beam: largest rectangle in histogram (O(n) stack) with brute-force tests

wizard-work/beam/largest_rect_hist.py

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+"""Largest Rectangle in Histogram.
+
+Given bar heights, find area of largest rectangle using contiguous bars.
+O(n) via monotonic increasing stack of indices with a sentinel 0.
+Brute-force oracle included for verification.
+"""
+from typing import List
+
+
+def largest_rectangle_area(heights: List[int]) -> int:
+    if not heights:
+        return 0
+    stack: List[int] = []
+    best = 0
+    h = list(heights) + [0]
+    for i, height in enumerate(h):
+        while stack and h[stack[-1]] > height:
+            idx = stack.pop()
+            left = stack[-1] if stack else -1
+            width = i - left - 1
+            area = h[idx] * width
+            if area > best:
+                best = area
+        stack.append(i)
+    return best
+
+
+def _brute(heights: List[int]) -> int:
+    n = len(heights)
+    best = 0
+    for i in range(n):
+        mn = heights[i]
+        for j in range(i, n):
+            mn = min(mn, heights[j])
+            area = mn * (j - i + 1)
+            if area > best:
+                best = area
+    return best

wizard-work/beam/test_largest_rect_hist.py

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+import random, sys
+sys.path.insert(0, "/root/.hermes/wizard-outputs/beam")
+from largest_rect_hist import largest_rectangle_area, _brute
+
+def test_random():
+    rng = random.Random(2024)
+    for _ in range(5000):
+        n = rng.randint(0, 30)
+        hs = [rng.randint(0, 8) for _ in range(n)]
+        assert largest_rectangle_area(hs) == _brute(hs), hs
+
+def test_edges():
+    assert largest_rectangle_area([]) == 0
+    assert largest_rectangle_area([2,1,5,6,2,3]) == 10
+    assert largest_rectangle_area([2,4]) == 4
+    assert largest_rectangle_area([1]) == 1
+    assert largest_rectangle_area([0,0,0]) == 0
+
+test_random()
+test_edges()
+print("ALL OK")