7405: Tandem Bicycle(Problem J5)

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?

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

The second line will contain N (1≤N≤100).

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

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

Each person's speed will be an integer between 1 and 1000000.

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.

1
3
5 1 4
6 2 4

12

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.