Problem
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.
Constraints
0 ≤ length ≤ 200,000; 0 ≤ height ≤ 1,000,000,000
Examples
Example 1
Input:
heights = [2, 1, 5, 6, 2, 3]
Expected output:
expected = 10Input:
std::vector<long long> heights = {2, 1, 5, 6, 2, 3};
Expected output:
long long expected = 10;Input:
long[] heights = new long[] {2, 1, 5, 6, 2, 3};
Expected output:
long expected = 10;Explanation
Bars 5 and 6 together give a 2-wide rectangle of height 5: area 10.
Example 2
Input:
heights = [4]
Expected output:
expected = 4Input:
std::vector<long long> heights = {4};
Expected output:
long long expected = 4;Input:
long[] heights = new long[] {4};
Expected output:
long expected = 4;Explanation
A single bar of height 4 has area 4.
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.