Robot Arms

AtCoder

IDkeyence2020_b

Time2000ms

Memory256MB

Difficulty—

In a factory, there are $N$ robots placed on a number line. Robot $i$ is placed at coordinate $X_i$ and can extend its arms of length $L_i$ in both directions, positive and negative. We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect. Here, for each $i$ ($1 \leq i \leq N$), the movable range of arms of Robot $i$ is the part of the number line between the coordinates $X_i - L_i$ and $X_i + L_i$, excluding the endpoints. Find the maximum number of robots that we can keep. ## Constraints * $1 \leq N \leq 100,000$ * $0 \leq X_i \leq 10^9$ ($1 \leq i \leq N$) * $1 \leq L_i \leq 10^9$ ($1 \leq i \leq N$) * If $i \neq j$, $X_i \neq X_j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $X_1$ $L_1$ $X_2$ $L_2$ $\vdots$ $X_N$ $L_N$ [samples]

Samples

Input #1

Output #1

3

By removing Robot $2$, we can keep the other three robots.

Input #2

2
8 20
1 10

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Robot Arms",
    "description": {
      "content": "In a factory, there are $N$ robots placed on a number line. Robot $i$ is placed at coordinate $X_i$ and can extend its arms of length $L_i$ in both directions, positive and negative. We want to remove",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "keyence2020_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In a factory, there are $N$ robots placed on a number line. Robot $i$ is placed at coordinate $X_i$ and can extend its arms of length $L_i$ in both directions, positive and negative.\nWe want to remove...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments