回答 1 已采纳 Description
Mike is frantically scrambling to finish his thesis at the last minute. He needs to assemble all his research notes into vaguely coherent form in the next 3 days. Unfortunately, he notices that he had been extremely sloppy in his calculations. Whenever he needed to perform arithmetic, he just plugged it into a calculator and scribbled down as much of the answer as he felt was relevant. Whenever a repeating fraction was displayed, Mike simply reccorded the first few digits followed by "...". For instance, instead of "1/3" he might have written down "0.3333...". Unfortunately, his results require exact fractions! He doesn't have time to redo every calculation, so he needs you to write a program (and FAST!) to automatically deduce the original fractions.
To make this tenable, he assumes that the original fraction is always the simplest one that produces the given sequence of digits; by simplest, he means the the one with smallest denominator. Also, he assumes that he did not neglect to write down important digits; no digit from the repeating portion of the decimal expansion was left unrecorded (even if this repeating portion was all zeroes).
There are several test cases. For each test case there is one line of input of the form "0.dddd..." where dddd is a string of 1 to 9 digits, not all zero. A line containing 0 follows the last case.
For each case, output the original fraction.
回答 1 已采纳 Description
Rocky rolled over in his bed and looked at his LED alarm clock. He saw what was displayed and went back to sleep. Later, he woke up again and once again glanced at the alarm clock. Although he did not know if all the LED segments were working, he was able to determine with certainty the time. Could you?
Rocky's LED clock uses four 7-segment displays to show the time.
Each 7-segment display has seven bars on it, and displays different numbers by turning on different bars:
_ _ _ _ _ _ _ _
| | | _| _| |_| |_ |_ | |_| |_|
|_| | |_ _| | _| |_| | |_| _|
Using a bit to represent each segment, we can describe a display with seven bits. For example, if the segments are numbered as such:
Then the display:
can be represented with bits:
And the numbers therefore could be represented by:
Number Bit 1 Bit 2 Bit 3 Bit 4 Bit 5 Bit 6 Bit 7
0 1 1 1 1 1 1 0
1 0 1 1 0 0 0 0
2 1 1 0 1 1 0 1
3 1 1 1 1 0 0 1
4 0 1 1 0 0 1 1
5 1 0 1 1 0 1 1
6 1 0 1 1 1 1 1
7 1 1 1 0 0 0 0
8 1 1 1 1 1 1 1
9 1 1 1 1 0 1 1
If a segment on the display is "burnt out", however, it will not display even though it should. For example, if the number three were to be displayed, but the segment corresponding with bit 7 were burnt out, the display would instead be:
The first line contains a single integer n indicating the number of data sets.
Each data set is a single line containing eight 7-bit strings representing the LED displays observed. The first four strings will represent the first time displayed and the next four strings will represent the second time displayed. All of the strings will be separated by a single space. Note: It is not given in the input which segments are burnt out.
For each data set, there will be exactly one line of output. This line will simply be the second time observed in the LED display, in the format HH:MM. The segments that are burnt out will be consistent between the first and second time displayed. There will only be one possible solution for each data set.
All times (for input and output) will be represented in standard (non-military) format, with no leading zeros (nine o'clock is 9:00, not 09:00).
0110000 1101101 1111110 1111111 0000000 1111011 1111110 1111111
0000000 0000000 1000001 1111111 0100000 0000001 0000000 0110000
回答 1 已采纳 Description
There are rumors that there are a lot of computers having a problem with the year 2000. As they use only two digits to represent the year, the date will suddenly turn from 1999 to 1900. In fact, there are also many other, similar problems. On some systems, a 32-bit integer is used to store the number of seconds that have elapsed since a certain fixed date. In this
way, when 2^32 seconds (about 136 Years) have elapsed, the date will jump back to whatever the fixed date is.
