Create largest_rectangle_histogram.py

data_structures/stacks/largest_rectangle_histogram.py

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+"""
+Author: Ansh Dulewale
+GitHub: github.com/ansh-dulewale
+
+Explanation:  http://www.codingdrills.com/tutorial/stack-data-structure/largest-rectangle-in-histogram
+
+THESE ARE THE ALGORITHM'S RULES:
+RULE 1: Scan `heights` array in left to right direction
+        if the height at this index is greater than the height at the top position of `stack`
+        we push the index at `stack`.
+
+RULE 2: If the `height` at the current `index` is smaller than the `height` at the top of the `stack`
+        process the stack now. Pop top `index` from `stack`.
+        The `height` of the rectangle = `height` at popped `index`.
+        Calculate `width` of the rectangle:
+        if the `stack` is not empty.
+        Then the `width` extends from `begin` of the `histogram` till current `index`.
+        If the stack is not empty, the width stretches from a current index to an index that immediately comes after new stack top
+
+RULE 3: area = height width if it is greater than max_area so far
+                update max_area.
+
+RULE 4: Repeat Rules 2 and 3 until the current height is no longer less than the height at the top index of the `stack`.
+        Push the current index onto the `stack`.
+
+RULE 5: After the entire `heights` array has been traversed, the maximum area found, stored in `max_area`,
+        represents the area of the largest rectangle in the histogram.
+
+NOTE:   It only works with whole numbers.
+"""
+
+__author__ = "Ansh Dulewale"
+
+
+def largestRectangleArea(heights):
+    stack = []
+    max_area = 0
+    heights.append(0)  # Add a zero height to pop all remaining heights in stack.
+
+    for i in range(len(heights)):
+        while stack and heights[i] < heights[stack[-1]]:
+            h = heights[stack.pop()]
+            w = i if not stack else i - stack[-1] - 1
+            max_area = max(max_area, h * w)
+        stack.append(i)
+
+    heights.pop()  # Restore the original heights array.
+    return max_area
+
+
+# Get input from the user
+user_input = input()
+heights = list(map(int, user_input.split()))
+
+print(largestRectangleArea(heights))