Simple Knapsack

AtCoder

IDarc073_b

Time2000ms

Memory256MB

Difficulty—

You have $N$ items and a bag of strength $W$. The $i$\-th item has a weight of $w_i$ and a value of $v_i$. You will select some of the items and put them in the bag. Here, the total weight of the selected items needs to be at most $W$. Your objective is to maximize the total value of the selected items. ## Constraints * $1 ≤ N ≤ 100$ * $1 ≤ W ≤ 10^9$ * $1 ≤ w_i ≤ 10^9$ * For each $i = 2,3,...,N$, $w_1 ≤ w_i ≤ w_1 + 3$. * $1 ≤ v_i ≤ 10^7$ * $W$, each $w_i$ and $v_i$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $W$ $w_1$ $v_1$ $w_2$ $v_2$ : $w_N$ $v_N$ [samples]

Samples

Input #1

Output #1

11

The first and third items should be selected.

Input #2

Output #2

13

The second and fourth items should be selected.

Input #3

Output #3

400

You can take everything.

Input #4

Output #4

0

You can take nothing.

API Response (JSON)

{
  "problem": {
    "name": "Simple Knapsack",
    "description": {
      "content": "You have $N$ items and a bag of strength $W$. The $i$\\-th item has a weight of $w_i$ and a value of $v_i$. You will select some of the items and put them in the bag. Here, the total weight of the sele",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc073_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You have $N$ items and a bag of strength $W$. The $i$\\-th item has a weight of $w_i$ and a value of $v_i$.\nYou will select some of the items and put them in the bag. Here, the total weight of the sele...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments