Stone Game

Table of Contents

Problem #

Alice and Bob play a game with piles of stones. There are an even number of piles arranged in a row, and each pile has a positive integer number of stones piles[i].

The objective of the game is to end with the most stones. The total number of stones across all the piles is odd, so there are no ties.

Alice and Bob take turns, with Alice starting first. Each turn, a player takes the entire pile of stones either from the beginning or from the end of the row. This continues until there are no more piles left, at which point the person with the most stones wins.

Assuming Alice and Bob play optimally, return true if Alice wins the game, or false if Bob wins.

Thoughts #

Naively, we can solve this problem recursively by simulating the game.
For this problem, Alice can decide to take all even indexed piles or all odd indexed piles.

Example #

Initally, we have piles = [5, 3, 4, 5].
If Alice takes the first pile(index 0), Bob can only take odd indexed piles(index 1 or 3).
- And Alice can keep taking even indexed piles(index 2) until there are no more piles left.
If Alice takes the last pile(index 3), Bob can only take even indexed piles(index 0 or 2).
- And Alice can keep taking odd indexed piles(index 1) until there are no more piles left.

Since the total number of stones is odd, Alice will always win the game by taking either all even indexed piles or all odd indexed piles.

Solution #

class Solution:
    def stoneGame(self, piles: List[int]) -> bool:
        return True

Explanation #

Just return True :)