Hi @skjhzzang
Please have a look at the following resource, which tries to solve the N-Queens problems using several programming languages: https://rosettacode.org/wiki/N-queens_problem#SAS
You can easily put the '8' in a macrovariable inside a macro-program.
Hope this helps,
Best,
'Pure' macro is really not the environment for typical recursion and fundamental computation. Regardless, it's not impossible.
Example:
%* translated to SAS macro - Richard DeVenezia %* Based on code at https://www.geeksforgeeks.org/n-queen-problem-backtracking-3/; %* contributed by Princi Singh ; %macro logBoard(N); %* requires: macro symbols BOARD_1_1 to BOARD_<N>_<N> to exist in callers scope; %local i j row; %put NOTE: ------------- &=N; %do i = 1 %to &N; %let row = ; %do j = 1 %to &N; %let row = &row &&BOARD_&I._&J.; %end; %put NOTE: &row; %end; %put NOTE: -------------; %mend; %macro isSafePlace(row, col, N); %* requires: macro symbols BOARD_1_1 to BOARD_<N>_<N> to exist in callers scope; %local i j index; %do j = 1 %to &col; %if &&BOARD_&ROW._&J. %then %do; 0 /* not safe */ %return; %end; %end; %let i = &row; %let j = &col; %do index = 1 %to &N; %if &&BOARD_&I._&J. %then %do; 0 /* not safe */ %return; %end; %let i = %eval(&i-1); %if &i < 1 %then %goto leave1; %let j = %eval(&j-1); %if &j < 1 %then %goto leave1; %end; %leave1: %let i = &row; %let j = &col; %do index = 1 %to &N; %if &&BOARD_&I._&J. %then %do; 0 /* not safe */ %return; %end; %let i = %eval(&i+1); %if &i > &N %then %goto leave2; %let j = %eval(&j-1); %if &j < 1 %then %goto leave2; %end; %leave2: 1 /* is safe */ %mend; %macro queensRecursion(col, N); %local i j; %if &col > &N %then %do; 1 /* solution found */ %return; %end; %do i = 1 %to &N; %if %isSafePlace(&i, &col, &N) %then %do; %let BOARD_&I._&COL. = 1; %if %queensRecursion(%eval(&col+1), &N) %then %do; 1 %return; %end; /* backtrack */ %let BOARD_&I._&COL. = 0; %end; %end; 0 /* could not be placed safely */ %mend; %macro queens(N); %local i j; %do i = 1 %to &N; %do j = 1 %to &N; %local BOARD_&I._&J; %let BOARD_&I._&J = 0; %end; %end; %if not %queensRecursion(1, &N) %then %do; %put WARNING: No Queens solution found for &=N; %return; %end; %logBoard(&N) %mend; options mprint nomlogic nosymbolgen; %queens(6)
Log
758 %queens(6) ------------- N=6 NOTE: 0 0 0 1 0 0 NOTE: 1 0 0 0 0 0 NOTE: 0 0 0 0 1 0 NOTE: 0 1 0 0 0 0 NOTE: 0 0 0 0 0 1 NOTE: 0 0 1 0 0 0 -------------
When n=6 , there are four solutions .
EDITED.
EDITED again.
%let n=6 ; data have; do i=1 to &n; do j=1 to &n; output; end; end; run; data want(keep=path); set have(obs=&n); if _n_=1 then do; array row{%eval(&n*&n)} _temporary_; array col{%eval(&n*&n)} _temporary_; array flag{%eval(&n*&n)} _temporary_; length path _path $ 400 temp $ 20; declare hash pa(ordered:'y'); declare hiter hi_path('pa'); pa.definekey('n'); pa.definedata('n','path'); pa.definedone(); end; count=1;n=1;path=catx(' ',i,j);pa.add(); do while(hi_path.next()=0); if n ne 1 then pa.remove(key:_n);_n=n; idx=0; do i=1 to &n; do j=1 to &n; idx+1;row{idx}=i;col{idx}=j;flag{idx}=0; end; end; do k=1 to countw(path,'|'); temp=scan(path,k,'|'); first=input(scan(temp,1),best.); second=input(scan(temp,-1),best.); /*Remove - | / \ nodes*/ do idx=1 to &n*&n; if first=row{idx} or second=col{idx} or abs(first-row{idx})=abs(second-col{idx}) then flag{idx}=1; end; end; _path=path; do idx=1 to &n*&n; if row{idx}=k and flag{idx}=0 then do; count+1;n=count; path=catx('|',path,catx(' ',row{idx},col{idx})); pa.add(); if countw(path,'|')=&n then output; path=_path; end; end; end; pa.clear(); run; data temp; set want; array var{&n} $ 20; do k=1 to &n; var{k}=scan(path,k,'|'); end; keep var1-var&n ; run; data _null_; set temp end=last; call execute(catt("data solution_",_n_,";array var{&n};do i=1 to &n;do j=1 to &n; if findw('",catx('|',of var1-var&n),"',catx(' ',i,j),'|') then var{j}=1;else var{j}=0;end; output;end;drop i j;run;")); run;
Better using PROC OPTMODEL .and calling @RobPratt
Please see this documentation example for the constraint programming solver in PROC OPTMODEL.
You can change the value of n to whatever you want. If you want to find all solutions, use the FINDALLSOLNS in the SOLVE statement.
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