Problem
1. Implement Dijkstra's algorithm using the modifiable_priority_queue.
2. Implement Prim's algorithm using the modifiable_priorty_queue.
3. A maze can be constructed from a series of concentric circles. Between the circles there are walls placed, and around the circles there are doors. The walls divide the areas between the circles into chambers, and the doors permit movement between chambers. The positions of the doors and walls are given in degrees measured counterclockwise from the horizontal. For example, the maze shown in the figure can be described as follows
Write a program that inputs a description of a maze in this format and finds the shortest path from the outside to the innermost circle. The shortest path is the one that goes through the fewest number of chambers.