Find the Summit

Medium

The array profile describes a mountain: its values strictly increase up to the summit and then strictly decrease. Both the climb and the descent have at least one step. Return the index of the summit (0-based). Scanning the whole array for the maximum is easy; solve it in O(log n).

Example 1

profile=[2, 5, 9, 7, 3] → 2

Heights rise to 9 at position 2 and only fall after it.

Example 2

profile=[0, 4, 1] → 1

The shortest possible mountain: one step up, one step down.

Example 3

profile=[1, 3, 6, 10, 15, 14] → 4

Constraints

3 ≤ len(profile) ≤ 10⁵
0 ≤ profile[i] ≤ 10⁶
profile strictly increases up to the summit and strictly decreases after it; the summit is not at either end

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Topics

Array Binary Search

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Input

profile=[2, 5, 9, 7, 3]

Expected

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