IT5001 Lab 6 -Multi-dimensional Arrays Solution

Part 1 Matrix Operations
In this part, you can assume that all matrix entries are integers.
Task 1 Transpose
Write a function transpose(m) that takes in a matrix m with dimensions r x c and returns the transpose of m which has dimensions c x r.
>>> pprint(m)
[[1, 1, 1, 0, 1, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 1, 1, 0, 0, 0, 1, 1, 0],
[0, 1, 1, 1, 1, 0, 0, 0, 1, 1]]
>>> pprint(transpose(m)) [[1, 1, 0, 0],
[1, 0, 0, 1],
[1, 1, 1, 1],
[0, 0, 1, 1],
[1, 0, 0, 1],
[0, 0, 0, 0],
[0, 1, 0, 0],
[1, 0, 1, 0],
[0, 0, 1, 1],
[1, 0, 0, 1]]
Task 2 Multiplication
Write a function matMul(m1,m2) that returns the result of multiplying matrix m1 by m2.
>>> m1 = [[1,2,3],[5,6,7],[9,10,11],[13,14,15]]
>>> m2 = [[4,3,2,1,8,1],[1,2,3,4,3,1],[5,6,7,8,1,2]]
>>> pprint(matMul(m1,m2))
[[21, 25, 29, 33, 17, 9],
[61, 69, 77, 85, 65, 25],
[101, 113, 125, 137, 113, 41],
[141, 157, 173, 189, 161, 57]]
Task 3 Minor Matrix
Write a function minorMatrix(m,i,j) that returns the minor matrix of m without row i and column j.
>>> pprint(m)
[[21, 25, 29, 33, 17, 9],
[61, 69, 77, 85, 65, 25],
[101, 113, 125, 137, 113, 41],
[141, 157, 173, 189, 161, 57]]
>>> pprint(minorMatrix(m,2,3))
[[21, 25, 29, 17, 9], [61, 69, 77, 65, 25], [141, 157, 173, 161, 57]]
Task 4 Determinant
Write a function det(m) that returns the determinant of matrix m.
>>> m = [[6,1,1],[4,-2,5],[2,8,7]]
>>> det(m)
-306
>>> m = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]
>>> det(m)
0
Part 2 Maze
Let’s assume a maze is an r x c grid that consists of 0s and 1s, where 0 represents an empty space and 1 represents a blocked space.
Task 1 Random Maze
Write a function createRandomMaze(r,c) which returns a maze of size r x c where every space has an equal random chance of being empty or blocked.
>>> maze = createRandomMaze(8,14)
>>> mTightPrint(maze)
01111111010011
00000001000000
10000100100000
10110010000010
00001100011001
10000101010100
10001001011000
10010100110100
Task 2 Solvable
Suppose you can enter a r x c maze from its top left corner at position (0,0) and exit from its lower right corner at position (r-1,c-1). Write a function isSolvableMaze(m) that takes in a maze m and returns True if you can eventually reach the exit from the entrance, and False otherwise. In other words, determine if the maze is solvable. (You can only move horizontally or vertically, not diagonally.)
Extra Tasks
• Write some code to find a maze generated by Task 1 that has a size of 15 x 30 and is also solvable.
• Other than mTightPrint(), write your own function to beautify your maze presentation.
• When you find out a maze is solvable, leave a trace (e.g. replace the space with a ‘.’) to show the path found.