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.

Contraintes

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

Exemples

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

Sortie attendue :
expected = 6

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

Sortie attendue :
long long expected = 6;

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

Sortie attendue :
long expected = 6;

Entrée :
heights = [3, 2, 1]

Sortie attendue :
expected = 0

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

Sortie attendue :
long long expected = 0;

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

Sortie attendue :
long expected = 0;

Références

Ce défi a été adapté pour CodeUtility. Suivez l'énoncé et les contraintes ci-dessus.

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