Problem J5: Tandem Bicycle

Problem DescriptionCopy Anchor Link

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 SpecificationCopy Anchor Link

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

The second line contains $N$ ($1 \leq N \leq 100$).

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 SpecificationCopy Anchor Link

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

Sample Input 1Copy Anchor Link

1
3
5 1 4
6 2 4

Output for Sample Input 1Copy Anchor Link

12

Explanation for Output for Sample Input 1Copy Anchor Link

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 2Copy Anchor Link

2
3
5 1 4
6 2 4

Output for Sample Input 2Copy Anchor Link

15

Explanation for Output for Sample Input 2Copy Anchor Link

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 3Copy Anchor Link

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

Output for Sample Input 3Copy Anchor Link

2016

Explanation for Output for Sample Input 3Copy Anchor Link

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 $202+540+189+589+496=2016$.