Solutions to some programming problems.

solutions.js

/*
 
  Five Programming Problems
  a software developer should be able
  to solve in less than an hour
  https://blog.svpino.com/2015/05/07/five-programming-problems-every-software-engineer-should-be-able-to-solve-in-less-than-1-hour
 
  Thomas Frank, Solutions in JS, time taken: 
  45 minutes (almost all time spent on problem 4 and 5)
  
  Update:
  Got stuck on failed edge cases on problem 4. 
  Eventually solved it with brute force.
  For me problem 4 turned out to be the hardest one to solve.
  (Although the actual sort solution is devilishly simple and elegant.)
 
  Comment: All statements marked "copy list - avoid destryoing original"
  reflects that JS always handles arrays by reference and it's polite
  not to destroy someone elses array (by sorting, shifting, popping)
  when they entrust it to your function :D
 
*/
 
 
/*
  Problem 1
  Write three functions that compute the sum of the numbers in a given list
  using a for-loop, a while-loop, and recursion.
*/
 
function sumFor(list){
  var sum = 0;
  for(var i = 0; i < list.length; i++){
     sum += list[i];
  }
  return sum;
}
 
function sumWhile(list){
  var sum = 0;
  list = list.slice(); // copy list - avoid destroying original
  while(list.length){
    sum += list.shift();
  }
  return sum;
}
 
function sumRec(list){
  list = list.slice(); // copy list - avoid destroying original
  function rec(list){
    return list.shift() + (list.length && rec(list));
  }
  return rec(list);
}
 
 
/*
  Problem 2
  Write a function that combines two lists by alternatingly taking elements.
  For example: given the two lists [a, b, c] and [1, 2, 3],
  the function should return [a, 1, b, 2, c, 3].
*/
 
function altCombine(list1,list2){
  var combined = [];
  list1 = list1.slice(); list2 = list2.slice(); // copy lists - avoid destroying originals
  while(list1.length || list2.length){
    list1.length && combined.push(list1.shift());
    list2.length && combined.push(list2.shift());
  }
  return combined;
}
 
 
/*
  Problem 3
  Write a function that computes the list of the first 100 Fibonacci numbers.
  By definition, the first two numbers in the Fibonacci sequence are
  0 and 1, and each subsequent number is the sum of the previous two.
  As an example, here are the first 10 Fibonnaci numbers:
  0, 1, 1, 2, 3, 5, 8, 13, 21, and 34.
*/
 
function fibonacciNaive(howMany){
  // this solution won't really work
  // because with howMany = 100
  // we will try to handle bigger numbers
  // than Number.MAX_SAFE_INTEGER
  howMany = howMany || 100;
  var nums = [0,1];
  while(nums.length < howMany){
    nums.push(nums[nums.length-2] + nums[nums.length-1]);
  }
  return nums;
}

function fibonacci(howMany){

  function addBigNums(a,b){
    a = String(a).split('');
    b = String(b).split('');
    var sum = [], mem = 0, part;
    while(a.length || b.length){
      part = String(
        Number(a.pop() || 0) + Number(b.pop() || 0) +
        Number(mem)
      ).split('');
      sum.unshift(part.pop());
      mem = part.join('');
    }
    sum.unshift(mem);
    return sum.join('');
  }

  howMany = howMany || 100;
  var nums = ["0","1"];
  while(nums.length < howMany){
    nums.push(
      addBigNums(nums[nums.length-2],nums[nums.length-1])
    );
  }
  return nums; 
}
 
 
/*
  Problem 4
  Write a function that given a list of non negative integers,
  arranges them such that they form the largest possible number.
  For example, given [50, 2, 1, 9], the largest formed number is 95021.
*/
     
function largestPosNum(list){

  // thanks to github.com/cerneal and svpino for this solution

  list = list.slice(); // copy list - avoid destroying original
  
  return list.sort(function(x, y){
    return (x+''+y < y+''+x) ? 1 : -1;
  }).join('')/1;
}


function largestPosNumBrute(list){

  // a (slower, brute force variant)
  // go through all permutations to find the largest number
  var largest = 0;
  function permute(list, mem) {
    var cur;
    mem = mem || [];
    list.forEach(function(x,i){
      cur = list.splice(i,1);
      var num = mem.concat(cur).join("")/1;
      largest = !list.length && largest < num ? num : largest;
      permute(list.slice(),mem.concat(cur));
      list.splice(i,0,cur[0]);
    });
  }
  permute(list);
  
  return largest;

}


/*
  Problem 5
  Write a program that outputs all possibilities to put + or - or 
  nothing between the numbers 1, 2, ..., 9 (in this order) such 
  that the result is always 100. 
  For example: 1 + 2 + 34 – 5 + 67 – 8 + 9 = 100.
*/

function allPossibilities(){
 
  // brute force solution
 
  // first calculate all possible combinations
  // of numbers and operators
  var mem = ["1"], combos;
  for(var i = 2; i <= 9; i++){
    combos = [];
    mem.forEach(function(x){
      combos.push(x + i, x + " +" + i, x + " -" + i);
    });
    mem = combos;
  }
 
  // Now filter out the ones that equal 100
  return combos.filter(function(combo){
    // split a combo into numbers, sum them using reduce
    return combo.split(" ").reduce(function(x,y){
      return x/1+y/1;
    }) == 100; // and check if the sum is 100
  })
  // format output by adding some spaces
  .map(function(x){
    return x.replace(/([+-])/g,'$1 ');
  });
 
}

If your question is correct then number four can easily be solved as ==>

Function largestPossibleNum(arr){

Let myArray = arr;

return myArray.sort().reverse().join('')

}

Console.log(largestPossibleNum([50,2,1,9]))