Simple Mapping Treatise

Currently there are a lot of instances that we need to map data from the user interfaces or user interfaces to data.

premise #1: That greater number is divisible by the lower number.

#X = number of X elements

#Y = number of Y elements

Xr = X ratio against Y

Yr = Y ratio against X

R = range of single element of greater size

M = map

if #X == #Y, mapping is 1:1

if #X > #Y, mapping is Xr:Yr, where Xr > Yr

if #X < #Y, mapping is Xr:Yr, where Xr < Yr

Constant R is:

                        X/Y, where X > Y or

                        Y/X, where X < Y

Mapping from X -> Y, where X > Y:

                        X/R = q,           if q has zero remainder then M is q or

                                                If q has a remainder then M is q+ 1

                                                until X=1

Mapping from X -> Y, where X < Y:

X*R = p,          M is p - (R-1)

Example 1:

            If X=20, Y=5

            R =  20/5 = 4

            M,  X->Y :

20/4=5             = q , then 20 -> 5

19/4=4.? = q+1,  then 19->5

18/4=4.? = q+1, then 18->5

17/4=4.? = q+1, then 17->5

            So, 20,19,18,17 ->5

16/4=4 = q, then 16->4

15/4=3 = q+1, then 15->4

14/4=3.? = q+1, then 14->4

…

7/4=1.? = q+1, then 7->2

…

4/4=1 = q, then 4->1

¾= 0  = q+1, then 3->1

2/4 =0 = q+1, then 2->1

¼=0 =  q+1, then  1->1

            So, 4,3,2,1 -> 1

Example 2:

            If X=3, Y=15

            R = 15/3 = 5

            X*R = 3*5=15

                        15-(R-1) = 15-(5-1)=11

                        15-(4-1-1) = 15-(4-1)=12

                        15-(3-1) = 15-(3-1) = 13

                        …

                        15-(1-1) = 15-(1-1)=15

            So, 3 -> 11,12,13,14,15

            If X=1,

            X*R = 1*5=5

                        5-(5-1)=1

                        5-(4-1)=2

                        5-(3-1)=3

                        5-(2-1)=4

                        5-(1-1)=5

            So, 1 -> 1,2,3,4,5

                       

                       

Sample Code:

Int main()
{

UINT x=300,y=5;

                        CMapping mapper;

                        mapper.StartMap(x,y);

                        mapper.DisplayMapToTerminal();

                        CArray map;

                        mapper.FindMap(3,map);

                        mapper.DisplayFindMap(map);

                        UINT z=0;

                        mapper.FindMap(108,z);

                        cout << "\n" << z << "\n";

                        system("PAUSE");

}