Discrete Math 2-1 Copyright © Genetic Computer School 2007 Lesson 2 More uses of Matrices Arrays.

Copyright © Genetic Computer School 2007 Discrete Math 2-1

Lesson 2

More uses of Matrices Arrays


Lesson 2 Overview

Building arrays from raw dataAdding rows or columnsArray arithmeticArrays for pricingMore about matrices

An array exampleBinary treesBack and trace pointersNetworksNetworks as arrays


Building arrays from raw data

One dimension arrayArr: array[1..3] of Real=

(10.25, -20.15, 30.85);

Multi-dimension array Arr: array[1..2,1..3] of Real=

((10.25, -20.15, 30.85), (14.50, 14.45, 10.75));


Adding rows or columns

Var arr:Array[1..2,1..3] of Integer;…(* adding row 2 *)Result:=0;For i:=1 to 3 do

Result:=Result + arr[2][i];


Array arithmetic

Add/Subtract arrays: Arrays must be same format (same number of columns and number of rows) “Scalar" multiplication: Multiply the “scalar” with all elements of the array Multiply two array: in order to multiply arrays A and B the number of columns in A must equal the number of rows in B


Arrays for pricing

Array multiplication for order costing

178

106

205

195

6

9

2

13

8

201983

38401

212734

82457


More about matrices

The common operations on a matrix Add a constant vector/matrix to a matrix Multiply/divide a scalar to a matrix Add/Subtract from another matrix Cell-by-cell multiplication Multiply by a row/column vector Multiply, selectively, by a square matrix Multiply by another matrix


An array example

“A manufacturing company, in factories at Andover and Bristol respectively, employs the following numbers of people in 4 grades for each of 6 job-categories and at different monthly pay scales”


Binary trees

1

2

3

4

5


Binary treesGreat-Great-Grand-parents

Great-Grand-parents

Grand-parents

Parents

Sons and Daughters


Back and trace pointers

BACK POINTERS can be added to each node so that it is possible to work up the tree from any node to trace its ancestors.TRACE POINTER can also be added which, from any node, would allow to trace the next in alphabetical (or numerical) sequence.


Networks

A

B

C

D


Networks as arrays

Star networkA B C D

A 0 1 1 1S = B 1 0 0 0

C 1 0 0 0D 1 0 0 0


Networks as arrays

RingA B C D

A 0 0 0 0R = B 0 0 1 1

C 0 1 0 1D 0 1 1 0


Networks as arrays

LANA B C D

A 0 0 1 1L = B 0 0 0 0

C 1 0 0 1D 1 0 1 0

Discrete Math 2-1 Copyright © Genetic Computer School 2007 Lesson 2 More uses of Matrices Arrays.

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Transcript of Discrete Math 2-1 Copyright © Genetic Computer School 2007 Lesson 2 More uses of Matrices Arrays.