C. Three displays

Codeforces

IDCF987C

Time1000ms

Memory256MB

Difficulty—

brute forcedpimplementation

English · Original

Chinese · Translation

Formal · Original

It is the middle of 2018 and Maria Stepanovna, who lives outside Krasnokamensk (a town in Zabaikalsky region), wants to rent three displays to highlight an important problem. There are $n$ displays placed along a road, and the $i$\-th of them can display a text with font size $s_i$ only. Maria Stepanovna wants to rent such three displays with indices $i < j < k$ that the font size increases if you move along the road in a particular direction. Namely, the condition $s_i < s_j < s_k$ should be held. The rent cost is for the $i$\-th display is $c_i$. Please determine the smallest cost Maria Stepanovna should pay. ## Input The first line contains a single integer $n$ ($3 \le n \le 3\,000$) — the number of displays. The second line contains $n$ integers $s_1, s_2, \ldots, s_n$ ($1 \le s_i \le 10^9$) — the font sizes on the displays in the order they stand along the road. The third line contains $n$ integers $c_1, c_2, \ldots, c_n$ ($1 \le c_i \le 10^8$) — the rent costs for each display. ## Output If there are no three displays that satisfy the criteria, print _\-1_. Otherwise print a single integer — the minimum total rent cost of three displays with indices $i < j < k$ such that $s_i < s_j < s_k$. [samples] ## Note In the first example you can, for example, choose displays $1$, $4$ and $5$, because $s_1 < s_4 < s_5$ ($2 < 4 < 10$), and the rent cost is $40 + 10 + 40 = 90$. In the second example you can't select a valid triple of indices, so the answer is _\-1_.

现在是2018年中期，住在克拉斯诺卡门斯克（扎巴伊卡利斯基地区的一个城镇）外的玛丽亚·斯捷潘诺夫娜想租用三块显示屏来突出一个重要问题。沿路摆放着 $n$ 块显示屏，第 $i$ 块显示屏只能显示字体大小为 $s_i$ 的文本。玛丽亚·斯捷潘诺夫娜希望租用三块显示屏，其下标满足 $i < j < k$，且沿道路某一方向移动时，字体大小递增。即需满足条件 $s_i < s_j < s_k$。第 $i$ 块显示屏的租金为 $c_i$。请确定玛丽亚·斯捷潘诺夫娜应支付的最小租金。第一行包含一个整数 $n$（$3 lt.eq n lt.eq 3 thin 000$）——显示屏的数量。第二行包含 $n$ 个整数 $s_1, s_2, dots.h, s_n$（$1 lt.eq s_i lt.eq 10^9$）——沿道路顺序排列的显示屏的字体大小。第三行包含 $n$ 个整数 $c_1, c_2, dots.h, c_n$（$1 lt.eq c_i lt.eq 10^8$）——每个显示屏的租金。如果没有三块显示屏满足条件，请输出 _-1_。否则输出一个整数——满足 $i < j < k$ 且 $s_i < s_j < s_k$ 的三块显示屏的最小总租金。在第一个例子中，你可以选择显示屏 $1$、$4$ 和 $5$，因为 $s_1 < s_4 < s_5$（$2 < 4 < 10$），租金为 $40 + 10 + 40 = 90$。在第二个例子中，无法选出满足条件的三元组下标，因此答案为 _-1_。 ## Input 第一行包含一个整数 $n$（$3 lt.eq n lt.eq 3 thin 000$）——显示屏的数量。第二行包含 $n$ 个整数 $s_1, s_2, dots.h, s_n$（$1 lt.eq s_i lt.eq 10^9$）——沿道路顺序排列的显示屏的字体大小。第三行包含 $n$ 个整数 $c_1, c_2, dots.h, c_n$（$1 lt.eq c_i lt.eq 10^8$）——每个显示屏的租金。 ## Output 如果没有三块显示屏满足条件，请输出 _-1_。否则输出一个整数——满足 $i < j < k$ 且 $s_i < s_j < s_k$ 的三块显示屏的最小总租金。 [samples] ## Note 在第一个例子中，你可以选择显示屏 $1$、$4$ 和 $5$，因为 $s_1 < s_4 < s_5$（$2 < 4 < 10$），租金为 $40 + 10 + 40 = 90$。在第二个例子中，无法选出满足条件的三元组下标，因此答案为 _-1_。

Given: - $ n \in \mathbb{N} $, $ 3 \leq n \leq 3000 $ - Two sequences $ s = (s_1, s_2, \dots, s_n) $, $ c = (c_1, c_2, \dots, c_n) $, where $ s_i \in [1, 10^9] $, $ c_i \in [1, 10^8] $ Find: - Minimum value of $ c_i + c_j + c_k $ over all triples $ (i, j, k) $ such that $ 1 \leq i < j < k \leq n $ and $ s_i < s_j < s_k $ If no such triple exists, return $ -1 $.

Samples

Input #1

5
2 4 5 4 10
40 30 20 10 40

Output #1

Input #2

3
100 101 100
2 4 5

Output #2

\-1

Input #3

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

Output #3

API Response (JSON)

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    "name": "C. Three displays",
    "description": {
      "content": "It is the middle of 2018 and Maria Stepanovna, who lives outside Krasnokamensk (a town in Zabaikalsky region), wants to rent three displays to highlight an important problem. There are $n$ displays p",
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    "platform": "Codeforces",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
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      "statement_type": "Markdown",
      "content": "现在是2018年中期，住在克拉斯诺卡门斯克（扎巴伊卡利斯基地区的一个城镇）外的玛丽亚·斯捷潘诺夫娜想租用三块显示屏来突出一个重要问题。\n\n沿路摆放着 $n$ 块显示屏，第 $i$ 块显示屏只能显示字体大小为 $s_i$ 的文本。玛丽亚·斯捷潘诺夫娜希望租用三块显示屏，其下标满足 $i < j < k$，且沿道路某一方向移动时，字体大小递增。即需满足条件 $s_i < s_j < s_k$。\n\n第 ...",
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      "statement_type": "Markdown",
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