11. Container With Most Water

Problem Statement

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, height[i]).

Find two lines that together with the x-axis form a container, such that the container contains the most water.

Return the maximum amount of water a container can store.

Notice that you may not slant the container.

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.

Example 2:

Input: height = [1,1]
Output: 1

Constraints:

n == height.length
2 <= n <= 105
0 <= height[i] <= 104

Intuition

Approach:

Start from the edges
And now from there, greedily search for large walls 

Towards inward

Links

https://leetcode.com/problems/container-with-most-water/description/

Video Links

Approach 1:

C++

class Solution {
public:
    int maxArea(vector<int>& arr) {
        int low=0, high=arr.size()-1;
        int ans=0;

        while(low<high){
            int area = min(arr[low], arr[high]) * (high-low);
            ans = max(ans, area);

            if(arr[low] > arr[high])
                high--;
            else
                low++;
        }

        return ans;
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++