Fifty items and a capacity of 850 form a real knapsack instance, parsed from the same model file the external solver reads. No solving happens yet; the data includes four items that weigh nothing at all.
highlighted = computed this step
A bigger instance
The instance has 50 items and capacity 850. Why: chapters one through three fill a table for four items; this instance is real data from the same model family the external solver reads, parsed from that model file rather than typed in.
n=50,W=850
No computation yet
No item has been chosen. Why: this lesson only states the data — fifty exact weight and value pairs and one capacity — before any solving happens, the same separation chapter one draws between stating the problem and filling the table.
data only, no solve yet
A wrinkle in the data
Four items weigh nothing at all. Why: real data is not always convenient — a zero-weight, positive-value item costs no capacity, so any optimal packing takes it for free; the DP table and the external solver both have to handle that edge case correctly, not just the typical case.
4 zero-weight items
Diagram note
Every cell shows the item's own weight and value, parsed from the real model file. No cell is highlighted yet — selection happens once the instance is actually solved. Pixel positions are rounded for layout; every number shown is exact.