A city is served by a number of fire stations. Some residents have complained that the distance from their houses to the nearest station is too far, so a new station is to be built. You are to choose the location of the fire station so as to reduce the distance to the nearest station from the houses of the disgruntled residents.
The city has up to 500 intersections, connected by road segments of various lengths. No more than 20 road segments intersect at a given intersection. The location of houses and firestations alike are considered to be at intersections (the travel distance from the intersection to the actual building can be discounted). Furthermore, we assume that there is at least one house associated with every intersection. There may be more than one firestation per intersection.
]]>
Soundex coding groups together words that appear to sound alike based on their spelling. For example, "can" and "khawn", "con" and "gone" would be equivalent under Soundex coding.
Soundex coding involves translating each word into a series of digits in which each digit represents a letter:
1 represents B, F, P, or V
2 represents C, G, J, K, Q, S, X, or Z
3 represents D or T
4 represents L
5 represents M or N
6 represents R
The letters A, E, I, O, U, H, W, and Y are not represented in Soundex coding, and repeated letters with the same code digit are represented by a single instance of that digit. Words with the same Soundex coding are considered equivalent.
Each line of input contains a single word, all upper case, less than 20 letters long. For each line of input, produce a line of output giving the Soundex code.
]]>
Before bridges were common, ferries were used to transport cars across rivers. River ferries, unlike their larger cousins, run on a guide line and are powered by the river's current. Two lanes of cars drive onto the ferry from one end, the ferry crosses the river, and the cars exit from the other end of the ferry.
The cars waiting to board the ferry form a single queue, and the operator directs each car in turn to drive onto the port (left) or starboard (right) lane of the ferry so as to balance the load. Each car in the queue has a different length, which the operator estimates by inspecting the queue. Based on this inspection, the operator decides which side of the ferry each car should board, and boards as many cars as possible from the queue, subject to the length limit of the ferry. Your job is to write a program that will tell the operator which car to load on which side so as to maximize the number of cars loaded.
]]>
A large field has a dog and a gopher. The dog wants to eat the gopher, while the gopher wants to run to safety through one of several gopher holes dug in the surface of the field.
Neither the dog nor the gopher is a math major; however, neither is entirely stupid. The gopher decides on a particular gopher hole and heads for that hole in a straight line at a fixed speed. The dog, which is very good at reading body language, anticipates which hole the gopher has chosen, and heads at double the speed of the gopher to the hole, where it intends to gobble up the gopher. If the dog reaches the hole first, the gopher gets gobbled; otherwise, the gopher escapes.
You have been retained by the gopher to select a hole through which it can escape, if such a hole exists.
The first line of input contains four floating point numbers: the (x,y) coordinates of the gopher followed by the (x,y) coordinates of the dog. Subsequent lines of input each contain two floating point numbers: the (x,y) coordinates of a gopher hole. All distances are in metres, to the nearest mm.
Your output should consist of a single line. If the gopher can escape the line should read "The gopher can escape through the hole at (x,y)." identifying the appropriate hole to the nearest mm. Otherwise the output line should read "The gopher cannot escape." If the gopher may escape through more than one hole, any one will do. If the gopher and dog reach the hole at the same time either answer may be given. There are not more than 1000 gopher holes and all coordinates are between -10000 and +10000.
]]>2.000 2.000 1.000 1.000 1.500 1.500 2.500 2.500
The gopher can escape through the hole at (2.500,2.500).]]>
Many gas stations use plastic digits on an illuminated sign to indicate prices. When there is an insufficient quantity of a particular digit, the attendant may substitute another one upside down.
The digit "6" looks much like "9" upside down. The digits "0", "1" and "8" look like themselves. The digit "2" looks a bit like a "5" upside down (well, at least enough so that gas stations use it).
Due to rapidly increasing prices, a certain gas station has used all of its available digits to display the current price. Fortunately, this shortage of digits need not prevent the attendant from raising prices. She can simply rearrange the digits, possibly reversing some of them as described above.
Your job is to compute, given the current price of gas, the next highest price that can be displayed using exactly the same digits. The input consists of several lines, each containing between 2 and 30 digits (to account for future prices) and a decimal point immediately before the last digit. There are no useless leading zeroes; that is, there is a leading zero only if the price is less than 1. You are to compute the next highest price that can be displayed using the same digits and the same format rules. An input line containing a decimal point alone terminates the input. If the price cannot be raised, print "The price cannot be raised."
]]>