Minimum Cost to Connect Sticks (via extremes, priority-queue idea)

In the equipment room, Zayan must repeatedly combine bamboo practice sticks (cost = sum of the two combined lengths) until only one remains, and wants to MINIMIZE total combining cost. Given N stick lengths, repeatedly combine any two sticks into one (cost = sum of their lengths, and the new stick replaces both) until one stick remains. Minimize total cost. (Think: is picking the two SHORTEST sticks each time optimal? Prove it or find a counterexample before coding.)

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