NOWINNER - Editorial

editorial
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PROBLEM LINK:

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

Author: notsoloud
Tester: mexomerf
Editorialist: iceknight1093

DIFFICULTY:

TBD

PREREQUISITES:

None

PROBLEM:

Alice, Bob, and Cameron have scores of A, B, C respectively.
After M more matches, each of which exactly one person can get a point in, is it possible for some two of them to have the same score?

EXPLANATION:

Let’s see if Alice and Bob can be made to have the same score.

Let d_{AB} = |A-B| be the initial difference between their scores.
In each match, d_{AB} can decrease by at most 1. We want it to become 0.
So,

  • If d_{AB} \gt M, it’s impossible to make it 0, so Alice and Bob can’t have equal scores.
  • Otherwise, we can use d_{AB} matches to make Alice and Bob have equal scores (make the one with a lower score win each one).
    All the remaining M - d_{AB} matches can be played between say Alice and Cameron, and Cameron can win so as to not change the scores of Alice and Bob.

So, quite simply, if d_{AB} \leq M then Alice and Bob can have equal scores after all M matches, otherwise they cannot.
The same logic applies to the other pairs: if d_{AC} \leq M or d_{BC} \leq M, those two players can be made to have equal scores, otherwise they cannot.

This makes the answer Yes if \min(d_{AB}, d_{AC}, d_{BC}) \leq M, and No otherwise.

TIME COMPLEXITY:

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (Python) 
for _ in range(int(input())):
    a, b, c, m = map(int, input().split())
    mndif = min(abs(a-b), abs(a-c), abs(b-c))
    print('Yes' if mndif <= m else 'No')
2

upload C++ code please.