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.

Vincoli

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

Esempi

Input:
heights = [2, 1, 5, 6, 2, 3]

Output atteso:
expected = 10

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

Output atteso:
long long expected = 10;

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

Output atteso:
long expected = 10;

Input:
heights = [4]

Output atteso:
expected = 4

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

Output atteso:
long long expected = 4;

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

Output atteso:
long expected = 4;

Riferimenti

Questa sfida è adattata per CodeUtility. Segui la traccia e i vincoli sopra.

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