Digit Sum Minimization

AtCoder

IDarc130_c

Time2000ms

Memory256MB

Difficulty—

Given are positive integers $a, b$, where none of the digits is $0$. Permute the digits of each of $a$ and $b$ so that the sum of the digits in $a+b$ is minimized. ## Constraints * $1\leq a, b< 10^{100000}$ * None of the digits of $a$ and $b$ is $0$. ## Input Input is given from Standard Input in the following format: $a$ $b$ [samples]

Samples

Input #1

253
286

Output #1

532
268

We have $532 + 268 = 800$, whole digits sum to $8+0+0=8$.
Other solutions will also be accepted, such as $(a, b) = (325, 682)$.

Input #2

345
556

Output #2

435
565

We have $435+565=1000$, whole digits sum to $1+0+0+0=1$.

Input #3

123
987987

Output #3

312
799788

We have $312 + 799788 = 800100$, whole digits sum to $8+0+0+1+0+0=9$.

Input #4

11111111111111111111
111111111111111111111111111111

Output #4

11111111111111111111
111111111111111111111111111111

API Response (JSON)

{
  "problem": {
    "name": "Digit Sum Minimization",
    "description": {
      "content": "Given are positive integers $a, b$, where none of the digits is $0$. Permute the digits of each of $a$ and $b$ so that the sum of the digits in $a+b$ is minimized.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc130_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are positive integers $a, b$, where none of the digits is $0$.\nPermute the digits of each of $a$ and $b$ so that the sum of the digits in $a+b$ is minimized.\n\n## Constraints\n\n*   $1\\leq a, b< 10...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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