Editorial: Alice and Bob playing an easy game

Notations & Definitions

• $N$ — the number of rounds in the game
• $A_{\text{wins}}$ — the number of rounds won by Alice
• $B_{\text{wins}}$ — the number of rounds won by Bob
• Since exactly one player wins each round: $A_{\text{wins}} + B_{\text{wins}} = N$

Subtask 1 ($N = 1$)

When there is only one round, the winner of that single round is the overall winner of the game.

Algorithm:

1. Read the single character from the input
2. If the character is A, Alice wins the game
3. If the character is B, Bob wins the game

Time Complexity: $O(1)$
Space Complexity: $O(1)$

Subtask 2 (General Case, $N \leq 9$)

For the general case, we need to count how many rounds each player won and determine who has more wins.

Key Observation:
Since $N$ is always odd, there cannot be a tie. Therefore, one player will always have strictly more wins than the other.

Algorithm:

1. Read the number of rounds $N$
2. Read the string of round results
3. Count the number of A characters to get $A_{\text{wins}}$
4. Count the number of B characters to get $B_{\text{wins}}$ (alternatively, $B_{\text{wins}} = N - A_{\text{wins}}$)

Time Complexity: $O(N)$ — for counting characters in the string
Space Complexity: $O(N)$ — for storing the input string (or $O(1)$ if we count while reading)

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Code Solutions