/ol>\n<\/div>\n
Implementation of Dijkstra’s Algorithm<\/h2>\n
The algorithm can be implemented using a variety of data structures, but the most common implementation uses a priority queue to keep track of unexplored nodes sorted by their tentative distances. The algorithm can also be implemented using an array.
\nHere is an implementation of Dijkstra’s algorithm using Python in both data structures – minHeap<\/a> and Array.<\/p>\nDijkstra’s Algorithm implementation using
minHeap<\/code><\/h2>\n
![\"Dijkstras](\"https:\/\/vmlogger.com\/algorithms\/wp-content\/uploads\/sites\/15\/2023\/04\/Screenshot-2023-04-04-at-17.07.45-1024x131.png\")