The Runtime Theory
hardLeetCode#dynamic-programming#counting

Distinct Subsequences

Count subsequences of s equal to t while preserving character order.

The Runtime Theory Team25 min read
Solve it

Solving happens on the judge — come back and mark it done

Sample cases

ins="rabbbit", t="rabbit"

out3

ins="babgbag", t="bag"

out5

ins="abc", t=""

out1

Count subsequences of s equal to t while preserving character order.

A good solution should

  • State the invariant or decision rule that makes the approach correct.
  • Explain time and space costs in terms of input size and required output.
  • Handle empty, minimal, duplicate, and boundary-shaped inputs.

Reasoning prompt

When characters match, count both using and skipping the source character. Iterate target states backward in a one-dimensional optimization.

Use the linked judge for the canonical challenge. The examples above are compact TRT checks; create additional tests around the boundary most likely to break your invariant.

More practice in this topic

One dispatch a week

The trace behind each problem, the tradeoff that explains it, and one technical dispatch per week — no noise.

One technical dispatch per week. No noise.

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