[USACO23JAN] Moo Route S

Luogu

IDLGP9015

Time2000ms

Memory512MB

DifficultyP3

贪心USACO2023Special Judge构造

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 $x=0.5,1.5,2.5, \cdots ,(N−1).5$, given by an array $A_0,A_1, \cdots ,A_{N−1} (1 \le N \le 10^5, 1 \le A_i \le 10^6, \sum A_i \le 10^6)$. Bessie never reaches $x>N$ nor $x<0$. In particular, Bessie's route can be represented by a string of $T= \sum\limits_{i=0}^{N-1}A_i$ $L$s and $R$s where the $i$-th character represents the direction Bessie moves in during the ith 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 The first line contains $N$. The second line contains $A_0,A_1,\cdots ,A_{N−1}$. ## Output Output a string $S$ of length $T=\sum\limits_{i=0}^{N-1}A_i$ 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. [samples] ## Note ### Explanation for Sample 1 There is only $1$ valid route, corresponding to the route $0 \rightarrow 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 1 \rightarrow 0$. Since this is the only possible route, it also has the minimum number of direction changes. ### Explanation for Sample 2 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 $3-10$: $T=A_0+A_1+ \cdots +A_{N−1} \le 5000$ - Inputs $11-20$: No additional constraints.

Samples

Input #1

2
2 4

Output #1

RRLRLL

Input #2

3
2 4 4

Output #2

RRRLLRRLLL

API Response (JSON)

{
  "problem": {
    "name": "[USACO23JAN] Moo Route S",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 524288
    },
    "difficulty": {
      "LuoguStyle": "P3"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9015"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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