Problem - Minimum Cost to Connect Sticks

You have sticks of various lengths. To connect two sticks, the cost is the sum of their lengths. Connect all sticks into one with minimum cost.

For $sticks = [2,4,3]$: connect $2+3=5$ (cost $5$), then $5+4=9$ (cost $9$). Total cost $14$. Or: $2+4=6$ (cost $6$), then $6+3=9$ (cost $9$). Total cost $15$. The first way is better.

Constraint: you can only connect two sticks at a time. Each merge produces a new stick whose length is the sum. Order matters: merging small sticks early keeps costs low.