我发现我的棋盘board数组不能只开（n+1）*（n+1）的大小，否则会越界。如果访问了超过棋盘本身的下标，实际意义是什么呢

#include <iostream>
#include<vector>
#include<string>
#include<cstring>
#include<stack>
#include<queue>
#include<algorithm>
using namespace std;
#define LL long long
int cmp(int a, int b, int c, int d)
{
    a = max(a, b);
    c = max(c, d);
    return max(a, c);
}
int main() {
    ios_base::sync_with_stdio(false);// 关闭同步流
    cin.tie(nullptr);
    cout.tie(nullptr);
    int n;
    cin >> n;
    vector<vector<int>>board(20, vector<int>(20, 0));
    vector<vector<vector<int>>>dp(2 * n+1, vector<vector<int>>(n + 1, vector<int>(n + 1, 0)));
    //步数，y1，y2
    int a, b, c;
    do
    {
        cin >> a >> b >> c;
        board[a][b] = c;
    } while (!(a == 0 && b == 0 && c == 0));
    for (int k = 1; k <= 2*n; k++)
        for (int i = 1; i <= min(k, n); i++)
            for (int j = 1; j <= min(k, n); j++)
            {
                dp[k][i][j] = cmp(dp[k - 1][i][j], dp[k - 1][i - 1][j], dp[k - 1][i][j - 1], dp[k - 1][i - 1][j - 1]) + board[k - i + 1][i] + board[k - j + 1][j];
                if (i == j) dp[k][i][j] -= board[k - i + 1][i];
            }
    dp[2*n][n][n] = cmp(dp[2 * n - 1][n][n - 1], dp[2 * n - 1][n - 1][n], dp[2 * n - 1][n][n], dp[2 * n - 1][n - 1][n - 1]);
    cout << dp[2*n][n][n];
    return 0;
}