DSA topic · Stage 6

Dynamic Programming interview preparation

Reuse overlapping subproblem results under a clearly defined state and transition.

DSA prep Practice 6 questions

Concept

DP questions reward precise state definitions more than memorized recurrence formulas.

Complexity lens

Multiply the number of states by transition cost and identify reducible dimensions.

Common mistakes

Choosing a state that lacks needed context
Incorrect base cases
Optimizing space before proving the recurrence

Recognition

Decide from constraints, not labels.

These clues narrow the model. They do not replace an invariant or complexity check.

Recognition clues

Different decision paths revisit the same subproblem
Optimal value or count depends on smaller states
A state can summarize all future-relevant history

Implementation options

Top-down memoization
Bottom-up table
Rolling state when transitions only need a bounded prior frontier

Interview behavior

Define state and transition in a sentence
Prove base cases before optimizing space
Count states times transition work

Patterns that operate on this topic

1D DPdp[i] has one precise meaning for the first i items or state i, and every transition reads only already-correct dependency states.DFSEach active frame owns one node and the unfinished neighbors or child results needed before that frame can resolve.2D DPdp[i][j] has a fixed meaning at the intersection of two prefixes/coordinates, and iteration follows its dependency directions.

Representative problems

6 current Dynamic Programming questions.

Exact active distribution: 1 easy, 4 medium, 1 hard. External records contain metadata and original guidance only.

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Maximum Subarray
Express the decision to extend or restart a running segment.
Arrays Dynamic Programming 1D DP
MediumFree / publicSolve problem
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House Robber
Define the best result up to each position using take-or-skip.
Dynamic Programming Arrays 1D DP
MediumFree / publicSolve problem
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Coin Change
Build minimum solutions from smaller reachable amounts.
Dynamic Programming 1D DP
MediumFree / publicSolve problem
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Longest Increasing Path in a Matrix
Memoize an acyclic increasing traversal from each cell.
Graphs Dynamic Programming Arrays Matrix & Grid Traversal DFS 2D DP
HardFree / publicSolve problem
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Climbing Stairs
Introduces state and recurrence with minimal problem-specific machinery.
Dynamic Programming 1D DP
EasyFree / publicSolve problem
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Unique Paths
Extends state and recurrence reasoning into two dimensions without advanced transitions.
Dynamic Programming 2D DP
MediumFree / publicSolve problem

Review state

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Review prompts

Did the state encode enough history?
Was the iteration order consistent with dependencies?
Did space compression overwrite a needed value?

Prerequisites and next step

Advanced Interview Patterns

Combine ordering, proof, range structure, and compact representation.

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