Ezvor

2060. Check if an Original String Exists Given Two Encoded Strings

HardString Preparing judge… LeetCode

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'.

 

Constraints:

  • 1 <= s1.length, s2.length <= 40
  • s1 and s2 consist of digits 1-9 (inclusive), and lowercase English letters only.
  • The number of consecutive digits in s1 and s2 does not exceed 3.
StringDynamic Programming

Hints

Hint 1
For s1 and s2, divide each into a sequence of single alphabet strings and digital strings. The problem now becomes comparing if two sequences are equal.
Hint 2
A single alphabet string has no variation, but a digital string has variations. For example: "124" can be interpreted as 1+2+4, 12+4, 1+24, and 124 wildcard characters.
Hint 3
There are four kinds of comparisons: a single alphabet vs another; a single alphabet vs a number, a number vs a single alphabet, and a number vs another number. In the case of a number vs another (a single alphabet or a number), can you decrease the number by the min length of both?
Hint 4
There is a recurrence relation in the search which ends when either a single alphabet != another, or one sequence ran out, or both sequences ran out.