Knapsack 1

AtCoder

IDdp_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ items, numbered $1, 2, \ldots, N$. For each $i$ ($1 \leq i \leq N$), Item $i$ has a weight of $w_i$ and a value of $v_i$. Taro has decided to choose some of the $N$ items and carry them home in a knapsack. The capacity of the knapsack is $W$, which means that the sum of the weights of items taken must be at most $W$. Find the maximum possible sum of the values of items that Taro takes home. ## Constraints * All values in input are integers. * $1 \leq N \leq 100$ * $1 \leq W \leq 10^5$ * $1 \leq w_i \leq W$ * $1 \leq v_i \leq 10^9$ ## 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

90

Items $1$ and $3$ should be taken. Then, the sum of the weights is $3 + 5 = 8$, and the sum of the values is $30 + 60 = 90$.

Input #2

5 5
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Output #2

5000000000

The answer may not fit into a 32-bit integer type.

Input #3

Output #3

17

Items $2, 4$ and $5$ should be taken. Then, the sum of the weights is $5 + 6 + 3 = 14$, and the sum of the values is $6 + 6 + 5 = 17$.

API Response (JSON)

{
  "problem": {
    "name": "Knapsack 1",
    "description": {
      "content": "There are $N$ items, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), Item $i$ has a weight of $w_i$ and a value of $v_i$. Taro has decided to choose some of the $N$ items and carry them ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dp_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ items, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), Item $i$ has a weight of $w_i$ and a value of $v_i$.\nTaro has decided to choose some of the $N$ items and carry them ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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