You want to reduce the memory used by A*. You come up with the following idea: you keep in the queue only the N best nodes (i.e, the nodes with lower costs), for some positive value of N. When the queue is full and a new node has to be stored, the worst node is deleted from the queue and removed from consideration.

1. If an admissible heuristic is used, will the modified algorithm find the optimal solution? Explain why (or why not). Are there any additional constraints?
2. If a perfect heuristic is used, i.e. for all n h(n)=h*(n), where h*(n) is the cost of the optimal path from n to goal, will the modified algorithm find the optimal solution? Explain