firstProblem.js

const _mergeArrays = (a, b) => {
  const c = []

  while (a.length && b.length) {
    if( a[0][0] == b[0][0] ) {
      if( a[0][1] < b[0][1] ) {
        c.push(a.shift());
      } else {
        c.push(b.shift());
      }
    } else {
      if( a[0][0] < b[0][0] ) {
        c.push(a.shift());
      } else {
        c.push(b.shift());
      }
    }
   
  }

  //if we still have values, let's add them at the end of `c`
  while (a.length) {
    c.push(a.shift())
  }
  while (b.length) {
    c.push(b.shift())
  }

  return c
}

const mergeSort = (a) => {
  if (a.length < 2) return a
  const middle = Math.floor(a.length / 2)
  const a_l = a.slice(0, middle)
  const a_r = a.slice(middle, a.length)
  const sorted_l = mergeSort(a_l)
  const sorted_r = mergeSort(a_r)
  return _mergeArrays(sorted_l, sorted_r)
}



const sortArray = (array) => {
  freqItems = {};
  // O(n) to count frequency of items
  for( let i = 0 ; i < array.length; i++) {
    let item = array[i];
    if( item in freqItems ) {
      freqItems[item] = freqItems[item] + 1;
    } else {
      freqItems[item] = 1;
    }
  }

  items = []
  for(const [key, value] of Object.entries(freqItems)) {
   
     items.push([value, parseInt(key)]);
  }

  sorted_items = mergeSort(items);
  ans = []
  for( let i = 0 ; i < sorted_items.length; i++ ) {
    while(sorted_items[i][0]-- ) {
       ans.push(sorted_items[i][1]);
    }
   
  }

  console.log(ans);

}


input = [3, 6, 4, 5, 4, 5];
sortArray(input);

secondProblem.js

class HistoryList{
  constructor(maxCapacity) {
    this.maxSize = maxCapacity;
    this.cache = {}
    this.stack = [];
  }
  addToHistory(item) {
    if( item in this.cache ) {
      this.stack.pop(item);
    } 
    if( this.stack.length == this.maxSize) {
      this.stack.shift();
    }
    this.stack.push(item);
  }
  getMostRecent() {
    if( this.stack.length == 0 ) {
      return undefined;
    } else {
      return this.stack[this.stack.length - 1 ];
    }
  }
  printList() {
    console.log(this.stack);
  }

}

let lru = new HistoryList(2);

lru.addToHistory("one");
console.log(lru.getMostRecent());
lru.addToHistory("two");
console.log(lru.getMostRecent());
lru.printList();
lru.addToHistory("one");
console.log(lru.getMostRecent());
lru.addToHistory("five");
lru.printList();
console.log(lru.getMostRecent());
lru.addToHistory("one");
console.log(lru.getMostRecent());
lru.printList();