Problem A: Adventures in Moving - Part IV

To help you move from Waterloo to the big city, you are considering renting a moving truck. Gas prices being so high these days, you want to know how much the gas for such a beast will set you back.

The truck consumes a full litre of gas for each kilometre it travels. It has a 200 litre gas tank. When you rent the truck in Waterloo, the tank is half full. When you return it in the big city, the tank must be at least half full, or you'll get gouged even more for gas by the rental company. You would like to spend as little as possible on gas, but you don't want to run out along the way.

Input is all integers. The first integer is the distance in kilometres from Waterloo to the big city, at most 10000. Next comes a set of up to 100 gas station specifications, describing all the gas stations along your route, in non-decreasing order by distance. Each specification consists of the distance in kilometres of the gas station from Waterloo, and the price of a litre of gas at the gas station, in tenths of a cent, at most 2000.

Output is the minimum amount of money that you can spend on gas to get you from Waterloo to the big city. If it is not possible to get from Waterloo to the big city without running out of gas along the way, output "Impossible".

Problem B: Pairsumonious Numbers

For 10 > N > 2 numbers we form N*(N-1)/2 sums by adding every pair of the numbers. Your task is to find the N numbers given the sums. Each line of input contains N followed by N*(N-1)/2 integer numbers separated by a space. For each line of input, output one line containing N integers in non-descending order such that the input numbers are pairwise sums of the N numbers. If there is more than one solution, any one will do; if there is no solution, print "Impossible".

Problem C: Snow Clearing

As the days become shorter and the nights become longer we turn our thoughts to snow clearing. Due to budget cuts, the Big Noisy City has exactly one snow plow. The plow can clear exactly one lane of a road in a single pass. Whenever there is snow on the ground, the plow departs from its hangar and tours the city, plowing as it goes. What is the minimum time that the plow needs to clear every lane of every road?

The first line of input contains two integers: the x,y coordinates of the hangar (in metres). Up to 100 lines follow. Each gives the coordinates (in metres) of the beginning and end of a street. All roads are perfectly straight, with one lane in each direction. The plow can turn any direction (including a U-turn) at any intersection, and can turn around at the end of any street. The plow travels at 20 km/h if it is plowing, and 50 km/h if the lane it is driving on has already been plowed. It is possible to reach all streets from the hangar.

Your output should be the time, in hours and minutes, required to clear the streets and return to the hangar. Round to the nearest minute.

Problem D: Adventures in Moving - Part V

To save money you are considering renting a small cube van to transport your belongings to the Big City. The interior of the van is a rectangular box with width w, height h, and length l. The box has a sliding door that lifts but only to height H. That is, there is an immovable overhang of height H-h at the top of the door.

You have a large rectangular box that you wish to load on the truck. Can you get it on the truck subject to the following constraints:

• The box must fit through the door, tilting it forward or sideways (but not both) as necessary (see figure below).
• The box must be placed with one side flat against the floor.
• The box must be placed with one side flat against the front wall.
• The door must close once the box is in place.

You may assume there are no obstructions (such as a ceiling or the ground) outside the truck that might interfere with loading.

There are several test cases, each represented by two lines of input. The first line of each contains 4 integers: w, h, l, H. The next line contains 3 integers - the dimensions of the box. For each test case, print "The box goes on the truck." if it is possible to load the box on the truck; otherwise print "The box will not go on the truck." You may assume that you start with an empty truck for each test case.

Problem E: Stack 'em Up

A standard playing card deck contains 52 cards, 13 values in each of four suits. The values are named 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace. The suits are named Clubs, Diamonds, Hearts, Spades. A particular card in the deck can be uniquely identified by its value and suit, typically denoted <value> of <suit>. For example, "9 of Hearts" or "King of Spades". Traditionally a new deck is ordered first alphabetically by suit, then by value in the order given above.

The Big City has many Casinos. In one such casino the dealer is a bit crooked. She has perfected several shuffles; each shuffle rearranges the cards in exactly the same way whenever it is used. A very simple example is the "bottom card" shuffle which removes the bottom card and places it at the top. By using various combinations of these known shuffles, the crooked dealer can arrange to stack the cards in just about any particular order.

You have been retained by the security manager to track this dealer. You are given a list of all the shuffles performed by the dealer, along with visual cues that allow you to determine which shuffle she uses at any particular time. Your job is to predict the order of the cards after each in a sequence of shuffles.

Input consists of an integer n <= 100, the number of shuffles that the dealer knows. 52n integers follow. Each consecutive 52 integers will comprise all the integers from 1 to 52 in some order. Within each set of 52 integers, i in position j means that the shuffle moves the i^th card in the deck to position j.

Several lines follow; each containing an integer k between 1 and n indicating that you have observed the dealer applying the k^th shuffle given in the input.

Assume the dealer starts with a new deck ordered as described above. After each shuffle, give the names of the cards in the deck, in the new order, followed by an empty line.