Between Two Binary Strings

AtCoder

IDarc132_d

Time2000ms

Memory256MB

Difficulty—

Let us define the **beauty** of the string as the number of positions where two adjacent characters are the same. For example, the beauty of `00011` is $3$, and the beauty of `10101` is $0$. Let $S_{n,m}$ be the set of all strings of length $n+m$ formed of $n$ `0`s and $m$ `1`s. For $s_1,s_2 \in S_{n,m}$, let us define the **distance** of $s_1$ and $s_2$, $d(s_1,s_2)$, as the minimum number of swaps needed when rearranging the string $s_1$ to $s_2$ by swaps of two adjacent characters. Additionally, for $s_1,s_2,s_3\in S_{n,m}$, $s_2$ is said to be **between** $s_1$ and $s_3$ when $d(s_1,s_3)=d(s_1,s_2)+d(s_2,s_3)$. Given $s,t\in S_{n,m}$, print the greatest beauty of a string between $s$ and $t$. ## Constraints * $2 \le n + m\le 3\times 10^5$ * $0 \le n,m$ * Each of $s$ and $t$ is a string of length $n+m$ formed of $n$ `0`s and $m$ `1`s. ## Input Input is given from Standard Input in the following format: $n$ $m$ $s$ $t$ [samples]

Samples

Input #1

2 3
10110
01101

Output #1

2

Between `10110` and `01101`, whose distance is $2$, we have the following strings: `10110`, `01110`, `01101`, `10101`. Their beauties are $1$, $2$, $1$, $0$, respectively, so the answer is $2$.

Input #2

4 2
000011
110000

Output #2

4

Between `000011` and `110000`, whose distance is $8$, the strings with the greatest beauty are `000011` and `110000`, so the answer is $4$.

Input #3

12 26
01110111101110111101001101111010110110
10011110111011011001111011111101001110

Output #3

API Response (JSON)

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  "problem": {
    "name": "Between Two Binary Strings",
    "description": {
      "content": "Let us define the **beauty** of the string as the number of positions where two adjacent characters are the same. For example, the beauty of `00011` is $3$, and the beauty of `10101` is $0$. Let $S_{n",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc132_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let us define the **beauty** of the string as the number of positions where two adjacent characters are the same. For example, the beauty of `00011` is $3$, and the beauty of `10101` is $0$.\nLet $S_{n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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