Educational DP Contest AtCoder Q - Flowers

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Points: 15 (partial)
Time limit: 1.4s
Memory limit: 512M

Problem types

These problems are from the AtCoder DP contest, and were transferred onto DMOJ. All problem statements were made by several AtCoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please open a ticket by clicking the "Report an issue" button at the bottom of the page.

There are N flowers arranged in a row. For each i (1 \le i \le N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively. Here, h_1, h_2, \dots, h_N are all distinct.

Taro is pulling out some flowers so that the following condition is met:

  • The heights of the remaining flowers are monotonically increasing from left to right.

Find the maximum possible sum of the beauties of the remaining flowers.

Constraints

  • All values in input are integers.
  • 1 \le N \le 2 \times 10^5
  • 1 \le h_i \le N
  • h_1, h_2, \dots, h_N are all distinct.
  • 1 \le a_i \le 10^9

Input Specification

The first line will contain the integer N.

The next line will contain N integers, h_i.

The next line will contain N integers, a_i.

Output Specification

Print the maximum possible sum of the beauties of the remaining flowers.

Sample Input 1

4
3 1 4 2
10 20 30 40

Sample Output 1

60

Explanation For Sample 1

We should keep the second and fourth flowers from the left. Then, the heights would be 1, 2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20+40 = 60.

Sample Input 2

1
1
10

Sample Output 2

10

Explanation For Sample 2

The condition is met already at the beginning.

Sample Input 3

5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Explanation For Sample 3

The answer may not fit into a 32-bit integer type.

Sample Input 4

9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5

Sample Output 4

31

Explanation For Sample 4

We should keep the second, third, sixth, eighth and ninth flowers from the left.


Comments


  • 5
    anishmahto  commented on Jan. 17, 2019, 5:15 p.m.

    It isn't mentioned here, but assuming the randomly generated test data complies with the original problem's constraints, 1 \leq h_i \leq N. In other words, the heights form a permutation of the integers from 1 to N.

    https://atcoder.jp/contests/dp/tasks/dp_q