11 Container With Most Water 1

Joel Castillo Espinosa 2

DESCRIPTION

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the $i^{th}$ 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.

Notice that you may not slant the container.

Examples

Fig 1. Diagram for example 1

  • Example 1:
    • 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.
  • Example 2:
    • Input: height = [1,1]
    • Output: 1

Constraints:

  • $n = height.length$
  • 2 ≤ n ≤ $10^{5}$
  • 0 ≤ height[i] ≤ $10^{4}$

SOLUTION 3

container <- function(height, n){
  maxarea <- 0 
  for (i in 0:max(height)) {
    # in each iteration, the height increase by 1 
    # for this height keep the columns that are >= (save in vector ind)
    ind <- grep(TRUE,  height >= i)
    # if at least 2 columns in vector ind -> calculate the max area 
    if(length(ind) >= 2) {
      # for a fixed height, the max area is calculated with the two columns 
        # more distanced (max width: the first and last element in vector ind)
      # the max area is height*width
      area <- i*(ind[length(ind)] -ind[1])
    } else {area <- 0} # otherwise max area is 0
    # comparing the max area with the calculated area
    if(maxarea <= area){ 
      maxarea <- area 
    }
  }
  return(maxarea)
}

Examples using the function

We can use the examples presented before.

container(c(1,8,6,2,5,4,8,3,7))

## [1] 49

container(height = c(1,1))

## [1] 1

  1. This problem is originally from LeetCode, you can find it in Leetcode. ↩

  2. Email: jocastillo@colmex.mx. For more content visit my website: https://joelcastillo.netlify.app
    If you have any questions or suggestions, I’d be grateful to hear from you. ↩

  3. This solution is entirely my own work. It was developed using R version 4.4.1 (2024-06-14 ucrt). ↩