How to Find Counterexamples

When you suspect greedy might fail:

$1.$ Start with $n = 2$ or $n = 3$ items.

$2.$ Try inputs where greedy's first choice is different from intuition.

$3.$ Compute greedy's answer and brute-force the optimal.

$4.$ If they differ, you found a counterexample. For $0$/$1$ knapsack, I tried several examples before finding one where greedy fails. Small examples make verification easy since you can try all possibilities. Systematically testing small cases catches errors early.