​

    sA = [ 5, 1, 2, 3, 0, 4 ] ;

​

    sB = [ 6, 2, 3, 5, 1, 8] ;

​

    sAB = productEncodedPolynoms ( sA, sB );

​

    console.log(printEncodedArray(sA));

    console.log(printEncodedArray(sB));

    console.log(printEncodedArray(sAB));

​

function productEncodedPolynoms( sA, sB) {

   var aIndex = 0 ;

   var bIndex = 0 ;

   var resIndex = 0 ;

   var resHash = {} ;

   // for loop within sA, moving 2 items at a time

   for (aIndex = 0; aIndex < sA.length ; aIndex+=2) {

       // for loop within sB, moving 2 items at a time

       for (bIndex = 0; bIndex < sB.length ; bIndex+=2 ) {

           resIndex = sA[aIndex]+sB[bIndex] ;

           // create key/value pair if none created

           if (resHash[resIndex]===undefined)  resHash[resIndex]=0;

           // add this product to right coefficient

           resHash[resIndex] += sA[aIndex+1]*sB[bIndex+1];

       }

   } 

   // now unpack the hash into an encoded sparse array

   // get hash keys

   var coeff = Object.keys(resHash);

   // sort keys in reverse order

   coeff.sort(reverseSort);

   encodedResult = [];

   for (var i=0; i<coeff.length; i++ ) {

     if (resHash[coeff[i]]) {

       encodedResult.push(+coeff[i]);          // (+ converts to int)

       encodedResult.push(+resHash[coeff[i]]);

     }

   }

   return encodedResult;

}

​

function printEncodedArray(sA) {

  res='';

  for (var i=0; i<sA.length; i+=2) {

    if (sA[i+1]) {

        if (sA[i+1] != 1 || sA[i]==0) res+=sA[i+1];

        if (sA[i]!=0) res+='x^'+sA[i];

        if (i!=sA.length-2) res+='+';

    }

  }

  return res;

}

​

// utilities

function reverseSort(a,b) { return b-a ; }

​

​