Step by Step solution about How to resolve the algorithm 2048 step by step in the Mathematica/Wolfram Language programming language

Wolfram Language Program for Visualizing 2D Matrices

This program written in Wolfram Language allows you to create and visualize 2D matrices and manipulate them using arrow keys. Here's a detailed explanation of the code:

1. Event Actions for Notebook:

SetOptions[InputNotebook[], NotebookEventActions->{
"LeftArrowKeyDown":>(stat=Coalesce[stat];AddNew[]),
"RightArrowKeyDown":>(stat=Reverse/@Coalesce[Reverse/@stat];AddNew[]),
"UpArrowKeyDown":>(stat=Coalesce[stat\[Transpose]]\[Transpose];AddNew[]),
"DownArrowKeyDown":>(stat=(Reverse/@(Coalesce[Reverse/@(stat\[Transpose])]))\[Transpose];AddNew[])
}
];

This code sets event actions for the notebook. When the left arrow key is pressed, it calls the AddNew function; the right arrow key calls AddNew after reversing the matrix; the up arrow key transposes the matrix and calls AddNew; and the down arrow key transposes the matrix, reverses it, and calls AddNew.

2. Initialization:

n=4;
bgcolor=GrayLevel[0.84];
colorfunc=Blend[{{0,Gray},{1/2,Red},{1,Blend[{Yellow,Orange}]}},#]&;

• n is set to 4, which defines the size of the square matrix (n×n).
• bgcolor is the background color of the matrix.
• colorfunc is a function that assigns colors to matrix elements based on their values.

3. Functions:

a. AddNew:

AddNew[]:=(stat=AddRandomNumber[stat])

Adds a random number (either 2 or 4) to a random empty position in the matrix stat.

b. PrintStat:

PrintStat[stat_]:=Module[{gr1,gr2,gr3,dr=0.2,cols,nstat=stat,positions},

This function is responsible for visualizing the matrix. It creates graphics objects gr1 (background rectangle), gr2 (colored rectangles representing matrix elements), and gr3 (text labels for non-zero elements).

c. Coalesce and SubCoalesce:

Coalesce[stat_]:=SubCoalesce/@stat
SubCoalesce[statlist_]:=...

These functions combine adjacent equal elements in the matrix. Coalesce calls SubCoalesce on each row of the matrix. SubCoalesce iterates over the row and combines consecutive equal elements, updating the values in the row.

d. AddRandomNumber:

AddRandomNumber[stat_,n_:2]:=With[{pos=Position[stat,0,{2}]},If[Length[pos]>0,ReplacePart[stat,RandomChoice[pos]->n],stat]]

This function adds a random number (either 2 or 4) to a random empty position in the matrix stat. It takes an optional parameter n to specify the number to add (default value is 2).

4. Main Execution:

stat=Nest[AddRandomNumber[#,RandomChoice[{2,4}]]&,ConstantArray[0,{n,n}],4];
Dynamic[PrintStat@stat]

• stat is initialized as a 4×4 matrix of zeros.
• Nest applies AddRandomNumber to the matrix 4 times, adding random numbers to empty positions.
• Dynamic displays an interactive visualization of the matrix that updates in real-time as the matrix changes.

SetOptions[InputNotebook[],NotebookEventActions->{
"LeftArrowKeyDown":>(stat=Coalesce[stat];AddNew[]),
"RightArrowKeyDown":>(stat=Reverse/@Coalesce[Reverse/@stat];AddNew[]),
"UpArrowKeyDown":>(stat=Coalesce[stat\[Transpose]]\[Transpose];AddNew[]),
"DownArrowKeyDown":>(stat=(Reverse/@(Coalesce[Reverse/@(stat\[Transpose])]))\[Transpose];AddNew[])
}
];

n=4;
bgcolor=GrayLevel[0.84];
colorfunc=Blend[{{0,Gray},{1/2,Red},{1,Blend[{Yellow,Orange}]}},#]&;

ClearAll[AddNew,PrintStat,Coalesce,SubCoalesce,AddRandomNumber]
AddNew[]:=(stat=AddRandomNumber[stat])
PrintStat[stat_]:=Module[{gr1,gr2,gr3,dr=0.2,cols,nstat=stat,positions},
gr1={bgcolor,Rectangle[-dr{1,1},n+dr{1,1},RoundingRadius->dr]};
cols=Map[If[#==0,0,Log2[#]]&,nstat,{2}];
cols=Map[If[#==0,Lighter@bgcolor,colorfunc[#/Max[cols]]]&,cols,{2}];
positions=Table[{i,n-j+1},{j,n},{i,n}];
gr2=MapThread[{#2,Rectangle[#3-{1,1}(1-dr/3),#3-{1,1}dr/3,RoundingRadius->dr/2]}&,{stat,cols,positions},2];
gr3=MapThread[If[#1>0,Style[Text[#1,#2-0.5{1,1}],20,White],{}]&,{stat,positions},2];
Graphics[{gr1,gr2,gr3},PlotRange->{{-0.5,n+0.5},{-0.5,n+0.5}},ImageSize->500]
]
Coalesce[stat_]:=SubCoalesce/@stat
SubCoalesce[statlist_]:=Module[{st=statlist,n=Length[statlist],pairs},
st=Split[DeleteCases[st,0]];
st=Partition[#,2,2,1,{}]&/@st;
st=Map[If[Length[#]==2,Total[#],#]&,st,{2}];
Join[Flatten[st],ConstantArray[0,n-Length[Flatten[st]]]]
]
AddRandomNumber[stat_,n_:2]:=With[{pos=Position[stat,0,{2}]},If[Length[pos]>0,ReplacePart[stat,RandomChoice[pos]->n],stat]]

stat=Nest[AddRandomNumber[#,RandomChoice[{2,4}]]&,ConstantArray[0,{n,n}],4];
Dynamic[PrintStat@stat]