Rainwater Trapping

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ArrayDynamic ProgrammingMonotonic StackTwo Pointers

Given an array of integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.

Example 1

Input

[
  0,
  1,
  0,
  2,
  1,
  0,
  3,
  1,
  0,
  1,
  2
]

Output

Explanation. After the rain, water is trapped between the elevations. The area of water trapped is 8.

Example 2

Input

[
  4,
  2,
  0,
  3,
  2,
  5
]

Output

Explanation. Water can be trapped on top of the bars between the indices 1 through 4 and 3 through 5.

Example 3

Input

[
  3,
  0,
  2
]

Output

Explanation. Water is trapped between the bars at index 0 and 2, directly above index 1.

Example 4

Input

[
  0,
  2,
  0
]

Output

Explanation. No elevation surrounds a low point to contain water.

Follow-up: Can you implement an solution that runs in O(n) time and uses O(1) extra space?

Constraints:

The number of elements in the array is greater than 0 and less than 10,000. All elements in the array will be non-negative integers less than or equal to 100,000.

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