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 = ;
 const int MAXE = 1e5+;
 const int MAXV = 1e5+;
 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 ; //leave
     if (dp[l][r] > ) 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-)*dfs(i+, 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]-);
     print(root[l][r]+, r);
 }
 int main()
 {
     //freopen("in.txt", "r", stdin);
     while (cin >> n)
     {
         for (int i = ; i <= n; i++) cin >> a[i];
         memset(dp, , sizeof(dp));
         cout << dfs(, n) << endl;
         print(, n);
         cout << endl;
     }
     return ;

 }