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SOS DP Ladder

This lane is for the first time a mask problem stops being "add one bit to the state" and becomes "precompute one aggregate for every mask on the full cube."

It is intentionally narrow:

  • one exact starter
  • one flagship complement-mask witness rep
  • strong compare points back to Bitmask DP and Broken Profile

Who This Is For

Use this lane if:

  • Bitmask DP already feels comfortable
  • you can already read complement masks and subset relations without hesitation
  • the real bottleneck is repeated all-submask or all-supermask aggregation

Warm-Up

  • complement-mask modeling
  • subset direction vs superset direction
  • why this is not ordinary dp[mask] with add-one-bit transitions

Warm-up compare points:

Target skill:

  • say clearly whether the task wants subset aggregation, superset aggregation, or one witness carried along the same sweep

Core

Target skill:

  • turn a bitwise predicate into one complement-mask query on a transformed full-cube array

Stretch

Target skill:

  • know when the starter still fits directly and when the real work is modeling several subset/superset counts in one problem

Retrieval Layer

Exit Criteria

You are ready to move on when:

  • you can state whether the query wants submasks or supersets before coding
  • you know when to query mask directly and when to query full ^ mask
  • you can reuse the same sweep skeleton for sums and for one witness value
  • you know not to use this lane when the state is really one evolving subset DP

External Practice