Treasure Hunting

AtCoder

IDabc227_f

Time3000ms

Memory256MB

Difficulty—

We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i, j)$ denote the square at the $i$\-th row from the top and $j$\-th column from the left. $(i, j)$ contains an integer $A_{i,j}$. Takahashi will depart $(1, 1)$ and repeatedly move one square right or down until reaching $(H, W)$. It is not allowed to exit the grid. The cost of this travel is defined as: > the sum of the $K$ greatest integers among the integers written on the $H+W-1$ squares traversed. Find the minimum possible cost. ## Constraints * $1 \leq H,W \leq 30$ * $1 \leq K < H+W$ * $1 \leq A_{i,j} \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $K$ $A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,W}$ $A_{2,1}$ $A_{2,2}$ $\ldots$ $A_{2,W}$ $\vdots$ $A_{H,1}$ $A_{H,2}$ $\ldots$ $A_{H,W}$ [samples]

Samples

Input #1

1 3 2
3 4 5

Output #1

9

There is only one way to travel, where the traversed squares contain the integers $5$, $4$, $3$ from largest to smallest, so we print $9(=5+4)$.

Input #2

2 2 1
3 2
4 3

Output #2

3

The minimum cost is achieved by traversing $(1,1)$, $(1,2)$, $(2,2)$ in this order.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Treasure Hunting",
    "description": {
      "content": "We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. $(i, j)$ contains an integer $A_{i,j}",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc227_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. $(i, j)$ contains an integer $A_{i,j}...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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