PROBLEM LINK:
Practice
Contest: Division 1
Contest: Division 2
Contest: Division 3
Contest: Division 4
Author: notsoloud
Testers: iceknight1093, rivalq
Editorialist: iceknight1093
DIFFICULTY:
TBD
PREREQUISITES:
None
PROBLEM:
Anna, Bob, and Claudio have initial health levels of A, B, and C respectively. Each pair will fight exactly once.
When two players with health x and y fight, both of their health decreases by \min(x, y).
Is there an order of fights that will leave Anna with strictly positive health in the end?
EXPLANATION:
Since Anna wants to have lots of health remaining, ideally the others should have as little as possible when she fights them.
So, it’s optimal for Bob and Claudio to fight first.
After this fight, their new health levels are B - \min(B, C) and C - \min(B, C) respectively.
Now make both people fight Anna, and check if her remaining health is positive or not.
Note that the order in which she fights them now is irrelevant.
A little analysis should tell you that this can be reduced to the condition
which can be checked using an if statement.
TIME COMPLEXITY
\mathcal{O}(1) per test case.
CODE:
Editorialist's code (Python)
for _ in range(int(input())):
a, b, c = map(int, input().split())
print('Yes' if a > max(b, c) - min(b, c) else 'No')