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Drone altitudes: [1, 5, 2, 8, 4, 3] What is a "mountain (bitonic)"? • Strictly increasing for a while (rise) • Exactly one peak • Then strictly decreasing (fall) • Keep order, skipping allowed Example: [1, 2, 8, 4, 3] → rises 1<2<8, falls 8>4>3!
You are choreographing a nighttime drone light show. Each drone in the hangar has a fixed maximum altitude, and you can only launch them in the order they sit in the hangar (skipping some is allowed). The crowd loves the "mountain" shape best: the altitudes of the chosen drones must keep rising for a while, hit a single peak, and then keep falling (a "bitonic" shape). No two consecutive chosen altitudes may be equal (strictly increasing, then strictly decreasing). A purely rising or purely falling run still counts as a mountain. Find the maximum number of drones you can launch while keeping the hangar order.
6 1 5 2 8 4 3
5
Launching altitudes [1, 2, 8, 4, 3] rises 1<2<8, peaks at 8, then falls 8>4>3. Five drones — the longest mountain.
5 3 3 3 3 3
1
All altitudes are equal, so no strict rise or fall is possible. Only a single drone can fly (length 1 still counts).