added largest rectangle histogram function

data_structures/stacks/largest_rectangle_histogram.py

@@ -0,0 +1,39 @@
+def largest_rectangle_area(heights: list[int]) -> int:
+    """
+    Given an array of integers representing the heights of bars,
+    this function returns the area of the largest rectangle that can be formed
+
+    >>> largest_rectangle_area([2, 1, 5, 6, 2, 3])
+    10
+
+    >>> largest_rectangle_area([2, 4])
+    4
+
+    >>> largest_rectangle_area([6, 2, 5, 4, 5, 1, 6])
+    12
+
+    >>> largest_rectangle_area([1])
+    1
+    """
+    stack: list[int] = []
+    max_area = 0
+    heights = [*heights, 0]  # make a new list by appending the sentinel 0
+    n = len(heights)
+
+    for i in range(n):
+        # make sure the stack remains in increasing order
+        while stack and heights[i] < heights[stack[-1]]:
+            h = heights[stack.pop()]  # height of the bar
+            # if stack is empty, it means entire width can be taken from index 0 to i-1
+            w = i if not stack else i - stack[-1] - 1  # calculate width
+            max_area = max(max_area, h * w)
+
+        stack.append(i)
+
+    return max_area
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()