Largest Rectangle in a Histogram

A histogram has bars of width 1 with the given heights. Find the area of the largest rectangle that lies entirely within the bars. A monotonic stack gives an O(n) solution.

Implement largest_rectangle(heights).

Input

heights: Bar heights from left to right.

Output

Return the largest area.

Contraintes

0 ≤ length ≤ 200,000; 0 ≤ height ≤ 1,000,000,000

Exemples

Entrée :
heights = [2, 1, 5, 6, 2, 3]

Sortie attendue :
expected = 10

Entrée :
std::vector<long long> heights = {2, 1, 5, 6, 2, 3};

Sortie attendue :
long long expected = 10;

Entrée :
long[] heights = new long[] {2, 1, 5, 6, 2, 3};

Sortie attendue :
long expected = 10;

Entrée :
heights = [4]

Sortie attendue :
expected = 4

Entrée :
std::vector<long long> heights = {4};

Sortie attendue :
long long expected = 4;

Entrée :
long[] heights = new long[] {4};

Sortie attendue :
long expected = 4;

Références

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

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