11. Container With Most Water

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.

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.

Two Pointer

public int maxArea(int[] height) {
  int maxArea = 0;
  int left = 0, right = height.length - 1;

  while (left < right) {
    int minHeight = Math.min(height[left], height[right]);
    int currentArea = (right - left) * minHeight;
    maxArea = Math.max(maxArea, currentArea);

    if (height[left] < height[right]) {
      left++;
    } else {
      right--;
    }
  }
  return maxArea;
}

Time Complexity	Space Complexity
\(\mathcal{O}(n)\)	\(\mathcal{O}(1)\)