Find the Highest Altitude

Description

There is a biker going on a road trip. The road trip consists of n + 1 points at different altitudes. The biker starts his trip on point 0 with altitude equal 0. You are given an integer array gain of length n where gain[i] is the net gain in altitude between points i and i + 1 for all (0 <= i < n). Return the highest altitude of a point.

Example 1:
Input: gain = [-5, 1, 5, 0, -7]
Output: 1
Explanation: The altitudes are [0, -5, -4, 1, 1, -6]. The highest is 1.

Example 2:
Input: gain = [-4, -3, -2, -1, 4, 3, 2]
Output: 0
Explanation: The altitudes are [0, -4, -7, -9, -10, -6, -3, -1]. The highest is 0 (the starting point).

Constraints

n == gain.length
1 <= n <= 100
-100 <= gain[i] <= 100

Signature

def solution(gain: list[int]) -> int: ...

Complexity

Time: O(n)
Space: O(1)

Hints

Pattern: Prefix sum / Running sum
Approach: Start at altitude 0. Add each gain to current altitude. Track the maximum altitude seen (including the starting 0).
Complexity: Track running altitude and max altitude in single pass

Solutions

Python

def solution(gain):
    highest = 0
    curr = 0
    for i in range(len(gain)):
        # alt[0] = 0
        # alt[1] = gains[1] - alt[0]
        # alt[2] = gain[2] - alt[1]
        # ...
        alt = gain[i] + curr
        highest = max(highest, alt)
        curr = alt

    return highest