Spiderman
Time Limit: 1000MS | Memory Limit: 65536K | |||
Total Submissions: 1032 | Accepted: 364 | Special Judge |
Description
Staying
fit is important for every superhero, and Spiderman is no exception.
Every day he undertakes a climbing exercise in which he climbs a
certain height of a tall building, rests for a minute, then climbs
again, rests again, and so on. The exercise is described by a sequence
of heights d1, d2, d3, ... , dm telling how many meters he is to climb
before the first break, before the second break, and so on. From an
exercise perspective it does not really matter if he climbs up or down
at the ith climbing stage, but it is practical that sometimes climbs up
and sometimes climbs down, so that he both starts and finishes at
street level. Obviously, he can never be below street level! Also, he
would like to climb as short a building as possible (he does not like
to admit it, but he is actually afraid of heights). The building must
be at least 2 meters higher than the highest point his feet reach
during the workout.
He wants your help in determining when he should go up and when he should go down. The answer must be legal: it must start and end at street level (0 meters above ground) and it may never go below street level. Among the legal solutions he wants one that minimizes the required building height. When looking for a solution, you may not reorder distances.
If the distances are 20 20 20 20, he can either climb up, up, down, down or up, down, up, down. Both are legal, but the second one is better (in fact optimal) because it only requires a building of height 22, whereas the first one requires a building of height 42. If the distances are 3 2 5 3 1 2, an optimal legal solution is to go up, up, down, up, down, down. Note that for some distance sequences there is no legal solution at all (e.g., for 3 4 2 1 6 4 5).
He wants your help in determining when he should go up and when he should go down. The answer must be legal: it must start and end at street level (0 meters above ground) and it may never go below street level. Among the legal solutions he wants one that minimizes the required building height. When looking for a solution, you may not reorder distances.
If the distances are 20 20 20 20, he can either climb up, up, down, down or up, down, up, down. Both are legal, but the second one is better (in fact optimal) because it only requires a building of height 22, whereas the first one requires a building of height 42. If the distances are 3 2 5 3 1 2, an optimal legal solution is to go up, up, down, up, down, down. Note that for some distance sequences there is no legal solution at all (e.g., for 3 4 2 1 6 4 5).
Input
The
first line of the input contains an integer N giving the number of test
cases. The following 2N lines specify the test cases, two lines per
test case: the first line gives a positive integer M, which is the
number of heights, and the following line contains the M positive
integer heights. For any test case, the total distance climbed (the sum
of the heights in that test case) is at most 1000.
Output
For
each test case a single line should be output. This line should either
be the string "IMPOSSIBLE" if no legal solution exists, or it should be
a string of length M, containing only the characters "U" and "D", where
the ith character indicates if Spiderman should climb up or down at the
ith stage. If there are several different legal and optimal solutions,
output one of them (it does not matter which one as long as it is
optimal).
Sample Input
3
4
20 20 20 20
6
3 2 5 3 1 2
7
3 4 2 1 6 4 5
Sample Output
UDUD
UUDUDD
IMPOSSIBLE
Source
設mn[i][j]爲走完第i個在j高度時候達到的最小的最高值是什麼
在構造最優解的時候出現了下述錯誤,找了很久。
原因:
1.邏輯不清;
2.查代碼看的不全面,要注意這種關係。
3.樣例出現了毛病,應該多測幾組,各個情況應予以考慮。