#!/usr/local/bin/gawk -f
#
#       Check magic squares by "Magic square condition"
#
#                                                           by F. Poyo
#
function help() {
#  print "\033[2J"
    printf "\033[33mUsage...\033[m\n"
    print " "
    printf "  \033[36mDefault usage..\033[m\n"
    print " "
    print "    gawk -f magic.awk"
    print " "
    printf "  \033[36mGet seed matrix from file.\033[m\n";
    print " "
    print "    gawk -f magic.awk magic.dat"
    print "                      ~~~~~~~~~<--¹File name would be"
    print "                                  vary."
    exit;
}
#
#
#
function check_magic(i,j,x,y,ok_or_not,row_err,col_err,diagonal_err,pan_diagonal_err,seq,NN) {
# Check the calculation by "Magic square condition".

  NN=N*N;
  ok_or_not=1;
  for(i=0;i<=NN;i++)
  {
    seq[i] = 0;
  }
  min=10000000;
  max=-10000000;
  for(i=0;i<N;i++)
  {
    for(j=0;j<N;j++)
    {
      if(M[i,j]<min) min=M[i,j];
      if(M[i,j]>max) max=M[i,j];
      seq[M[i,j]]++;
      x[M[i,j]]=i;
      y[M[i,j]]=j;
    }
  }
  d=(max-min)/(NN-1);
  for(i=min;i<=max;i+=d) {
    if(seq[i] != 1) {
        ok_or_not=0; break;
    }
  }
  sum=N*((NN-1)*d/2+min);
  printf("N=%d  SUM=%d\n",N,sum);
  if(ok_or_not==1) 
    printf "Check 1:OK ... Elements are sequential natural numbers(%d ... %d:d=%d)\n",min,max,d 
  else {
    print "Since the elements are not sequential natural numbers,"
    print "it's not a magic square."
    print "Number of appeariing time which must be all 1s."
    for(i=0;i<N;i++)
    {
      for(j=0;j<N;j++)
      {
         printf("%2d ",seq[M[i,j]]);
      }
      print "";
    }
    print "-------------";
  }
  col_err=0;
  row_err=0;
  diagonal_err=0;
  pan_diagonal_err=0;
  for(i=0;i<N;i++) {
    sumc[i]=0;sumr[i]=0;
    sumdp[i]=0;
    sumdm[i]=0;
    for(j=0;j<N;j++) {
        sumc[i]+=M[i,j];
        sumr[i]+=M[j,i];
        sumdp[i] += M[(i+j)%N,j];
        sumdm[i] += M[(N+i-j)%N,j];
    }
    if(sumc[i] != sum) {col_err=1;}
    if(sumr[i] != sum) {row_err=1;}
    if(i==0) { if(sumdp[i] != sum) {diagonal_err=1;}}
    else { if(sumdp[i] != sum) {pan_diagonal_err=1;}}
    if(i==(N-1)) { if(sumdm[i] != sum) {diagonal_err=1;}}
    else { if(sumdm[i] != sum) {pan_diagonal_err=1;}}
  }
  format=sprintf("%s-%dd ","%",int(log(sum)/log(10))+1);
  if ((col_err == 1)||(row_err == 1)||(diagonal_err == 1)) {
     print "... but it's not a magic square,";
     print "    there is an error in the sum of the elements in";
     printf("       ");
     for(i=0;i<N;i++) { printf(format,i); } print "";
  } else {
     print "It's magic square.";
  }
  if(col_err == 1) {
     printf("Colmn: ");
     for(i=0;i<N;i++) { printf(format,sumc[i]); } print "";
  }
  if(row_err == 1) {
     printf(" Rows: ");
     for(i=0;i<N;i++) { printf(format,sumr[i]); } print "";
  }
  if(pan_diagonal_err == 1) {
     if(!((col_err == 1)||(row_err == 1)||(diagonal_err == 1))) {
        printf("       ");
        for(i=0;i<N;i++) { printf(format,i); } print "";
     }
     printf("Diag+: ");
     for(i=0;i<N;i++) { printf(format,sumdp[i]); } print "";
     printf("Diag-: ");
     for(i=0;i<N;i++) { printf(format,sumdm[i]); } print "";
  }
  if(col_err==0)
  printf "Check 2:OK ... The sum of the elements for each the column vector is %d.\n", sum
  if(row_err==0)
  printf "Check 2:OK ... The sum of the elements for each the row vector is %d.\n", sum
  if(pan_diagonal_err == 0) {
  printf "Check 3:OK ... The sum of the elements for each the pan-diagonal vector is %d.\n", sum
  } else {
    if(pan_diagonal_err == 0) {
     printf "Check 3:OK ... The sum of the elements for each the diagonal vector is %d.\n", sum
    }
  }
  if ((col_err == 1)||(row_err == 1)||(diagonal_err == 1)||(pan_diagonal_err == 1)) {
  } else {
     print "It's COMPLETE magic square.";
  }
}
#
#
#
BEGIN {j=1; count=0;}
(j!=1) && /[0-9]* *[0-9]* */{
     line="" $0;
#     printf("N=%d\n",split(line,a,/ /));
     tmp=split(line,a,/ /);
     if(tmp != N) {printf("N=%d     N'=%d",N,tmp);exit}
     for(i=1;i<=N;i++) { M[j-1,i-1]=a[i];
# printf "%d ",M[j,i];
     }
#     printf("\n");
     j++;
     if(j>N) {check_magic();count++;N=0;j=1;next;}
}
(j==1) && /[0-9]+ +[0-9]+ +/{
     line=$0;
#     print line;
     N=split("" line,a,/ /);
#     printf("N=%d\n",N);
     for(i=1;i<=N;i++) { M[j-1,i-1]=a[i];
# printf "%d ",M[j,i];
     }
#     printf("\n");
     j++;
     next;
}
/End/{exit}
{}
END{if(count==0) help();}