#11 - Container With Most Water

MediumTwo Pointers

Given an integer array height of length n, where each element represents the height of a vertical line drawn at index i, find two lines that together with the x-axis form a container that holds the most water. Return the maximum amount of water the container can store. The container may not be slanted.

Input	Output
height = [1,8,6,2,5,4,8,3,7]	49
height = [1,1]	1
height = [4,3,2,1,4]	16

Solution Space

Try it

/**
 * Finds the maximum area of water a container formed by two lines can hold.
 *
 * @param height Array of line heights
 * @returns Maximum water area
 */
export function maxArea(height: number[]): number {
  let left = 0;
  let right = height.length - 1;
  let max = 0;

  while (left < right) {
    const width = right - left;
    const h = Math.min(height[left], height[right]);
    max = Math.max(max, width * h);

    // Moving the shorter line inward is the only way to potentially increase area
    if (height[left] < height[right]) left++;
    else right--;
  }

  return max;
}

Approach: two pointers (greedy) – maintain left and right pointers, moving the pointer with the smaller height inward to maximize the area.

Time: O(n) – each pointer moves at most n steps total.

Space: O(1) – only a few variables.

Alternative approaches:

Approach	Idea	Time	Space
Brute force	Try every pair (i, j) and track the max area.	O(n²)	O(1)

Why the two-pointer method is preferred:

• Reduces O(n²) brute force to O(n) by exploiting the insight that moving the shorter line inward is the only move that can improve the result; the wider container with a shorter line can never beat the current best once that shorter line is the bottleneck.

#1768 Merge Strings Alternately

#283 Move Zeroes