Output 1: 3 0 1 3 4 2 5 7 8 6
0 1 3
4 2 5
7 8 6
1 0 3
4 2 5
7 8 6
1 2 3
4 0 5
7 8 6
1 2 3
4 5 0
7 8 6
1 2 3
4 5 6
7 8 0
Move made: 5
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Output 2: 4 1 2 3 4 5 0 6 8 9 10 7 11 13 14 15 12
1 2 3 4
5 0 6 8
9 10 7 11
13 14 15 12
1 2 3 4
5 6 0 8
9 10 7 11
13 14 15 12
1 2 3 4
5 6 7 8
9 10 0 11
13 14 15 12
1 2 3 4
5 6 7 8
9 10 11 0
13 14 15 12
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 0
Move made: 5
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Output 3: 3 1 2 3 4 5 6 8 7 0
Unsolvable
============
How our program works: Using a priority queue, we wrap a Board object inside of a Node class. This Node class provides us the ability to combine Board's manhattan method with the current amount of moves made for a solution branch in Solver, which is ultimately our priority function. This priority function will thus be used for our Comparator function when using a PQ. We will utilize a recursive function that generates and explores the neighbors of each minimum element popped from the PQ, and ideally, this minimum branch will become our solution set.