State one precise answer
Say what dp[i] means in a full sentence before coding.
One-Dimensional DP
5 chapters · 13 challenges · The Memory Mines
Understand the idea, practise through play, then prove it in code. Choose your next quest below.
Visual introduction to this topic
Start here · 3 minute mental model
What is one-dimensional dynamic programming?
Dynamic programming stores answers to overlapping smaller problems. In one-dimensional DP, each state is usually identified by one changing position, amount, or time.
Think of trail checkpoints. At checkpoint i, reuse the best outcomes already recorded at earlier checkpoints instead of replaying every route from the beginning.
Define dp[i], write its transition, establish bases, then choose an evaluation order.
Transition from solved states
Every dependency must already be available when the current state is computed.
Compress only after clarity
Keep the full table first; reduce memory once dependencies are obvious.
What you will learn firstStair Memories
Begin the guided lesson Build today from two smaller answers
01
State Transition
0/3 completePractice state transition through 3 visual expeditions.
02
Take Or Skip
0/3 completePractice take or skip through 3 visual expeditions.
03
Unbounded Choice
0/3 completePractice unbounded choice through 3 visual expeditions.
04
Subsequence
0/2 completePractice subsequence through 2 visual expeditions.
05
State Compression
0/2 completePractice state compression through 2 visual expeditions.
Source reviewed
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This track is checked against the sources below. Visual traces still carry their own complete or guided coverage label, so unfinished explanations are not presented as complete executions.