Question

1. An Triangular matrix is a square matrix whose elements below the diagonal are defined to be 0. For example, the matrix element Mr,c = 0 if r > c. The following is an example matrix of size 4.
   

	0	1	2	3
0	100	200	300	400
1	0	500	600	700
2	0	0	800	900
3	0	0	0	1000

While it is possible to use a regular 2D array to represent an Triangular matrix, doing so is wasteful with memory. Instead, we plan on creating an ADT that stores only the non-zero information as shown below:

   [0]      [1] [2]     [3] [4] [5]     [6] [7] [8] [9]

100

200

300

400

500

600

700

800

900

1000

   M0,0     M0,1    M0,2      M0,3     M1,1    M1,2     M1,3     M2,2     M2,3     M3,3

The basis of an effective ADT for an Triangular matrix requires two important computations:

Determine how many non-zero elements are required
Access function.

You are to write the following Python functions in a file named access.py that computes the access function for an Triangular. All of your functions should be O(1).

# Modify these functions. Add helper functions if you wish.

# These functions must be O(1).
def numNonZeros2DTriangular(N):
return 0
def access2DTriangular(N, row, col):
# return -1 if any parameters are nonsensical
return 0

Here are some examples of how your code should behave:

numNonZeros2DTriangular(4) → 10
numNonZeros2DTriangular(1) → 1
numNonZeros2DTriangular(5) → 15
access2DTriangular(4, 0, 0) → 0
access2DTriangular(4, 3, 3) → 9

access2DTriangular(4, 3, 0) → -1

YOU DO NOT HAVE TO IMPLEMENT THE ADT FOR TRIANGULAR MATRICES.

Answer 1

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