When to Use Knapsack DP

Use knapsack DP when you see these signals:

$1.$ Binary choices per item. You include or exclude each element.

$2.$ Additive constraints. Weights, counts, or sums that accumulate.

$3.$ Optimization or counting. Maximize value, minimize cost, or count ways.

The state typically tracks your current index and remaining capacity. Time complexity is $O(n \times W)$ where $n$ is items and $W$ is the constraint bound. Watch for when $W$ is large. You may need different techniques.