# MONOPOLY2 - Editorial

Author: jeevanjyot
Tester & Editorialist: iceknight1093

578

None

# PROBLEM:

Four companies — A, B, C, and D — made profits of rupees P, Q, R, and S lakh respectively, in the last year.
There’s a monopoly in the market if the profit made by one company is strictly larger than the sum of profits of the others.

Is there a monopoly in the market?

# EXPLANATION:

Check whether any of the four companies satisfies the monopoly condition, i.e, check if any one of

• A \gt B + C + D
• B \gt A + C + D
• C \gt A + B + D
• D \gt A + B + C

are true.
If at least one of them is true, the answer is Yes; else the answer is No.

For a slightly simpler solution, notice that it’s enough to check whether the company with largest profit satisfies the condition.
This gives us the condition \max(A, B, C, D) \gt A + B + C + D - \max(A, B, C, D), or 2\max(A, B, C, D) \gt A + B + C + D, which is a bit cleaner to implement since it only requires one if condition.

# TIME COMPLEXITY

\mathcal{O}(1) per test case.

# CODE:

Editorialist's code (Python)
for _ in range(int(input())):
a, b, c, d = map(int, input().split())
print('Yes' if 2*max(a, b, c, d) > a + b + c + d else 'No')