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Solution: Distinct Subsequences

Understand how to use dynamic programming to calculate the number of distinct subsequences in a string that match another string exactly. This lesson teaches space optimization techniques by reducing a 2D DP approach to a 1D array while preserving order constraints, and covers the time and space complexity analysis.

Statement

Given two strings, s and t, determine how many distinct subsequences of s match t exactly.

Note: A subsequence is formed by deleting zero or more characters from s without changing the relative order of the remaining characters.

You may assume the result will always fit within a 3232-bit signed integer.

Constraints:

  • 11 \leq s.length, t.length 1000\leq 1000 ...