[NEW] Add solution for Raab Game I

[ks-iitjmu]

🎯 Problem Information

• Problem Name: Raab Game I
• CSES Link: https://cses.fi/problemset/task/3399
• Category: Introductory Problem
• Estimated Difficulty: Medium

📋 Problem Description

[Nitin2332]

Hi @ks-iitjmu ,I would like to work on this issue and provide a solution for Raab Game I. Please assign it to me.

[ks-iitjmu]

@Nitin2332 Assigned

[Sitaram8472]

can I work in this issue @ks-iitjmu

[Nitin2332]

hi @ks-iitjmu , Has the solution for Raab Game 1 already been given? Can you clarify what needs to be done?

[ks-iitjmu]

@Nitin2332 currently it is assigned to you if u do not want then i can assign to @Sitaram8472

[ShristiC7]

@ks-iitjmu assign it to me please i have solution ready.

[ShristiC7]

@ks-iitjmu
Problem Summary

Two players each have n cards numbered 1..n.

On each turn, each player plays one card; higher card scores 1 point.

Input: n, final scores a (player 1) and b (player 2).

Output:

YES/NO → is this outcome possible?

If YES → give one example of card orderings that produce it.

Constraints:
1 ≤ t ≤ 1000, 1 ≤ n ≤ 100, 0 ≤ a,b ≤ n.

Approach

Check feasibility:

Maximum points a player can score = n.

Total points cannot exceed n (since each turn gives at most 1 point).

If a + b > n, impossible → NO.

Construct a valid game:

Use a simple greedy approach:

Assign a largest cards of player 1 to beat a smallest cards of player 2.

Assign b largest cards of player 2 to beat b smallest remaining cards of player 1.

Remaining cards can be paired arbitrarily (ties allowed).

This ensures a points for player 1 and b points for player 2.