A Independent Set

AtCoder

IDagc066_d

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ consisting of `A` and `B`. It is guaranteed that the number of `A`s in $S$ is at most $\frac{N+1}{2}$. Additionally, you are given a sequence of positive integers $(x_1, \ldots, x_{N-1})$. On this string, you can repeatedly perform the following operation: * Choose an integer $i$ such that $1\leq i\leq N-1$, and swap the $i$\-th and $(i+1)$\-th characters of $S$. The cost of this operation is $x_i$. Your goal is to rearrange $S$ so that no two `A`s are adjacent. Find the minimum total cost required to achieve this goal. $T$ test cases are given; solve each of them. ## Constraints * $1\leq T\leq 10^5$ * $2\leq N\leq 10^6$ * $S$ is a string of length $N$ consisting of `A` and `B`. * The number of `A`s in $S$ is at most $\frac{N+1}{2}$. * $1\leq x_i \leq 10^6$ * The sum of $N$ over all test cases in a single input is at most $10^6$. ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\vdots$ $\text{case}_T$ Each test case is given in the following format: $N$ $S$ $x_1$ $\ldots$ $x_{N-1}$ [samples]

Samples

Input #1

5
4
BAAB
3 4 5
5
BBBBB
1 2 3 4
7
BAAABBB
8 7 6 5 4 3
7
BAAABBB
100 7 6 5 4 3
20
BAABAABBBABAAABBBABB
12 85 37 44 25 14 36 29 71 53 15 47 13 80 14 74 53 76 19

Output #1

3
0
13
15
133

*   For the first test case, performing the operation with $i=1$ changes $S$ as `BAAB` → `ABAB`, achieving the goal. The total cost in this case is $x_1=3$.
*   For the second test case, performing nothing achieves the goal. The total cost in this case is $0$.
*   For the third test case, performing the operation with $i=1$ and $i=4$ changes $S$ as `BAAABBB` → `ABAABBB` → `ABABABB`, achieving the goal. The total cost in this case is $x_1+x_4=13$.
*   For the fourth test case, performing the operation with $i=4$, $i=3$, and $i=5$ changes $S$ as `BAAABBB` → `BAABABB` → `BABAABB` → `BABABAB`, achieving the goal. The total cost in this case is $x_4+x_3+x_5=15$.

API Response (JSON)

{
  "problem": {
    "name": "A Independent Set",
    "description": {
      "content": "You are given a string $S$ of length $N$ consisting of `A` and `B`. It is guaranteed that the number of `A`s in $S$ is at most $\\frac{N+1}{2}$. Additionally, you are given a sequence of positive integ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc066_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ consisting of `A` and `B`. It is guaranteed that the number of `A`s in $S$ is at most $\\frac{N+1}{2}$. Additionally, you are given a sequence of positive integ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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