Trapping Rain Water

Bars of width 1 have the given heights. After rain, water collects above each bar up to the lower of the tallest bars on its left and right. Compute the total trapped water. An O(n) two-pointer solution is expected.

Implement trapped_water(heights).

Input

heights: Bar heights from left to right.

Output

Return the total units of water.

Ограничения

0 ≤ length ≤ 200,000; 0 ≤ height ≤ 100,000

Примеры

Ввод:
heights = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]

Ожидаемый вывод:
expected = 6

Ввод:
std::vector<long long> heights = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};

Ожидаемый вывод:
long long expected = 6;

Ввод:
long[] heights = new long[] {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};

Ожидаемый вывод:
long expected = 6;

Ввод:
heights = [3, 2, 1]

Ожидаемый вывод:
expected = 0

Ввод:
std::vector<long long> heights = {3, 2, 1};

Ожидаемый вывод:
long long expected = 0;

Ввод:
long[] heights = new long[] {3, 2, 1};

Ожидаемый вывод:
long expected = 0;

Ссылки

Это задание адаптировано для CodeUtility. Следуйте условию и ограничениям выше.

• From Problems to Performance: Two Decades of Programming Contests in the CCSC Southeast