added Given an array heights representing histogram bar heights, find…

Problems/Stacks & Queues/largest_rectangle_in_histogram.py

@@ -0,0 +1,44 @@
+#Given an array heights representing histogram bar heights, find the maximum rectangular area that can be formed.
+#heights = [2, 1, 5, 6, 2, 3]
+#Output: 10
+
+
+def largestRectangleArea(heights):
+    stack = []  # stack to store indices
+    max_area = 0
+    heights.append(0)  # Add a sentinel to pop all remaining bars at the end
+
+    for i, h in enumerate(heights):
+        while stack and h < heights[stack[-1]]:
+            # Pop the top
+            height = heights[stack.pop()]
+            # Calculate width
+            if stack:
+                width = i - stack[-1] - 1
+            else:
+                width = i
+            # Update max_area
+            max_area = max(max_area, height * width)
+        stack.append(i)
+
+    return max_area
+
+# Example usage
+heights = [2, 1, 5, 6, 2, 3]
+print("Largest Rectangle Area:", largestRectangleArea(heights))
+
+
+
+#Output for Example:
+
+#Largest Rectangle Area: 10
+
+# How it Works
+
+# Stack keeps indices of bars in increasing height order.
+
+# When a smaller height is found, pop from stack and calculate the area using the popped bar as height.
+
+# Width = difference between current index i and the previous index in stack (i - stack[-1] - 1) or i if stack is empty.
+
+# Sentinel 0 at the end ensures all remaining bars are processed.