CareerCup

I don't think using Horner's method will be helpful here. The reason being, it will generate different hash-key values for anagrams, ie 'abcd' and 'bacd' will have different hash-key values.
A simple hash function could be adding squares of all ascii values of the characters.

var hashFunc = function (string) {
    var sum = 0;
    for (var i = 0; i < string.length; i++) {
        var asc = string.charCodeAt(i); //gets ASCII code for the character
        sum += (asc * asc);
    }
    return sum;
};

There can be 2 approaches. One is to sort each and every word, and form a key for the hash-map.
If sorting each and every word is not an option, then there is a second approach. You can actually form a "hash-key" such that its unique for each set of characters.

findDiffElements = function (arr1, arr2, diffArr){
    arr2.sort();
    diffArr.sort();
    for (var i = 0; i < arr1.length; i++) {
        var idx2 = arr2.length - 1;
        var idxDiff = 0;
        var arr1Elm = arr1[i];
        while (idx2 >= 0 && idxDiff < diffArr.length) {
            var sum = arr2[idx2] + diffArr[idxDiff];
            if(sum === arr1Elm) {
                console.log(arr1Elm + '-' + arr2[idx2] + '=' + diffArr[idxDiff]);
                idx2--;
            } else if(sum > arr1Elm) {
                idx2--;
            } else {
                idxDiff++;
            }
        }
    }
}

I dont think you need these 2 lines:

if (alen == 0) { i = -1; }
if (blen == 0) { i = k-1; }

@Punit, I follow the "syntax". It is so because the question says, you are given a function, and you have to complete it. You are not supposed to change the question !!

Input to the function should be - Node root, Node start, int k

inout to the function should be - Node root, Node start, int k

I guess this would be the initial code fragment provided ...

The solution in normal JavaScript (can be quickly written on browser, and executed:-), and following Binary Search:

//returns the starting point of an array-segment
var minList = function(arr) {
  var len = arr.length;
    //checks whether the array-segment is sorted
    if(arr[0] <= arr[len-1]) {
      return arr[0];  //returns the min value in an array-segment
    } else {
      //else continue till you find a sorted array segment
      var arr2 = arr.splice(arr.length/2);
      var min1 = minList(arr);
      var min2 = minList(arr2);
      return Math.min(min1,min2);
    }
};

Just one thing, you need not check where node 'e' points to, as it is the last node.