Find the Highest Altitude

Problem Statement

Imagine a biker embarking on a scenic road trip that consists of multiple points, each at varying altitudes. Starting from point 0 at sea level (altitude 0), the elevation at each subsequent point can either increase or decrease based on a given set of gains or losses. The biker's journey is represented by an array gain, where each element gain[i] indicates the net change in altitude between two consecutive points: from point i to point i + 1. Your objective is to determine the highest altitude reached during this trip.

Examples

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.

Constraints

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

Approach and Intuition

The problem requires simulating a biker's altitude changes over a sequence of elevation gains or losses and determining the highest point reached.

1. Initialize Altitude and Maximum Altitude:

   • Start at altitude 0 and initialize a variable max_altitude to 0.

2. Simulate the Journey:

   • Iterate through the gain array.
   • At each step, add gain[i] to the current altitude.
   • After each addition, check if the current altitude exceeds max_altitude. If so, update max_altitude.

3. Return the Result:

   • Once the array is fully traversed, return the highest altitude stored in max_altitude.

This linear simulation leverages the small constraint size (n ≤ 100) and ensures that the maximum is found with minimal overhead.

Solutions

class Solution {
public:
    int maxAltitude(vector<int>& heightChange) {
        int altitude = 0;
        int highest = altitude;
            
        for (int delta : heightChange) {
            altitude += delta;
            highest = max(highest, altitude);
        }
            
        return highest;
    }
};