Common Mistakes

$1.$ Forgetting to verify convexity. If $g(k)$ isn't convex, binary search won't find the right $\lambda$.

$2.$ Not handling ties properly. When multiple $k$ values give the same cost, track counts carefully.

$3.$ Wrong binary search bounds. Start with reasonable bounds on $\lambda$: typically $[0, \max\_cost]$.

$4.$ Precision issues with floating-point $\lambda$. Sometimes you need integer binary search with careful rounding.