#2060

Check if an Original String Exists Given Two Encoded Strings

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string · dynamic programming

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Description

An original string, consisting of lowercase English letters, can be encoded by the following steps:

- Arbitrarily split it into a sequence of some number of non-empty substrings.

- Arbitrarily choose some elements (possibly none) of the sequence, and replace each with its length (as a numeric string).

- Concatenate the sequence as the encoded string.

For example, one way to encode an original string "abcdefghijklmnop" might be:

- Split it as a sequence: ["ab", "cdefghijklmn", "o", "p"].

- Choose the second and third elements to be replaced by their lengths, respectively. The sequence becomes ["ab", "12", "1", "p"].

- Concatenate the elements of the sequence to get the encoded string: "ab121p".

Given two encoded strings s1 and s2, consisting of lowercase English letters and digits 1-9 (inclusive), return true if there exists an original string that could be encoded as both s1 and s2. Otherwise, return false.

Note: The test cases are generated such that the number of consecutive digits in s1 and s2 does not exceed 3.

Example 1:

Input: s1 = "internationalization", s2 = "i18n"
Output: true
Explanation: It is possible that "internationalization" was the original string.
- "internationalization"
-> Split: ["internationalization"]
-> Do not replace any element
-> Concatenate: "internationalization", which is s1.
- "internationalization"
-> Split: ["i", "nternationalizatio", "n"]
-> Replace: ["i", "18", "n"]
-> Concatenate: "i18n", which is s2

Example 2:

Input: s1 = "l123e", s2 = "44"
Output: true
Explanation: It is possible that "leetcode" was the original string.
- "leetcode"
-> Split: ["l", "e", "et", "cod", "e"]
-> Replace: ["l", "1", "2", "3", "e"]
-> Concatenate: "l123e", which is s1.
- "leetcode"
-> Split: ["leet", "code"]
-> Replace: ["4", "4"]
-> Concatenate: "44", which is s2.

Example 3:

Input: s1 = "a5b", s2 = "c5b"
Output: false
Explanation: It is impossible.
- The original string encoded as s1 must start with the letter 'a'.
- The original string encoded as s2 must start with the letter 'c'.

Solution