**Rook Jumping Maze Instructions**** :**
Starting at the circled cell in the upper-left corner, find a path to the goal
cell marked “G”. From each numbered cell, one may move that exact
number of cells horizontally or vertically in a straight line. How many
moves does the shortest path have?

Solution (select to reveal): [19 moves: RDLRUDRLRLUDLDRRUDD]

**Problem:** Generate and print a random *n*-by-*n* Rook Jumping Maze (RJM)
(5 £ *n*
£ 10) where there is a legal move (jump) from each non-goal state.

Let array row and column indices be (r_{min}, ..., r_{max}) and (c_{min},
..., c_{max}), respectively, where r_{max} - r_{min}+
1 = c_{max} - c_{min}+ 1 = *n*. The RJM is represented by a 2D-array of jump numbers. A
cell's *jump
number* is the number of array cells one must move in a straight line
horizontally or vertically from that cell. The start cell is located at
(r_{min}, c_{min}). For the goal cell, located at (r_{max}, c_{max}), let the jump number be zero. For all non-goal cells,
the randomly generated jump number must allow a legal move. In the example
5-by-5 maze above, legal jump numbers for the start cell are {1, 2, 3, 4},
whereas legal jump numbers for the center cell are {1, 2}. In
general, the minimum legal jump number for a non-goal cell is 1, and the maximum
legal jump number for a non-goal cell (r, c) is the maximum of r_{max} -
r, r - r_{min}, c_{max} - c, and c - c_{min}. This
defines a directed graph
where vertices are cells, edges are legal jumps, and the outdegree is 0 for the
goal cell vertex and positive otherwise.

**Input Format:** an integer 5 £ *n*
£ 10

**Output Format:**

- Initially prompt the user with "Rook Jumping Maze size (5-10)? ".
- Given valid input, print the randomly generated RJM 2D-array of jump numbers, with jump numbers separated by a single space.

**Sample Transcripts (input underlined):**

Rook Jumping Maze size (5-10)?53 2 4 4 4 3 1 2 2 2 2 1 1 2 2 1 3 2 2 1 2 4 4 3 0

Rook Jumping Maze size (5-10)? 6 5 2 1 1 1 2 4 3 4 3 1 5 5 2 3 1 4 1 3 1 2 1 4 1 3 4 1 1 4 5 4 3 4 5 2 0

Rook Jumping Maze size (5-10)? 10 6 2 4 6 6 8 3 7 2 5 3 7 1 6 2 6 8 8 8 5 8 8 7 4 3 6 5 6 5 2 1 8 1 6 1 4 5 7 5 1 7 5 6 4 5 4 1 7 4 9 3 8 4 2 3 3 3 6 4 9 8 3 1 2 3 5 1 4 5 4 5 8 3 1 7 2 7 3 5 9 9 1 4 5 7 5 7 6 8 2 4 6 3 7 6 2 5 9 1 0