Find the Highest Altitude

Find the Highest Altitude - Problem

A biker is going on a road trip consisting of n + 1 points at different altitudes. The biker starts at point 0 with altitude 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 reached during the trip.

Input & Output

Example 1 — Basic Case

$ Input: gain = [-3,1,5,-3,1]

› Output: 3

💡 Note: Altitudes: 0 → -3 → -2 → 3 → 0 → 1. The highest altitude reached is 3.

Example 2 — All Negative Gains

$ Input: gain = [-4,-3,-2,-1]

› Output: 0

💡 Note: Starting altitude 0 is the highest since all gains are negative: 0 → -4 → -7 → -9 → -10.

Example 3 — All Positive Gains

$ Input: gain = [1,2,3]

› Output: 6

💡 Note: Altitudes increase continuously: 0 → 1 → 3 → 6. Maximum is 6.

Constraints

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

Visualization

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Asked in

A Amazon 15 G Google 12 M Microsoft 8

The key insight is to use a running sum (prefix sum) to track current altitude while maintaining the maximum altitude seen. The optimal approach processes the array in a single pass with O(n) time and O(1) space.

Common Approaches

✓ Brute Force - Recalculate Each Altitude

⏱️ Time: O(n²) Space: O(1)

At each point i, calculate the altitude by summing gain[0] + gain[1] + ... + gain[i-1]. Track the maximum altitude seen across all points.

Prefix Sum - Single Pass Optimization

⏱️ Time: O(n) Space: O(1)

Maintain a running sum (current altitude) as we iterate through the gain array. At each step, update the current altitude and track the maximum altitude seen so far.

Brute Force - Recalculate Each Altitude — Algorithm Steps

For each point from 0 to n, calculate cumulative altitude
Sum all gains from start to current point
Track maximum altitude encountered

Visualization

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Step-by-Step Walkthrough

Point 0

Start at altitude 0

Point 1

Calculate: 0 + gain[0] = -3

Point 2

Recalculate: 0 + gain[0] + gain[1] = -3 + 1 = -2

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int solution(int* gain, int size) {
    int maxAltitude = 0; // Starting altitude
    
    // Check altitude at each point
    for (int i = 0; i <= size; i++) {
        int currentAltitude = 0;
        // Sum all gains up to point i
        for (int j = 0; j < i; j++) {
            currentAltitude += gain[j];
        }
        if (currentAltitude > maxAltitude) {
            maxAltitude = currentAltitude;
        }
    }
    
    return maxAltitude;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    line[strcspn(line, "\n")] = 0;
    
    // Parse array
    int gain[1000];
    int size = 0;
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        gain[size++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    printf("%d\n", solution(gain, size));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

For each of n points, we sum up to n gain values

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables for tracking

✓ Linear Space

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Related Problems

Common Approaches

Brute Force - Recalculate Each Altitude — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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