7. Trapping Rain Water

Trapping Rainwater

Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.

The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped. Thanks Marcos for contributing this image!

Example:

Input: [0,1,0,2,1,0,1,3,2,1,2,1]
Output: 6

• 計算每一個的左右的最高高度

def container(lst):
  n = len(lst)
  left_max = [0 for _ in range(n)]  #S:O(n)
  right_max = [0 for _ in range(n)] #S:O(n)

  current_left_max = 0
  for i in range(n): #T:O(n)
    current_left_max = max(current_left_max, lst[i])
    left_max[i] = current_left_max

  current_right_max = 0
  for i in range(n-1, -1, -1): #T:O(n)
    current_right_max = max(current_right_max, lst[i])
    right_max[i] = current_right_max

  total = 0
  for i in range(n): #T:O(n)
    total += min(left_max[i],  right_max[i]) - lst[i]

 return total