The two pointers approach efficiently searches for the maximum area by starting with the widest possible container and gradually narrowing it:
This approach works due to the observation that the area is limited by the shorter line, so the only way to get a larger area is to find a taller line.
Time Complexity: O(n), where n is the number of elements in the height array, due to the single traversal of the array.
Space Complexity: O(1) as only a few extra variables are used.
1function maxArea(height) {
2 let left = 0;
3 let right = height.length - 1;
4 let maxArea = 0;
5
6 while (left < right) {
7 const h = Math.min(height[left], height[right]);
8 maxArea = Math.max(maxArea, h * (right - left));
9
10 if (height[left] < height[right]) {
11 left++;
12 } else {
13 right--;
14 }
15 }
16
17 return maxArea;
18}
19
20console.log(maxArea([1, 8, 6, 2, 5, 4, 8, 3, 7]));Implemented in JavaScript, this solution adopts the two-pointer method to calculate maximum container area by appropriately adjusting the pointers based on the height comparison.
Although not optimal for large inputs, the brute force approach explores every possible pair of lines to find the maximum container area:
However, the complexity of this approach makes it unsuitable for large datasets due to its quadratic time complexity.
Time Complexity: O(n^2), where n is the number of elements as each pair is checked.
Space Complexity: O(1) due to a linear amount of extra space.
1function maxArea(height) {
2 let maxArea = 0;
3 for (let i = 0; i < height.length - 1; i++) {
4 for (let j = i + 1; j < height.length; j++) {
5 const h = Math.min(height[i], height[j]);
6 maxArea = Math.max(maxArea, h * (j - i));
7 }
8 }
9 return maxArea;
10}
11
12console.log(maxArea([1, 8, 6, 2, 5, 4, 8, 3, 7]));This JavaScript brute force approach iterates over each potential pair of heights, assessing and recording the maximum container area possible.