Algorithm for finding an object with different weights

Question

We are given N objects, of which exactly one object has a different weight (may be less or more). In addition, we are given M comparisons of the following three types -

• Weight (Set A) <Weight (Set B)
• Weight (Set A)> Weight (Set B)
• Weight (set A) = weight (set B)

Where Set A and Set B (both have the same number of objects) is a list of objects from the original N objects.

Given M such comparisons, I need to find an object with different weights, if possible. Otherwise, say that this list of comparisons M is not enough to detect one with the other weight.

Can someone suggest an algorithm to solve this problem?

Answer 1

, , , , .

, , ( ). :

• A < B: B.
• A > B: B.
• A = B: B.

, .. , - , , - , :

• solution = null, noFlagSolution = null, noFlagCount = 0.

• :

  • : continue.
  • : noFlagSolution = current, noFlagCount++
  • :
    • solution != null: return null ( ).
    • Else: solution = current

• solution != null: return solution ( , ).

• noFlagCount == 1: return noFlagSolution ( , , , ).

• .

Answer 2

2N - 1 , 1 , 2 , 2 ,..., N , N . , . , ( , i, ), . , . .

Answer 3

, , ceil (log3 (N)).

, . , 3- . , , , , . , , . , log3 (N), N 3, , N.

If you do not know if an object of different weights is heavier or lighter than the rest, then it takes about log3 / 2 (N), since in the worst case you can throw out only one of the three piles, thereby reducing the number of objects in two times.