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[AcWing 320] 能量项链

作者:互联网

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#include<iostream>
#include<cstring>

using namespace std;

typedef long long LL;

const int N = 210;
const int INF = 0x3f3f3f3f;

int n;
int w[N]; 
LL f[N][N];

int main()
{
    cin >> n;
    for (int i = 1; i <= n; i ++) {
        cin >> w[i];
        w[i + n] = w[i];
    }
    for (int len = 3; len <= n + 1; len ++)
        for (int l = 1; l + len - 1 <= 2 * n; l ++) {
            int r = l + len - 1;
            for (int k = l + 1; k < r; k ++)
                f[l][r] = max(f[l][r], f[l][k] + f[k][r] + w[l] * w[k] * w[r]);
        }
    LL res = 0;
    for (int i = 1; i <= n; i ++)
        res = max(res, f[i][i + n]);
    cout << res << endl;
    return 0;
}

  1. 状态表示
    \(f[i][j]\) 表示将第 \(i\) 个珠子到第 \(j\) 个珠子合并的最大能量
  2. 状态计算
    用 \(k\) 表示区间 \([l,r]\) 和 \([k,r]\) 合并的交点处
    \(f[l][r] = max(f[l][k] + f[k][r] + w[l] \cdot w[k] \cdot w[r])\)
  3. 枚举区间长度时,区间长度最小为 3,最大为 \(n + 1\),表示 \(l = r\)

标签:const,int,LL,long,320,len,项链,include,AcWing
来源: https://www.cnblogs.com/wKingYu/p/16456445.html