[ICPC 2022 Xi'an R] Cells Coloring

Luogu

IDLGP9359

Time1000ms

Memory512MB

DifficultyP5

2022三分网络流O2优化二分图ICPC西安

You are given an $n \times m$ grid. Some of the cells are obstacles, the others are empty. Choose a non-negative integer $k$ and color all empty cells with $k+1$ colors $0, 1, 2, \ldots k$. You can not color two cells in the same row or same column with the same **non-zero** color. You are given two non-negative integers $c$ and $d$. For a coloring plan, define $z$ as the number of the cells with color $0$. Define the cost of the plan is $ck+dz$. Find the minimum cost. ## Input The first line contains four integers $n$, $m$ ($1\leq n, m\leq 250$), $c$ and $d$ ($0\leq c, d\leq 10 ^ 9$). The $i$-th line of the next $n$ lines contains a string of $m$ characters. The $j$-th character is `*` if the cell in the $i$-th row and the $j$-th column is an obstacle. The $j$-th character is `.` if the cell in the $i$-th row and the $j$-th column is empty. ## Output Output a line with a single number, representing the answer. [samples] ## Note **Source**: The 2022 ICPC Asia Xi'an Regional Contest Problem B. **Author**: csy2005.

Samples

Input #1

3 4 2 1
.***
*..*
**..

Output #1

Input #2

3 4 1 2
.***
*..*
**..

Output #2

API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2022 Xi'an R] Cells Coloring",
    "description": {
      "content": "You are given an $n \\times m$ grid. Some of the cells are obstacles, the others are empty. Choose a non-negative integer $k$ and color all empty cells with $k+1$ colors $0, 1, 2, \\ldots k$. You can no",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 524288
    },
    "difficulty": {
      "LuoguStyle": "P5"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9359"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an $n \\times m$ grid. Some of the cells are obstacles, the others are empty. Choose a non-negative integer $k$ and color all empty cells with $k+1$ colors $0, 1, 2, \\ldots k$. You can no...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments