Solution: Shortest Common Supersequence

Explore how to solve the shortest common supersequence problem by applying dynamic programming techniques. Understand the connection between the longest common subsequence and shortest supersequence, learn to build a DP table for LCS lengths, and reconstruct the shortest supersequence by backtracking through this table. This lesson equips you to efficiently solve string subsequence problems with optimal time and space complexity.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given two strings, str1 and str2. Your task is to find the shortest common supersequence (SCS). The shortest possible string that contains both str1 and str2 as subsequences.

If multiple strings satisfy this condition, you may return any one of them.

Note: A string $s$ is considered a subsequence of another string $t$ if $s$ can be obtained by deleting zero or more characters from $t$ without changing the order of the remaining characters.

Constraints:

$1 \leq$ str1.length, str2.length $\leq 10^3$ ...