combinations.js

function ncmp(a, b) { return a - b; }
function format(set) { return JSON.stringify(set).replace(/\],\[/g,') (').replace('[[','[(').replace(']]','])'); }

function generate_combinations(dims) {
   "use strict";
   function next(el) { for(var i=dims.length-1;i>=0;i--) { if (++el[i]<dims[i]) return true; else el[i]=0; } return false; }
   function first() { return Array.apply(null, Array(dims.length)).map(function() { return 0; }); }
   function upperlimit() { var _ds = dims.slice().sort(ncmp); return _ds[0]*_ds[1]; }
   function valid(set,n) { for(var i=0;i<n;i++) { for(var c=0,di=0;di<set[n].length;di++) if (set[n][di]===set[i][di]) if (++c>1) return false; } return true; }

   var limit = upperlimit();
   var set = [];
   var n;
   var winner=[];
   var iteration=0;

   set[0] = first();                          //set[0] is fixed at the first value
   set[1] = set[0].slice();
   do { next(set[1]) } while(!valid(set,1))   //set[1] is fixed at the next valid value

   set[2] = set[1].slice(); n=2;              //PUSH
   while(n>1) {
      if (!next(set[n])){n--; continue;}      //POP
      if (!valid(set,n)) continue;            //NEXT

      if(!(++iteration%10000)) console.log(iteration, winner.length, format(set.slice(0,n)));

      //Valid!
      if (n>=winner.length) {
         winner = set.slice(0).map(function(s){return s.slice();});
         //console.log("new", winner.length, format(winner));
         if (winner.length == limit) return winner; //DONE.
      }
      //Descend
      set[n+1] = set[n].slice(); n++;    //PUSH
   }


   return winner;
}

//START node.js code - gets the dimensions from the command-line
if (process.argv.length<3) { console.error("Need dimensions"); process.exit(1); }
var dims = [];
for(i=2;i<process.argv.length;i++) {
   n = parseInt(process.argv[i]);
   if (!n) { console.error("Each dim must be numeric and >0"); process.exit(2); }
   dims.push(n);
}
//END node.js code - could substitute with eg var dims = [4,5,7,7];

dims.sort(ncmp);
for(i=2;i<=dims.length;i++) {
  _dims = dims.slice(0,i);
  solution = generate_combinations(_dims);
  console.log("N="+_dims.length+" C("+_dims.join(',')+") = "+solution.length+" values: "+format(solution));
}