Dijkstra Algorithm Questions Long
The Dijkstra Algorithm and the Iterative Deepening Search Algorithm are two different algorithms used in different contexts and have distinct characteristics. Here are the differences between them:
1. Purpose:
- Dijkstra Algorithm: It is primarily used to find the shortest path between a source node and all other nodes in a weighted graph.
- Iterative Deepening Search Algorithm: It is used to find the shortest path between a source node and a target node in an unweighted or weighted graph.
2. Graph Representation:
- Dijkstra Algorithm: It can be applied to both directed and undirected graphs with positive edge weights.
- Iterative Deepening Search Algorithm: It can be applied to both directed and undirected graphs, but it is commonly used for unweighted graphs.
3. Search Strategy:
- Dijkstra Algorithm: It uses a greedy approach, selecting the node with the smallest tentative distance at each step to explore the graph.
- Iterative Deepening Search Algorithm: It uses a depth-first search strategy with iterative deepening, gradually increasing the depth limit until the target node is found.
4. Memory Usage:
- Dijkstra Algorithm: It requires additional memory to store the distances from the source node to all other nodes, as well as the priority queue or min-heap to efficiently select the next node.
- Iterative Deepening Search Algorithm: It has a relatively low memory requirement as it only needs to store the current path being explored.
5. Time Complexity:
- Dijkstra Algorithm: It has a time complexity of O((V + E) log V), where V is the number of vertices and E is the number of edges in the graph.
- Iterative Deepening Search Algorithm: It has a time complexity of O(b^d), where b is the branching factor and d is the depth of the target node.
6. Optimal Solution:
- Dijkstra Algorithm: It guarantees finding the shortest path from the source node to all other nodes in the graph.
- Iterative Deepening Search Algorithm: It guarantees finding the shortest path from the source node to the target node, but it may not find the shortest path to other nodes in the graph.
In summary, the Dijkstra Algorithm is primarily used for finding the shortest path between a source node and all other nodes in a weighted graph, while the Iterative Deepening Search Algorithm is used for finding the shortest path between a source node and a target node in an unweighted or weighted graph. They differ in their purpose, graph representation, search strategy, memory usage, time complexity, and the optimality of the solution they provide.