Explain dynamic programming with a simple example
The short version: dynamic programming refers to solving problems by storing the answers to overlapping subproblems. A quick example makes it concrete — The nth Fibonacci number can be computed in O(n) with memoisation.
How to approach it step by step
Once one example makes sense, the method generalises: define the state, write the recurrence, then fill a table bottom up. In a visual interactive session the example is built on screen piece by piece, so you see which quantity changes at each step instead of only reading a final answer. Ask for a harder variant and the explanation adapts on the spot.
Worked example
The nth Fibonacci number can be computed in O(n) with memoisation.
The mistake most learners make
Applying it to problems without overlapping subproblems, where it adds no benefit.
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