Prefix Bubble Sort

AtCoder

IDarc181_d

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$. Consider the following operations $k\ (k=2,3,\dots,N)$ on this permutation. * Operation $k$: For $i=1,2,\dots,k-1$ in this order, if $P_i > P_{i+1}$, swap the values of the $i$\-th and $(i+1)$\-th elements of $P$. You are also given a **non-decreasing** sequence $A=(A_1,A_2,\dots,A_M)\ (2 \leq A_i \leq N)$ of length $M$. For each $i=1,2,\dots,M$, find the inversion number of $P$ after applying the operations $A_1, A_2, \dots, A_i$ in this order. What is the inversion number of a sequence? The inversion number of a sequence $x=(x_1,x_2,\dots,x_n)$ of length $n$ is the number of pairs of integers $(i,j)\ (1\leq i < j \leq n)$ such that $x_i > x_j$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq 2 \times 10^5$ * $2 \leq A_i \leq N$ * $P$ is a permutation of $(1,2,\dots,N)$. * $A_i \leq A_{i+1}$ for $i=1,2,\dots,M-1$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\dots$ $P_N$ $M$ $A_1$ $A_2$ $\dots$ $A_M$ [samples]

Samples

Input #1

6
3 2 4 1 6 5
2
4 6

Output #1

3
1

First, operation $4$ is performed. During this, $P$ changes as follows: $(3,2,4,1,6,5) \rightarrow (2,3,4,1,6,5) \rightarrow (2,3,4,1,6,5) \rightarrow (2,3,1,4,6,5)$. The inversion number of $P$ afterward is $3$.
Next, operation $6$ is performed, where $P$ eventually becomes $(2,1,3,4,5,6)$, whose inversion number is $1$.

Input #2

20
12 14 16 8 7 15 19 6 18 5 13 9 10 17 4 1 11 20 2 3
15
3 4 6 8 8 9 10 12 13 15 18 18 19 19 20

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Prefix Bubble Sort",
    "description": {
      "content": "You are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$. Consider the following operations $k\\ (k=2,3,\\dots,N)$ on this permutation. *   Operation $k$: For $i=1,2,\\dots,k-1$ in this or",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc181_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$.\nConsider the following operations $k\\ (k=2,3,\\dots,N)$ on this permutation.\n\n*   Operation $k$: For $i=1,2,\\dots,k-1$ in this or...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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