Dynamic programming in four steps

Dynamic programming Mid-level Python 3.13+ Reviewed By Best Latest Apps

Order the steps

Order the steps for designing a DP.

  • Write how a cell is built from smaller cells
  • Define what one cell of the table means
  • Choose a fill order where each cell's inputs are ready
  • Set the base cases

Choose an answer, then open Show answer below to check it.

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Answer: B A D C

  1. Define what one cell of the table means Everything else depends on this sentence.
  2. Write how a cell is built from smaller cells This is the transition, the heart of the solution.
  3. Set the base cases These cells need no computation.
  4. Choose a fill order where each cell's inputs are ready Then estimate cost and memory.

30-second answer

Work in four steps. 1) State: say in words what one cell means, such as 'fewest coins for amount a'. 2) Transition: how a cell is built from smaller cells. 3) Base cases: the cells you know without computing. 4) Order: fill cells so everything a cell needs is ready. Then the cost is states × work per state, and you can look for memory savings.

Practise saying it · 45 s. No recording, just a timer

Explain your DP process.

Say your answer out loud, then check which of these points you covered:

  • State
  • Transition
  • Base cases and order

Deep dive

Starting from a plain recursive solution and adding a cache is a valid way to find the state.

If you cannot say what a cell means in one sentence, the state is not clear yet.

Check the recurrence by hand on a tiny input before coding.

Common mistakes

  • Coding the table before naming the state.
  • Filling in an order that reads cells not yet computed.

Senior take & follow-ups

Literally say 'the state is …' early; it frames the rest of your answer.

Follow-up questions

Think of your answer first, then open the hint.

  1. How do you know a problem is DP?

    Show hint

    Choices at each step, an optimum or count over all choices, and repeated sub-questions.

  2. What if the state needs too many cells?

    Show hint

    Look for a dimension you can drop, or a greedy property that removes choices.

What each operation costs: Two Dimensional Arrays

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