Define State and Transition
Name what dp[i] means precisely.
Define State and Transition is a free Coding Interview Prep lesson on CoddyKit — lesson 2 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Coding Interview Prep learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
The Heart of DP
Every DP starts by naming a state: what does dp[i] actually represent? Get this sentence right and the rest follows.
State Must Be Precise
Write the meaning in words: dp[i] = the answer for the first i items. A fuzzy state definition leads to a buggy recurrence.
dp[i] = best total using items 0..i-1The Transition
The transition tells how dp[i] is built from earlier states. It is the recurrence equation at the core of your solution.
dp[i] = dp[i-1] + dp[i-2]Base Cases Anchor It
Base cases are the smallest states you know directly. Without correct anchors, every later value drifts wrong.
dp[0] = 1Pick an Evaluation Order
Each state must be filled after the states it depends on. That dependency rule fixes your loop direction.
for i in range(1, n+1): ...Where Is the Answer
Decide which cell holds the final result. Often it is dp[n], but sometimes it is the max over the whole table.
answer = dp[n] # or max(dp)Count the States
The number of distinct states sets your time budget. A 1D dp over n items is O(n) states to fill.
Cost Per Transition
Total time is states times the work per transition. An O(n) transition inside n states gives O(n squared).
Add a Dimension When Needed
If one index cannot capture the situation, add another. A second dimension turns dp[i] into dp[i][j].
dp = [[0]*(c+1) for _ in range(n+1)]Reconstruct the Choice
To recover the actual solution, store which transition won at each state, then walk backward from the answer.
choice[i] = "take"A Reusable Checklist
State, transition, base case, order, answer. Pin down those five and almost any DP recurrence falls into place.
Quick Check
You are designing a DP. What does dp[i] represent?
Recap: Name It, Then Solve It
You can now define a state, write its transition, set base cases, and locate the answer. That blueprint turns DP from guesswork into a recipe.
Frequently asked questions
Is the “Define State and Transition” lesson free?
Yes — the full text of “Define State and Transition” is free to read here on the web, and the Coding Interview Prep course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Coding Interview Prep course, upgrade to CoddyKit PRO.
What will I learn in “Define State and Transition”?
Name what dp[i] means precisely. You practise Coding Interview Prep with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Coding Interview Prep?
No prior experience is required. Coding Interview Prep on CoddyKit is structured for beginners through advanced learners; this is — lesson 2 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Define State and Transition” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Coding Interview Prep lesson?
Yes. Every Coding Interview Prep lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.
All lessons in this course
- Memoization vs Tabulation
- Define State and Transition
- Climbing Stairs & Coin Combinations
- Longest Increasing Subsequence