DSA/Dynamic Programming

Dynamic Programming

This is a premium interview-preparation course built around one goal: teaching you to **recognise** a DP problem the moment you see it, derive its state, and write the recurrence — then implement a clean, bottom-up Java 17 solution. You will start with the mental model (overlapping subproblems, optimal substructure, memoization vs tabulation) and then work through curated problems grouped by the patterns interviewers actually test: 1D, grid, sequence, knapsack, decision, string, and advanced interval / game DP.

Curated lessons

Learning modules

14h 39m

Est. study time

Target companies

What you'll learn

Recognise the tell-tale signs of a DP problem: choices, overlapping subproblems, and optimal substructure.
Derive the state definition and state transition (recurrence) systematically from a recursive formulation.
Convert top-down memoization into bottom-up tabulation and then into space-optimized DP.
Communicate your approach the way senior and staff interviewers expect: state, transition, complexity.

Your progress

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Learning roadmap

Work top to bottom — each module builds on the last.

1
Dynamic Programming Fundamentals
Identify state, transition, and base cases
The mental model: spot overlapping subproblems and optimal substructure, then choose memoization or tabulation.
11/11 problems1h 28m
2
1D Dynamic Programming
dp[i] from dp[i-1], dp[i-2] …
A single array of state where each cell depends on a constant number of previous cells — the gateway pattern.
6/6 problems1h 51m
3
Grid Dynamic Programming
dp[i][j] from dp[i-1][j], dp[i][j-1]
Two-dimensional state over a grid where each cell is reached from its top and left neighbours.
5/5 problems1h 50m
4
Sequence Dynamic Programming
dp[i][j] over two sequence indices
State indexed by positions in one or two sequences — subsequences, alignment, and edit operations.
4/4 problems2h
5
Knapsack Pattern
dp[capacity] over items, choose or skip
Choose or skip each item to hit a target capacity — the 0/1 and unbounded knapsack family.
5/5 problems2h 16m
6
Decision Dynamic Programming
dp[i] = OR / min over valid cuts j < i
Partition a value or string into pieces, where each cut is a decision validated against a set.
3/3 problems1h
7
String Dynamic Programming
dp over substring ranges / index pairs
Count or match over substrings, where state spans a range or a pair of positions in the strings.
3/3 problems1h 19m
8
Advanced Dynamic Programming
Interval DP, game DP, k-dimensional state
Interval DP, game theory, and multi-dimensional state — the hardest patterns interviewers reach for.
4/4 problems2h 55m

Modules

8 themed modules from fundamentals to advanced.

Dynamic Programming Fundamentals

The mental model: spot overlapping subproblems and optimal substructure, then choose memoization or tabulation.

11/11 problems1h 28m

1D Dynamic Programming

A single array of state where each cell depends on a constant number of previous cells — the gateway pattern.

6/6 problems1h 51m

Grid Dynamic Programming

Two-dimensional state over a grid where each cell is reached from its top and left neighbours.

5/5 problems1h 50m

Sequence Dynamic Programming

State indexed by positions in one or two sequences — subsequences, alignment, and edit operations.

4/4 problems2h

Knapsack Pattern

Choose or skip each item to hit a target capacity — the 0/1 and unbounded knapsack family.

5/5 problems2h 16m

Decision Dynamic Programming

Partition a value or string into pieces, where each cut is a decision validated against a set.

3/3 problems1h

String Dynamic Programming

Count or match over substrings, where state spans a range or a pair of positions in the strings.

3/3 problems1h 19m

Advanced Dynamic Programming

Interval DP, game theory, and multi-dimensional state — the hardest patterns interviewers reach for.

4/4 problems2h 55m

Full curriculum

30 problems and 11 concept lessons in learning order.

Techniques you'll master

0/1 Knapsack1D DP2D DP3D DPArrayArraysBase CasesBinary SearchBottom-UpBottom-Up DPCircular ArrayCombinationsCombinatoricsCorrectnessCountingDecision DPDynamic ProgrammingFibonacciFoundationsGame TheoryGrid DPHash SetInitializationInterval DPInterview FrameworkJavaLCSMathMatrixMaximisationMemoizationMinimaxMinimizationMinimum CountMulti-Agent DPObstaclesPalindromePartitionPartition DPPatience SortingPatternsPrefix DPRecurrenceRecursionRecursion TreesReverse DPRolling ArraySequence DPShortest PathSpace OptimizationState DesignState MachineStock TradingStringString DPStringsSubsequenceSubset SumTabulationTop-DownTrade-offsTransaction DPTransitionsTriangle DPTwo CapacitiesTwo PointersUnbounded Knapsack