Quickest way to find missing number in an array of numbers

You can do this in O(n). Iterate through the array and compute the sum of all numbers. Now, sum of natural numbers from 1 to N, can be expressed as Nx(N+1)/2. In your case N=100.

Subtract the sum of the array from Nx(N+1)/2, where N=100.

That is the missing number. The empty slot can be detected during the iteration in which the sum is computed.

// will be the sum of the numbers in the array.
int sum = 0;
int idx = -1;
for (int i = 0; i < arr.length; i++)
{
    if (arr[i] == 0)
    {
         idx = i; 
    }
    else 
    {
         sum += arr[i];
    }
}

// the total sum of numbers between 1 and arr.length.
int total = (arr.length + 1) * arr.length / 2;

System.out.println("missing number is: " + (total - sum) + " at index " + idx);