MediumLeetCode #11Two Pointers

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.

Constraints

n == height.length, 2 <= n <= 10^5, 0 <= height[i] <= 10^4

Examples

Input: height = [1,8,6,2,5,4,8,3,7]

Output: 49

Solution

Approach

Use two pointers at both ends. Calculate area and move the pointer pointing to the shorter line inward (greedy: we can only potentially improve by moving the shorter side).

def maxArea(height):
    left, right = 0, len(height) - 1
    max_area = 0
    while left < right:
        width = right - left
        h = min(height[left], height[right])
        max_area = max(max_area, width * h)
        if height[left] < height[right]:
            left += 1
        else:
            right -= 1
    return max_area

Complexity

Time:O(n)

Space:O(1)

Hints

1.Area is limited by the shorter line
2.Start with widest container
3.Moving shorter line might find taller one

Asked at

Google