Recognition Pattern

Overlapping Subproblems

A problem has overlapping subproblems when the recursion tree revisits the same smaller state multiple times. That repetition is the signal that memoization or tabulation can pay off.

SignalDuplicates

ActionCache once

Recursion Tree View

If the same node label appears again and again in different branches, you are paying for the same reasoning more than once.

DP Trigger

Duplicate states mean you can replace branch repetition with one stored answer per unique state.

Active Path

F(7)

Heat Map (Call Counts)

F(7)1 calls

F(6)1 calls

F(5)2 calls

F(4)3 calls

F(3)5 calls

F(2)8 calls

F(1)13 calls

F(0)8 calls

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