Now, what can you do about all that mess? Imagine you have two computers C1 and C with two different bugs: One with the ordinary Y2K-Bug (i. e. switching to a1 := 1900 instead of b1 := 2000) and one switching to a2 := 1904 instead of b2 := 2040. Imagine that the C1 displays the year y1 := 1941 and C2 the year y2 := 2005. Then you know the following (assuming that there are no other bugs): the real year can't be 1941, since, then, both computers would show the (same) right date. If the year would be 2005, y1 would be 1905, so this is impossible, too. Looking only at C1 , we know that the real year is one of the following: 1941, 2041, 2141, etc. We now can calculate what C2 would display in these years: 1941, 1905, 2005, etc. So in fact, it is possible that the actual year is 2141.
To calculate all this manually is a lot of work. (And you don't really want to do it each time you forgot the actual year.) So, your task is to write a program which does the calculation for you: find the first possible real year, knowing what some other computers say (yi) and knowing their bugs (switching to ai instead of bi ). Note that the year ai is definitely not after the year the computer was built. Since the actual year can't be before the year the computers were built, the year your program is looking for can't be before any ai .
The input file contains several test cases, in which the actual year has to be calculated. The description of each case starts with a line containing an integer n (1 <= n <= 20), the number of computers. Then, there is one line containing three integers yi,ai,bi for each computer (0 <= ai <= yi < bi < 10000). yi is the year the computer displays, bi is the year in which the bug happens (i. e. the first year which can't be displayed by this computer) and ai is the year that the computer displays instead of bi .
The input is terminated by a test case with n = 0. It should not be processed.
For each test case, output output the line "Case #k:", where k is the number of the situation. Then, output the line "The actual year is z.", where z is the smallest possible year (satisfying all computers and being greater or equal to u). If there is no such year less than 10000, output "Unkown bugs detected.". Output a blank line after each case.
1941 1900 2000
2005 1904 2040
1998 1900 2000
1999 1900 2000
The actual year is 2141.
Unknown bugs detected.
回答 1 已采纳 Description
City transportation planners are developing a light rail transit system to carry commuters between the suburbs and the downtown area. Part of their task includes scheduling trains on different routes between the outermost stations and the metro center hub.
Part of the planning process consists of a simple simulation of train travel. A simulation consists of a series of scenarios in which two trains, one starting at the metro center and one starting at the outermost station of the same route, travel toward each other along the route. The transportation planners want to find out where and when the two trains meet. You are to write a program to determine those results.
This model of train travel is necessarily simplified. All scenarios are based on the following assumptions.
All trains spend a fixed amount of time at each station.
All trains accelerate and decelerate at the same constant rate. All trains have the same maximum possible velocity.
When a train leaves a station, it accelerates (at a constant rate) until it reaches its maximum velocity. It remains at that maximum velocity until it begins to decelerate (at the same constant rate) as it approaches the next station. Trains leave stations with an initial velocity of zero (0.0) and they arrive at stations with terminal velocity zero. Adjacent stations on each route are far enough apart to allow a train to accelerate to its maximum velocity before beginning to decelerate.
Both trains in each scenario make their initial departure at the same time.
There are at most 30 stations along any route.
All input values are real numbers. Data for each scenario are in the following format.
d1 d2 ... dn 0.0
For a single route, the list of distances (in miles--there are 5,280 feet in a mile) from each station to the metro center hub,separated by one or more spaces. Stations are listed in ascending order, starting with the station closest to the metro center hub (station 1) and continuing to the outermost station. All distances are greater than zero. The list is terminated by the sentinel value 0.0.
The maximum train velocity, in feet/minute.
The constant train acceleration rate in feet/minute².
The number of minutes a train stays in a station.
The series of runs is terminated by a data set which begins with the number -1.0.
For each scenario, output consists of the following labeled data.
The number of the scenario (numbered consecutively, starting with Scenario #1).
The time when the two trains meet in terms of minutes from starting time. All times must be displayed to one decimal place.
The distance in miles between the metro center hub and the place where the two trains meet. Distances must be displayed to three decimal places. Also, if the trains meet in a station, output the number of the station where they meet.
Print a blank line after each scenario.
3.5 7.0 0.0
3.4 7.0 0.0
Meeting time: 7.8 minutes
Meeting distance: 7.500 miles from metro center hub
Meeting time: 4.0 minutes
Meeting distance: 3.500 miles from metro center hub, in station 1
Meeting time: 4.1 minutes
Meeting distance: 3.400 miles from metro center hub, in station 1