# 877. Stone Game

Alex and Lee 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 is odd, so there are no ties.

Alex and Lee take turns, with Alex starting first.  Each turn, a player takes the entire pile of stones from either the beginning or 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 Alex and Lee play optimally, return `True` if and only if Alex wins the game.

Example 1:

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

Note:

1. `2 <= piles.length <= 500`
2. `piles.length` is even.
3. `1 <= piles[i] <= 500`
4. `sum(piles)` is odd.

``````class Solution {
public:
bool stoneGame(vector<int>& piles) {
return helper(piles, 0, 0, 0, (int)piles.size() - 1, 0);
}
bool helper(vector<int>& piles, int cur0, int cur1, int left, int right, int player) {
if (left > right) return cur0 > cur1;
if (player == 0) {
return helper(piles, cur0 + piles[left], cur1, left + 1, right, 1) || helper(piles, cur0 + piles[right], cur1, left + 1, right, 1);
} else {
return helper(piles, cur0, cur1 + piles[left], left, right - 1, 0) || helper(piles, cur0, cur1 + piles[right], left, right - 1, 0);
}
}
};
``````

``````class Solution {
public:
bool stoneGame(vector<int>& piles) {
int n = piles.size();
vector<vector<int>> dp(n, vector<int>(n));
for (int i = 0; i < n; ++i) dp[i][i] = piles[i];
for (int len = 1; len < n; ++len) {
for (int i = 0; i < n - len; ++i) {
int j = i + len;
dp[i][j] = max(piles[i] - dp[i + 1][j], piles[j] - dp[i][j - 1]);
}
}
return dp[0][n - 1] > 0;
}
};
``````

``````class Solution {
public:
bool stoneGame(vector<int>& piles) {
return true;
}
};
``````

Github 同步地址:

https://github.com/grandyang/leetcode/issues/877

Burst Balloons

Nim Game

Flip Game II

Guess Number Higher or Lower II

Predict the Winner

https://leetcode.com/problems/stone-game/

https://leetcode.com/problems/stone-game/discuss/154610/DP-or-Just-return-true

 微信打赏 Venmo 打赏
（欢迎加入博主的知识星球，博主将及时答疑解惑，并分享刷题经验与总结，试运营期间前五十位可享受半价优惠～）

×

Help us with donation