Container With Most Water

Problem Statement

Given n non-negative integers a₁, a₂, ..., a_n, where each represents a point at coordinate (i, a_i). n vertical lines are drawn such that the two endpoints of line i is at (i, a_i) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water.

Note: You may not slant the container.

Source: https://leetcode.com/problems/container-with-most-water/
Programming Language: C#
Run Time Complexity: O(N)
Space Complexity: Constant space

Analysis:
In order to maximize the area we need to find out the farthest points with maximum possible.

Solution

public int MaxArea(IList<int> height)
{
    // Input validation
    if ((height == null) || (height.Count <= 1))
        return 0;

    // Track maxArea found so far
    int maxArea = Int32.MinValue;
    // Start index 
    int low = 0;
    // End Index
    int high = height.Count - 1;

    // While low is less than high
    while (low < high)
    {
        // Area equal to difference of high and low and min of heigh at that index
        int area = (high - low) * Math.Min(height[low], height[high]);

        // If area is greater than maxArea update
        maxArea = Math.Max(area, maxArea);

        // in an attemt to maximize the area 
        // increment the low if height at low is less than height at high
        if (height[low] < height[high])
            low = low + 1;
        // else decrement high
        else
            high = high - 1;
    }
    return maxArea;
}