Question

Given is a list containing all but 2 numbers between 1-20 (randomly ordered).
I need to find those 2 numbers.

This is the (working) program I came up with:

public static void main(String[] args) {
    int[] x= {1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19};
    ArrayList al= new ArrayList();
    Map map= new HashMap();
    for(int i=0;i<x.length;i++)
    {
        map.put(x[i], x[i]);
    }
    for(int i=1;i<=20;i++)
    {
        if(map.get(i)==null)
            al.add(i);
    }
    for(int i=0;i<al.size();i++)
    {
        System.out.println(al.get(i));
    }
}

I would like to know if the program is good from a performance point of view (memory and bigO(n))?

Answer 1

You don’t need a map. Just an additional boolean array with size 20.

for (int i = 0; i < input.length; i++)
   arr[input[i]] = true;

for (int i = 1; i <= 20; i++)
   if (arr[i] == false) {
      //number `i` is missing
   }     

Now I will expose a straightforward math solution.

First sum all numbers in the array. For example you have 5, 1, 4 for the numbers from 1, 2, 3, 4, 5. So 2 and 3 are missing. We can find them easily with math.

5 + 1 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

So we know x + y = 15 - 10 = 5
Now we will get a second equation:

1 * 4 * 5 = 20
1 * 2 * 3 * 4 * 5 = 120
=> x * y = 120 / 20 = 6

So:

x + y = 5
x * y = 6

=> x = 2, y = 3 or x = 3, y = 2 which is the same.

So x = 2, y = 3