FINDK3 - Editorial

editorial
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1

PROBLEM LINK:

Practice
Contest: Division 1
Contest: Division 2
Contest: Division 3
Contest: Division 4

Author: pols_agyi_pols
Tester & Editorialist: iceknight1093

DIFFICULTY:

802

PREREQUISITES:

None

PROBLEM:

Given integers X, Y, and Z, find any two integers A and B such that:

  • B equals one of the three numbers;
  • A equals the product of the remaining two numbers;
  • B divides A.

EXPLANATION:

B must be equal to one of X, Y, Z, which means there are only three choices for what B can be.
Once B is fixed, A is also fixed, being the product of the remaining elements.

It’s thus enough to just try all three options for B using if conditions.
That is,

  • If X divides (Y\cdot Z), then you can choose A = Y\cdot Z and B = X
  • If Y divides (X\cdot Z), then you can choose A = X\cdot Z and B = Y
  • If Z divides (X\cdot Y), then you can choose A = X\cdot Y and B = Z
  • If all three checks fail, the answer is -1.

TIME COMPLEXITY

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (Python) 
for _ in range(int(input())):
    x, y, z = map(int, input().split())
    if (y * z) % x == 0: print(y*z, x)
    if (x * z) % y == 0: print(x*z, y)
    elif (x * y) % z == 0: print(x*y, z)
    else: print(-1)
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