luoguP1040 区间DP(记忆化 加分二叉树

dp[l][r]记录中序序列为l, l+1..r的最大加分值

root[l][r]记录这个序列的根节点

转移

i 为根节点

dp[l][r] = max(dp[l][i-1]*dp[l+1][r]+a[i], dp[l][r])

顺势更新root[l][r]

#include <bits/stdc++.h>
#define pb push_back
#define po pop_back
#define fi first
#define se second

using namespace std;

typedef long long ll;
typedef pair<int, int> P;

const int MAXN = 37;
const int MAXE = 1e5+7;
const int MAXV = 1e5+7;
const int INF = 0x3f3f3f3f;

int a[MAXN];

int dp[MAXN][MAXN];
int root[MAXN][MAXN];
int n;

int dfs(int l, int r)
{
    if (l > r) return 1; //leave
    if (dp[l][r] > 0) return dp[l][r];
    if (l == r)
    {
        root[l][r] = l;
        dp[l][r] = a[l];
        return dp[l][r];
    }
    for (int i = l; i <= r; i++)
    {
        int res = dfs(l, i-1)*dfs(i+1, r)+a[i];
        if (res > dp[l][r])
        {
            dp[l][r] = res;
            root[l][r] = i;
        }
    }
    return dp[l][r];
}
void print(int l, int r)
{
    if (l > r) return ;
    if (l == r) 
    {
        printf("%d ", root[l][l]);
        return ;
    }
    printf("%d ", root[l][r]);
    print(l, root[l][r]-1);
    print(root[l][r]+1, r);
}
int main()
{
    //freopen("in.txt", "r", stdin);
    while (cin >> n)
    {
        for (int i = 1; i <= n; i++) cin >> a[i];
        memset(dp, 0, sizeof(dp));
        cout << dfs(1, n) << endl;
        print(1, n);
        cout << endl;
    }
    return 0;

}