dynamic-programming

Included with Lifetime

$97 forever

Solve problems with overlapping subproblems and optimal substructure using memoization or tabulation. Use when finding minimum cost, counting ways, or computing longest/shortest subsequences.

General

What this skill does


## When to use

Use dynamic programming when a problem has overlapping subproblems (same computation repeated) and optimal substructure (optimal solution built from optimal sub-solutions).

## Signs

"find minimum cost," "count the number of ways," "longest/shortest subsequence," "can you reach."

## Rules

- Define state (what changes between subproblems) and recurrence (how states relate)
- Top-down with @cache is easiest to write; bottom-up tabulation avoids recursion limits and is often faster
- ALWAYS check if you can reduce space by keeping only the previous row/state instead of the full table
- NEVER memoize without verifying overlapping subproblems exist

## Approach

1. Identify the state variables
2. Write the recurrence relation
3. Choose top-down (@cache) or bottom-up (tabulation)
4. Optimize space if possible

## Example

"Min coins for amount" → state = remaining amount. Recurrence: `dp(n) = 1 + min(dp(n - c) for c in coins)`. Use @cache for top-down; reduce to O(amount) space.

Files: 1

Size: 1.6 KB

Complexity: 10/100

Category: General

Source: https://github.com/knoopx/pi/tree/main/agent/skills/knowledge/dynamic-programming

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