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.
An Triangular matrix is a square matrix whose elements below the diagonal are defined to be...
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