FamousFrizzyEngineering created by hillal20 - https://repl.it/@hillal20/FamousFrizzyEngineering

AllSetADDedToANumber.js

let arr = [1,2,3,2]
//                 {} let start from the left elemnt (1)
//               /    \
//        {} not taken        {1} token 
//       /  \               /     \
//     {2}   {}         {1,2}      {1}
//    / \   / \        /    \      /   \
//{2,3}{2} {} {3} {1,2,3} {1,2} {1,3}. {1}



function countSet(arr,total){
    return rec(arr,total, arr.length - 1 )
}

function rec(arr, total,i){

   if(total === 0){
      return 1; // only ampty {}
   }
  else if (total < 0){
    return 0; // total finish 
  }
  else if ( i < 0){ // arr.length - 1  < 0 
    return 0;
  }

  ///// let recursion 
  else if ( total < arr[i]){ // if total smaller then an element in the set so it is 
  // impossibe for the sum  of the set to be less then the total , we trow that element from the set and we move to nex element 
  
    return rec(arr,total,i-1)
  }
  else{
    // we have 2 cases , we take the element and we dont take the element to cover all
    // possible sets as shown above 

    return rec(arr, total - arr[i], i - 1) +  // we deciced to take the element 
    rec(arr,total, i - 1) // we decide not to add the element 
  }


}
countSet(arr,3)









// let b = [1,2,3] // ['1','3','4','13','14','34','134']

// function possible(arr){
                                    
//   let result = []
//   let combination;
// function helper(str,newArr){

//       for(let i = 0; i < newArr.length; i++){
     
//         combination = str + newArr[i]      //  1  12  13  123   2  23  3  // 
//       result.push(combination)
//        helper(combination, newArr.slice(i+1))
//       }

//   }
//   helper('',arr)

//  return result

// }
// possible(b)