Explain multistage graph problem with example. Write an algorithm for multistage graph problem using forward approach.
Answer:
A multistage graph problem is to find the shortest path from a source node to a destination node in a directed, weighted graph that has its nodes divided into stages. The edges in the graph only connect nodes from one stage to the next stage, and there is no edge between nodes of the same stage or from a later stage to an earlier stage.
The general procedure to solve a multistage graph problem using forward approach is as follows:
- Start from the source node and assign its cost to zero.
- For each node in the next stage, calculate its cost as the minimum of the sum of the edge weight and the cost of the previous node in the previous stage.
- Repeat this process until reaching the destination node.
- Trace the path from the source node to the destination node by following the nodes with the minimum cost.
For example, consider the following multistage graph with four stages and seven nodes:
