CCC '16 S2 - Tandem Bicycle

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Points: 5 (partial)
Time limit: 2.0s
Memory limit: 64M

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Canadian Computing Competition: 2016 Stage 1, Junior #5, Senior #2

Since time immemorial, the citizens of Dmojistan and Pegland have been at war. Now, they have finally signed a truce. They have decided to participate in a tandem bicycle ride to celebrate the truce. There are N citizens from each country. They must be assigned to pairs so that each pair contains one person from Dmojistan and one person from Pegland.

Each citizen has a cycling speed. In a pair, the fastest person will always operate the tandem bicycle while the slower person simply enjoys the ride. In other words, if the members of a pair have speeds a and b, then the bike speed of the pair is \max(a,b). The total speed is the sum of the N individual bike speeds.

For this problem, in each test case, you will be asked to answer one of two questions:

  • Question 1: what is the minimum total speed, out of all possible assignments into pairs?
  • Question 2: what is the maximum total speed, out of all possible assignments into pairs?

Input Specification

The first line will contain the type of question you are to solve, which is either 1 or 2.

The second line contains N (1 \le N \le 100).

The third line contains N space-separated integers: the speeds of the citizens of Dmojistan.

The fourth line contains N space-separated integers: the speeds of the citizens of Pegland.

Each person's speed will be an integer between 1 and 1\,000\,000.

For 8 of the 15 available marks, questions of type 1 will be asked. For 7 of the 15 available marks, questions of type 2 will be asked.

Output Specification

Output the maximum or minimum total speed that answers the question asked.

Sample Input 1

1
3
5 1 4
6 2 4

Output for Sample Input 1

12

Explanation for Output for Sample Input 1

There is a unique optimal solution:

  • Pair the citizen from Dmojistan with speed 5 and the citizen from Pegland with speed 6.
  • Pair the citizen from Dmojistan with speed 1 and the citizen from Pegland with speed 2.
  • Pair the citizen from Dmojistan with speed 4 and the citizen from Pegland with speed 4.

Sample Input 2

2
3
5 1 4
6 2 4

Output for Sample Input 2

15

Explanation for Output for Sample Input 2

There are multiple possible optimal solutions. Here is one optimal solution:

  • Pair the citizen from Dmojistan with speed 5 and the citizen from Pegland with speed 2.
  • Pair the citizen from Dmojistan with speed 1 and the citizen from Pegland with speed 6.
  • Pair the citizen from Dmojistan with speed 4 and the citizen from Pegland with speed 4.

Sample Input 3

2
5
202 177 189 589 102
17 78 1 496 540

Output for Sample Input 3

2016

Explanation for Output for Sample Input 3

There are multiple possible optimal solutions. Here is one optimal solution:

  • Pair the citizen from Dmojistan with speed 202 and the citizen from Pegland with speed 1.
  • Pair the citizen from Dmojistan with speed 177 and the citizen from Pegland with speed 540.
  • Pair the citizen from Dmojistan with speed 189 and the citizen from Pegland with speed 17.
  • Pair the citizen from Dmojistan with speed 589 and the citizen from Pegland with speed 78.
  • Pair the citizen from Dmojistan with speed 102 and the citizen from Pegland with speed 496.

This sum yields 202+540+189+589+496=2016.


Comments


  • 27
    kobortor  commented on June 10, 2020, 1:47 a.m.

    DMOJistan declares victor over PEG!

    https://wcipeg.com/announcement/9383


    • 1
      glasa  commented on Aug. 1, 2020, 7:40 p.m.

      HOORAH! Glory to DMOJistan


  • 0
    fishingguy456  commented on Jan. 23, 2020, 2:22 p.m.

    Why is the answer for the first test case 12 and not 7? 1 can pair with 6, 5 can pair with 2 and 4 can pair with 4, giving an answer that is even smaller.


    • 1
      injust  commented on Jan. 23, 2020, 2:36 p.m.

      6 + 5 + 4 = 15


      • -1
        fishingguy456  commented on Jan. 23, 2020, 10:00 p.m.

        No, for the first test case where the sample output is 12.


        • 2
          leonzalion  commented on Jan. 23, 2020, 10:37 p.m. edit 8

          if the members of a pair have speeds 𝑎 and 𝑏, then the bike speed of the pair is 𝑚𝑎𝑥(𝑎,𝑏).

          As such, when you pair 1 with 6, the pair's bike speed is max(1, 6) = 6. Pairing 5 with 2 gives a bike speed of max(5, 2) = 5 and pairing 4 with 4 gives a bike speed of max(4, 4) = 4. 6 + 5 + 4 = 15

          However, there is a more optimal pairing to minimize the total speed by pairing 6 with 5 (giving a bike speed of 6), pairing 2 with 1 (giving a bike speed of 2), and pairing 4 with 4 (giving a bike speed of 4), resulting in 6 + 4 + 2 = 12, matching the sample output.

          I may be wrong, but I'm assuming you got 7 from adding min(a, b)s instead: 1 + 2 + 4 = 7


  • -1
    MakanDey  commented on Feb. 14, 2019, 9:19 p.m. edited

    For sample case one, shouldn't it be 10 instead of 12 if it wants the minimum?


    • 2
      GeoHD  commented on Feb. 14, 2019, 10:14 p.m.

      No, it should be 12. Look at the explanation. When you pair them up, you only take the sum of all the cyclist which cycles the fastest out of the pair.


  • 18
    d  commented on Feb. 29, 2016, 10:55 p.m.

    Check out the user profile of wcipeg.


  • 36
    PiMachine  commented on Feb. 20, 2016, 10:26 p.m.

    "DMOJ"istan and "PEG"land LOL XD


  • 10
    yellowsn0w1004  commented on Feb. 20, 2016, 3:46 p.m.

    So Tandem Bicycle is problem 5 on the junior exam and is supposed to be the hardest (according to order), but I found that it was significantly easier than problems 3 and 4.

    Am I wrong thinking that the problems are in order of difficulty?

    Anyone else find this weird?


    • 4
      odaniel  commented on Feb. 20, 2016, 6:03 p.m. edited

      It's a "big-data" question - designed to catch people with ultra-naive solutions. Note that the speeds can be as high as one million - if somebody tried to compare every single combination, it would take forever.