silver_Moo_Route (USACO January_Contest)
Time limit: 2 seconds | Memory limit: 256 MB | Task type: batch
Algorithms: greedy, constructive

Farmer Nhoj dropped Bessie in the middle of nowhere! At time $t=0$, Bessie is
located at $x=0$ on an infinite number line. She frantically searches for an
exit by moving left or right by $1$ unit each second. However, there actually is
no exit and after $T$ seconds, Bessie is back at $x=0$, tired and resigned.
Farmer Nhoj tries to track Bessie but only knows how many times Bessie crosses
$x=.5, 1.5, 2.5, \ldots, (N-1).5$, given by an array $A_0,A_1,\dots,A_{N-1}$
($1\leq N \leq 10^5$, $1 \leq A_i \leq 10^6$, $\sum A_i\le 10^6$). Bessie never
reaches $x>N$ nor
$x<0$.
In particular, Bessie's route can be represented by a string of
$T = \sum_{i=0}^{N-1} A_i$ $L$s and $R$s where the $i$th character represents
the direction Bessie moves in during the $i$th second. The number of direction
changes is defined as the number of occurrences of $LR$s plus the number of
occurrences of $RL$s.
Please help Farmer Nhoj find any route Bessie could have taken that is
consistent with $A$ and minimizes the number of direction changes. It is
guaranteed that there is at least one valid route.
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains $N$. The second line contains $A_0,A_1,\dots,A_{N-1}$.
OUTPUT FORMAT (print output to the terminal / stdout):
Output a string $S$ of length $T = \sum_{i=0}^{N-1} A_i$ where $S_i$ is $L$ or
$R$, indicating the direction Bessie travels in during second $i$. If there are
multiple routes minimizing the number of direction changes, output any.
SAMPLE INPUT:
2
2 4
SAMPLE OUTPUT:
RRLRLL
There is only 1 valid route, corresponding to the route
$0\to 1 \to 2 \to 1\to 2 \to 1\to 0$. Since this is the only possible route, it
also has the minimum number of direction changes.
SAMPLE INPUT:
3
2 4 4
SAMPLE OUTPUT:
RRRLLRRLLL
There are 3 possible routes:
RRLRRLRLLL
RRRLRLLRLL
RRRLLRRLLL
The first two routes have 5 direction changes, while the last one has only 3. 
Thus the last route is the only correct output.
SCORING:
Inputs 3-5: $N\le 2$
Inputs 3-10: $T = A_0 + A_1 + \cdots + A_{N-1} \leq 5000$
Inputs 11-20: No additional constraints.
Problem credits: Brandon Wang and Claire Zhang

Starter code:

Grader code:

Setup script:

Evaluation script: