Filters

AtCoder

IDabc196_e

Time2000ms

Memory256MB

Difficulty—

Given are integer sequences $A = (a_1, a_2, \dots, a_N)$, $T = (t_1, t_2, \dots, t_N)$, and $X = (x_1, x_2, \dots, x_Q)$. Let us define $N$ functions $f_1(x), f_2(x), \dots, f_N(x)$ as follows: $f_i(x) = \begin{cases} x + a_i & (t_i = 1)\\ \max(x, a_i) & (t_i = 2)\\ \min(x, a_i) & (t_i = 3)\\ \end{cases}$ For each $i = 1, 2, \dots, Q$, find $f_N( \dots f_2(f_1(x_i)) \dots )$. ## Constraints * All values in input are integers. * $1 ≤ N ≤ 2 \times 10^5$ * $1 ≤ Q ≤ 2 \times 10^5$ * $|a_i| ≤ 10^9$ * $1 ≤ t_i ≤ 3$ * $|x_i| ≤ 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $t_1$ $a_2$ $t_2$ $\vdots$ $a_N$ $t_N$ $Q$ $x_1$ $x_2$ $\cdots$ $x_Q$ [samples]

Samples

Input #1

3
-10 2
10 1
10 3
5
-15 -10 -5 0 5

Output #1

0
0
5
10
10

We have $f_1(x) = \max(x, -10), f_2(x) = x + 10, f_3(x) = \min(x, 10)$, thus:

*   $f_3(f_2(f_1(-15))) = 0$
*   $f_3(f_2(f_1(-10))) = 0$
*   $f_3(f_2(f_1(-5))) = 5$
*   $f_3(f_2(f_1(0))) = 10$
*   $f_3(f_2(f_1(5))) = 10$

API Response (JSON)

{
  "problem": {
    "name": "Filters",
    "description": {
      "content": "Given are integer sequences $A = (a_1, a_2, \\dots, a_N)$, $T = (t_1, t_2, \\dots, t_N)$, and $X = (x_1, x_2, \\dots, x_Q)$.   Let us define $N$ functions $f_1(x), f_2(x), \\dots, f_N(x)$ as follows: $f_i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc196_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are integer sequences $A = (a_1, a_2, \\dots, a_N)$, $T = (t_1, t_2, \\dots, t_N)$, and $X = (x_1, x_2, \\dots, x_Q)$.  \nLet us define $N$ functions $f_1(x), f_2(x), \\dots, f_N(x)$ as follows:\n$f_i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments