Rectangle Cutting

AtCoder

IDabc130_c

Time2000ms

Memory256MB

Difficulty—

There is a rectangle in a coordinate plane. The coordinates of the four vertices are $(0,0)$, $(W,0)$, $(W,H)$, and $(0,H)$. You are given a point $(x,y)$ which is within the rectangle or on its border. We will draw a straight line passing through $(x,y)$ to cut the rectangle into two parts. Find the maximum possible area of the part whose area is not larger than that of the other. Additionally, determine if there are multiple ways to cut the rectangle and achieve that maximum. ## Constraints * $1 \leq W,H \leq 10^9$ * $0\leq x\leq W$ * $0\leq y\leq H$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $W$ $H$ $x$ $y$ [samples]

Samples

Input #1

2 3 1 2

Output #1

3.000000 0

The line $x=1$ gives the optimal cut, and no other line does.

Input #2

2 2 1 1

Output #2

2.000000 1

API Response (JSON)

{
  "problem": {
    "name": "Rectangle Cutting",
    "description": {
      "content": "There is a rectangle in a coordinate plane. The coordinates of the four vertices are $(0,0)$, $(W,0)$, $(W,H)$, and $(0,H)$. You are given a point $(x,y)$ which is within the rectangle or on its borde",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc130_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a rectangle in a coordinate plane. The coordinates of the four vertices are $(0,0)$, $(W,0)$, $(W,H)$, and $(0,H)$. You are given a point $(x,y)$ which is within the rectangle or on its borde...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments