Compress Strings

AtCoder

IDabc343_g

Time5000ms

Memory256MB

Difficulty—

You are given $N$ strings $S_1, S_2, \ldots, S_N$. Find the minimum length of a string that contains all these strings as substrings. Here, a string $S$ contains a string $T$ as a substring if $T$ can be obtained by deleting zero or more characters from the beginning and zero or more characters from the end of $S$. ## Constraints * $N$ is an integer. * $1 \leq N \leq 20$ * $S_i$ is a string consisting of lowercase English letters whose length is at least $1$. * The total length of $S_1, S_2, \dots, S_N$ is at most $2\times 10^5$. ## Input The input is given from Standard Input in the following format: $N$ $S_1$ $S_2$ $\vdots$ $S_N$ [samples]

Samples

Input #1

3
snuke
kensho
uk

Output #1

9

The string `snukensho` of length $9$ contains all of $S_1$, $S_2$, and $S_3$ as substrings.
Specifically, the first to fifth characters of `snukensho` correspond to $S_1$, the fourth to ninth correspond to $S_2$, and the third to fourth correspond to $S_3$.
No shorter string contains all of $S_1$, $S_2$, and $S_3$ as substrings. Thus, the answer is $9$.

Input #2

3
abc
abc
arc

Output #2

Input #3

6
cmcmrcc
rmrrrmr
mrccm
mmcr
rmmrmrcc
ccmcrcmcm

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Compress Strings",
    "description": {
      "content": "You are given $N$ strings $S_1, S_2, \\ldots, S_N$. Find the minimum length of a string that contains all these strings as substrings. Here, a string $S$ contains a string $T$ as a substring if $T$ can",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc343_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ strings $S_1, S_2, \\ldots, S_N$.\nFind the minimum length of a string that contains all these strings as substrings.\nHere, a string $S$ contains a string $T$ as a substring if $T$ can...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments