Shipping Center

AtCoder

IDabc195_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ pieces of baggage called Baggage $1$ through $N$, and $M$ boxes called Box $1$ through $M$. Baggage $i$ has a size of $W_i$ and a value of $V_i$. Box $i$ can contain a piece of baggage whose size of at most $X_i$. It cannot contain two or more pieces of baggage. You will be given $Q$ queries. In each query, given two integers $L$ and $R$, solve the following problem: * Problem: Out of the $M$ boxes, $R-L+1$ boxes, Box $L,L+1,\ldots,R$, have become unavailable. Find the maximum possible total value of a set of baggage that we can put into the remaining boxes simultaneously. ## Constraints * $1 \leq N \leq 50$ * $1 \leq M \leq 50$ * $1 \leq Q \leq 50$ * $1 \leq W_i \leq 10^6$ * $1 \leq V_i \leq 10^6$ * $1 \leq X_i \leq 10^6$ * $1 \leq L \leq R \leq M$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $Q$ $W_1$ $V_1$ $\vdots$ $W_N$ $V_N$ $X_1$ $\ldots$ $X_M$ $\mathrm{Query}_1$ $\vdots$ $\mathrm{Query}_Q$ Each Query is in the following format: $L$ $R$ [samples]

Samples

Input #1

Output #1

20
0
9

In the $1$\-st query, only Box $4$ is unavailable. By putting Baggage $1$ into Box $1$, Baggage $3$ into Box $2$, and Baggage $2$ into Box $3$, we can put all baggage into boxes, making the total value of baggage in boxes $20$.
In the $2$\-nd query, all boxes are unavailable; the answer is $0$.
In the $3$\-rd query, only Box $4$ is available. By putting Baggage $1$ into Box $4$, we can make the total value of baggage in boxes $9$, which is the maximum possible result.

API Response (JSON)

{
  "problem": {
    "name": "Shipping Center",
    "description": {
      "content": "We have $N$ pieces of baggage called Baggage $1$ through $N$, and $M$ boxes called Box $1$ through $M$. Baggage $i$ has a size of $W_i$ and a value of $V_i$. Box $i$ can contain a piece of baggage who",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc195_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ pieces of baggage called Baggage $1$ through $N$, and $M$ boxes called Box $1$ through $M$.\nBaggage $i$ has a size of $W_i$ and a value of $V_i$.\nBox $i$ can contain a piece of baggage who...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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