Problem Statement
Given an array of nonnegative integers, where each integer represents the height
of a vertical line positioned at index i
. You need to find the two lines that, when combined with the xaxis, form a container that can hold the most water.
The goal is to find the maximum amount of water (area) that this container can hold.
Note: The water container's width is the distance between the two lines, and its height is determined by the shorter of the two lines.
Examples
Example 1:
 Input: [1,3,2,4,5]
 Expected Output: 9
 Justification: The lines at index 1 and 4 form the container with the most water. The width is 3 * (41), and the height is determined by the shorter line, which is 3. Thus, the area is 3 * 3 = 9.
Example 2:
 Input: [5,2,4,2,6,3]
 Expected Output: 20
 Justification: The lines at index 0 and 4 form the container with the most water. The width is 5 * (40), and the height is determined by the shorter line, which is 5. Thus, the area is 5 * 4 = 20.
Example 3:
 Input: [2,3,4,5,18,17,6]
 Expected Output: 17
 Justification: The lines at index 4 and 5 form the container with the most water. The width is 17 * (54), and the height is determined by the shorter line, which is 17. Thus, the area is 17 * 1 = 17.
Solution
Algorithm Description
The "Container With Most Water" problem can be efficiently solved using a twopointer approach. The essence of the solution lies in the observation that the container's capacity is determined by the length of the two lines and the distance between them.
By starting with two pointers at the extreme ends of the array and moving them toward each other, we can explore all possible container sizes. At each step, we calculate the area and update our maximum if the current area is larger. The key insight is to always move the pointer pointing to the shorter line, as this has the potential to increase the container's height and, thus, its capacity.

Initialization: Begin by initializing two pointers, one at the start (
left
) and one at the end (right
) of the array. Also, initialize a variablemaxArea
to store the maximum area found. 
Pointer Movement: At each step, calculate the area formed by the lines at the
left
andright
pointers. If this area is greater thanmaxArea
, updatemaxArea
. Then, move the pointer pointing to the shorter line towards the other pointer. This is because by moving the taller line, we might miss out on a larger area, but by moving the shorter line, we have a chance of finding a taller line and, thus a larger area. 
Termination: Continue moving the pointers until they meet. At this point, we have considered all possible pairs of lines.

Return: Once the pointers meet, return the
maxArea
.
Algorithm Walkthrough
Using the input [1,3,2,4,5]:
 Initialize
left
to 0 andright
to 4.maxArea
is 0.  Calculate area with
left
andright
: min(1,5) * (40) = 4. UpdatemaxArea
to 4.  Move the
left
pointer to 1 since height atleft
is shorter.  Calculate area with
left
andright
: min(3,5) * (41) = 9. UpdatemaxArea
to 9.  Move the
left
pointer to 2.  Calculate area with
left
andright
: min(2,5) * (42) = 4.maxArea
remains 9.  Move the
left
pointer to 3.  Calculate area with
left
andright
: min(4,5) * (43) = 4.maxArea
remains 9.  Pointers meet. Return
maxArea
which is 9.
Code
Complexity Analysis:
 Time Complexity: O(n)  We traverse the array once using two pointers.
 Space Complexity: O(1)  We use a constant amount of space.