REC09A - Editorial

editorial
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PROBLEM LINK:

Practice
Contest

Author: Ritesh Gupta
Tester: Romit Kumar
Editorialist: Ritesh Gupta

DIFFICULTY:

Simple

PREREQUISITES:

Ad-hoc, Math

PROBLEM:

You are given N distinct positive integer. You are required to add at most 1 positive integer such that

  • It is not equal to any given integer.
  • It is less than the maximum value of the given integer.
  • It is greater than the minimum value of the given integer.
  • And after the addition of this integer, the sum of all N+1 elements is equal to K.

EXPLANATION:

First, sum all the N elements and let it be S

  • if S > K then it is not possible to achieve as we can add only positive integers.
  • if S == K then answer is YES.
  • if S < K then answer is YES if and only if
    • K-S < maximum of N elements
    • K-S > minimum of N elements
    • K-S is not equal to any value from given N integer.

SOLUTIONS:

Setter’s Solution

Tester’s Solution