Common Mistakes

$1.$ Forgetting to prove QI: Don't assume it holds. Prove it for your cost function.

$2.$ Wrong iteration order (Knuth): Process by length, not by $i$ then $j$.

$3.$ Off-by-one errors: Bounds are $[opt[i][j-1], opt[i+1][j]]$. Check edge cases.

$4.$ Not storing opt: You need $opt$ values to bound future searches. These optimizations are tricky. Test on small inputs first.