> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Stone Game Python Solution with Tests

> Tested Python solution for LeetCode 877 with 18 pytest cases. Generate a practice environment with lcpy.

LeetCode 877, Medium. Topics: Array, Math, Dynamic Programming, Game Theory. [View on LeetCode](https://leetcode.com/problems/stone-game/description/).

Generate this problem as a practice environment: tested reference solution, 18 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 877   # by problem number
lcpy gen -s stone_game   # by problem name
```

## 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.

### Examples

```
Input: piles = [5,3,4,5]
Output: true
Explanation:
Alice starts first, and can only take the first 5 or the last 5.
Say she takes the first 5, so that the row becomes [3, 4, 5].
If Bob takes 3, then the board is [4, 5], and Alice takes 5 to win with 10 points.
If Bob takes the last 5, then the board is [3, 4], and Alice takes 4 to win with 9 points.
This demonstrated that taking the first 5 was a winning move for Alice, so we return true.
```

```
Input: piles = [3,7,2,3]
Output: true
```

### Constraints

* 2 \<= piles.length \<= 500
* `piles.length` is even.
* 1 \<= piles\[i] \<= 500
* `sum(piles[i])` is odd.

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/stone_game/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/stone_game/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n^2)
    # Space: O(n^2)
    def stone_game(self, piles: list[int]) -> bool:
        n = len(piles)
        # dp[i][j] = max net advantage current player can secure from piles[i..j]
        dp = [[0] * n for _ in range(n)]
        for i in range(n):
            dp[i][i] = piles[i]
        for length in range(2, n + 1):
            for i in range(n - length + 1):
                j = i + length - 1
                pick_left = piles[i] - dp[i + 1][j]
                pick_right = piles[j] - dp[i][j - 1]
                dp[i][j] = max(pick_left, pick_right)
        return dp[0][n - 1] > 0
```

## Complexity

| Time   | Space  |
| ------ | ------ |
| O(n^2) | O(n^2) |

## Tags

[NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).