Construct a distinct elements array with given size, sum and element upper bound in Python

Suppose we have one size variable N, we also have one variable SUM this is the total sum of all elements available in the array and another variable K such that there is no element in array is greater than K, We have to find one orthogonal array where all elements in the array are distinct. If there is no solution return -1.

So, if the input is like N = 4, SUM = 16 K = 9, then the output will be [1,2,4,9]

To solve this, we will follow these steps −

• minimum_sum := (N *(N + 1)) / 2

• maximum_sum := (N * K) -(N *(N - 1)) / 2

• if minimum_sum > SUM or maximum_sum < SUM, then

  • return -1

• res := one array of size N + 1 and fill with 0 to N

• sum := minimum_sum

• i := N

• while i >= 1, do

  • x := sum + (K - i)

  • if x < SUM, then

    • sum := sum +(K - i)

    • res[i] := K

    • K := K - 1

  • otherwise,

    • res[i] := res[i] +(SUM - sum)

    • sum := SUM

    • come out from the loop

  • i := i - 1

• return res

Example

Let us see the following implementation to get better understanding −

 Live Demo

def get_arr(N, SUM, K):
   minimum_sum = (N * (N + 1)) / 2
   maximum_sum = (N * K) - (N * (N - 1)) / 2
   if (minimum_sum > SUM or maximum_sum < SUM):
      return -1
   res = [i for i in range(N + 1)]
   sum = minimum_sum
   i = N
   while(i >= 1):
      x = sum + (K - i)
      if (x < SUM):
         sum = sum + (K - i)
         res[i] = K
         K -= 1
      else:
         res[i] += (SUM - sum)
         sum = SUM
         break
         i -= 1
   return res
N = 4
SUM = 16
K = 9
print(get_arr(N, SUM, K))

Input

4, 16, 9

Output

[0, 1, 2, 4.0, 9]