In this approach, we utilize the Breadth-First Search algorithm to explore the mutation process. The problem can be transformed into finding the shortest path in an unweighted graph (where nodes are gene strings and edges represent valid transformations as per the gene bank).

Steps involved:

• Use a queue to perform the BFS starting from the startGene.
• Use a set to store visited nodes to prevent re-processing.
• The queue will store pairs representing the current gene string and the number of mutations so far.
• Iteratively explore valid mutations (one letter changes) that are in the gene bank.
• If the endGene is reached, return the mutation count.
• If the queue is exhausted without finding the endGene, return -1.

This approach aims to optimize the BFS by conducting simultaneous searches from both the start and end genes. This reduces the search space effectively.

Steps:

• Initialize forward and backward sets with the startGene and endGene, respectively.
• Use a set for the gene bank to ensure quick look-up and process unvisited genes.
• Iteratively expand the forward and backward sets, swapping as necessary to always expand the smaller set.
• If a common gene is found in both sets, return the combined step count.
• If expansion is exhausted without finding an intersection, return -1.