n towers in a row, and tower i has height heights[i]. You stand on tower 0 and want to reach the last one, n - 1, hopping forward only.
From tower i you may hop to tower j > i in one of two cases:
- heights[i] ≤ heights[j], and every tower strictly between them is lower than heights[i];
- heights[i] > heights[j], and every tower strictly between them is at least heights[i].
Landing on tower j costs fees[j]. Return the minimum total cost of reaching the last tower (the starting tower is free).heights=[4, 1, 3, 5], fees=[0, 2, 6, 3] → 3
From tower 0 (height 4) you can hop straight to tower 3 (height 5), since both towers in between are lower than 4. That costs 3. The route 0 → 1 → 2 → 3 would cost 2 + 6 + 3 = 11, and tower 2 cannot be reached from tower 0 directly.
heights=[2, 2, 2], fees=[5, 1, 4] → 5
Tower 2 cannot be reached from tower 0 directly: the tower in between is just as tall, not lower. The only route is 0 → 1 → 2 for 1 + 4 = 5. You never pay for the starting tower.
heights=[7], fees=[9] → 0
heights=[4, 1, 3, 5], fees=[0, 2, 6, 3]
3
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