Minimize Max of Three Different Sorted Arrays in Python

Suppose we have three sorted arrays A, B, and C (these can be of different sizes), we have to find compute the minimum absolute difference between the maximum and minimum number of any triplet (A[i],B[j],C[k]) such that they are under arrays A, B and C respectively,

So, if the input is like A : [ 2, 5, 6, 9, 11 ], B : [ 7, 10, 16 ], C : [ 3, 4, 7, 7 ] , then the output will be 1 as by selecting A[i] = 6 B[j] = 7 and C[k] = 7, we will get the minimum difference as max(A[i], B[j], C[k]) - min(A[i], B[j], C[k])) = |7-6| = 1

To solve this, we will follow these steps −

• i := size of A - 1
• j := size of B - 1
• k := size of C - 1
• minimum_dfference := |maximum of A[i], B[j], C[k] - minimum of A[i], B[j], C[k]|
• while i is not same as -1 and j is not same as -1 and k is not same as -1, do
  • current_diff := |maximum of A[i], B[j], C[k] - minimum of A[i], B[j], C[k]|
  • if current_diff < minimum_dfference is non-zero, then
    • minimum_dfference := current_diff
  • maximum_term := maximum of A[i], B[j], C[k]
  • if A[i] is same as maximum_term, then
    • i := i - 1
  • otherwise when B[j] is same as maximum_term, then
    • j := j - 1
  • otherwise,
    • k := k - 1>
• return minimum_dfference

Example

Let us see the following implementation to get better understanding −

 Live Demo

def solve(A, B, C):
   i = len(A) - 1
   j = len(B) - 1
   k = len(C) - 1
   minimum_dfference = abs(max(A[i], B[j], C[k]) - min(A[i], B[j], C[k]))
   while i != -1 and j != -1 and k != -1:
      current_diff = abs(max(A[i], B[j], C[k]) - min(A[i], B[j], C[k]))
      if current_diff < minimum_dfference:
         minimum_dfference = current_diff
      maximum_term = max(A[i], B[j], C[k])
      if A[i] == maximum_term:
         i -= 1
      elif B[j] == maximum_term:
         j -= 1
      else:
         k -= 1
   return minimum_dfference
A = [ 2, 5, 6, 9, 11 ]
B = [ 7, 10, 16 ]
C = [ 3, 4, 7, 7 ]
print(solve(A, B, C))

Input

A = [ 2, 5, 6, 9, 11 ] B = [ 7, 10, 16 ] C = [ 3, 4, 7, 7 ]

Output

1