[ICPC 2024 Xi'an I] Make Them Straight

Luogu

IDLGP10556

Time2000ms

Memory512MB

DifficultyP4

2024O2优化枚举ICPC调和级数西安

There is a sequence $a$ of non-negative integers of length $n$, the $i$-th element of it is $a_i(1\leq i\leq n)$. A sequence is defined as 'good' if and only if there exists a non negative integer $k(0\leq k\leq 10^6)$ that satisfies the following condition: $a_{i}=a_{1}+(i-1)k$ for all $1\leq i\leq n$. To make this sequence 'good', for each $i(1\leq i\leq n)$, you can do nothing, or pay $b_i$ coin to replace $a_i$ with any non-negative integer. The question is, what is the minimum cost to make this sequence 'good'. ## Input The first line contains an integer $n(1\leq n\leq 2\times 10^5)$, described in the statement. The second line contains $n$ integers $a_1,...,a_n(0\leq a_i\leq 10^6)$. The third line contains $n$ integers $b_1,...,b_n(0\leq b_i\leq 10^6)$. ## Output One integer, the answer. [samples]

Samples

Input #1

5
1 4 3 2 5
1 1 1 1 1

Output #1

Input #2

5
1 4 3 2 5
1 9 1 1 1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2024 Xi'an I] Make Them Straight",
    "description": {
      "content": "There is a sequence $a$ of non-negative integers of length $n$, the $i$-th element of it is $a_i(1\\leq i\\leq n)$. A sequence is defined as 'good' if and only if there exists a non negative integer $k",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 524288
    },
    "difficulty": {
      "LuoguStyle": "P4"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP10556"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a sequence $a$ of non-negative integers of length $n$, the $i$-th element of it is $a_i(1\\leq i\\leq n)$.\n\nA sequence is defined as 'good' if and only if there exists a non negative integer $k...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments