Minimum Coloring

AtCoder

IDabc231_h

Time2000ms

Memory256MB

Difficulty—

We have a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the square at the $i$\-th row from the top and $j$\-th column from the left. On this grid, there are $N$ white pieces numbered $1$ to $N$. Piece $i$ is on $(A_i,B_i)$. You can pay the cost of $C_i$ to change Piece $i$ to a black piece. Find the minimum total cost needed to have at least one black piece in every row and every column. ## Constraints * $1 \leq H,W \leq 10^3$ * $1 \leq N \leq 10^3$ * $1 \leq A_i \leq H$ * $1 \leq B_i \leq W$ * $1 \leq C_i \leq 10^9$ * All pairs $(A_i,B_i)$ are distinct. * There is at least one white piece in every row and every column. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $N$ $A_1$ $B_1$ $C_1$ $\hspace{23pt} \vdots$ $A_N$ $B_N$ $C_N$ [samples]

Samples

Input #1

Output #1

1110

By paying the cost of $1110$ to change Pieces $2, 3, 4$ to black pieces, we can have a black piece in every row and every column.

Input #2

1 7 7
1 2 200000000
1 7 700000000
1 4 400000000
1 3 300000000
1 6 600000000
1 5 500000000
1 1 100000000

Output #2

2800000000

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Minimum Coloring",
    "description": {
      "content": "We have a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. On this grid, there are $N$ white pieces numbered $1$ to $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc231_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left.\nOn this grid, there are $N$ white pieces numbered $1$ to $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments