P12027 [USACO25OPEN] Ski Slope S

Bessie is going on a ski trip with her friends. The mountain has $N$ waypoints ($1\leq N \leq 10^5$) labeled $1, 2, \ldots, N$ in increasing order of altitude (waypoint $1$ is the bottom of the mountain). For each waypoint $i \gt 1$, there is a ski run starting from waypoint $i$ and ending at waypoint $p_i$ ($1\le p_i\lt i$). This run has difficulty $d_i$ ($0 \leq d_i \leq 10^9$) and enjoyment $e_i$ ($0 \leq e_i \leq 10^9$). Each of Bessie's $M$ friends ($1\leq M \leq 10^5$) will do the following: They ill pick some initial waypoint $i$ to start at, and then follow the runs downward (to $p_i$, then to $p_{p_i}$, and so forth) until they get to waypoint $1$. The enjoyment each friend gets is equal to the sum of the enjoyments of the runs they follow. Each friend also has a different skill level $s_j$ ($0 \leq s_j \leq 10^9$) and courage level $c_j$ ($0 \leq c_j \leq 10$), which limits them to selecting an initial waypoint that results in them taking at most $c_j$ runs with difficulty greater than $s_j$. For each friend, compute the maximum enjoyment they can get.

The first line contains $N$. Then for each $i$ from $2$ to $N$, a line follows containing three space-separated integers $p_i$, $d_i$, and $e_i$. The next line contains $M$. The next $M$ lines each contain two space-separated integers $s_j$ and $c_j$.

Output $M$ lines, with the answer for each friend on a separate line. **Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).**

1. The first friend cannot start any waypoint other than $1$, since any other waypoint would cause them to take at least one run with difficulty greater than $19$. Their total enjoyment is $0$. 2. The second friend can start at waypoint $4$ and take runs down to waypoint $2$ and then $1$. Their total enjoyment is $100+200=300$. They take one run with difficulty greater than $19$. 3. The third friend can start at waypoint $3$ and take runs down to waypoint $2$ and then $1$. Their total enjoyment is $300+200=500$. They take two runs with difficulty greater than $19$. #### SCORING: - Inputs 2-4: $N, M\le 1000$ - Inputs 5-7: All $c_j=0$ - Inputs 8-17: No additional constraints.