From 1b3f1b99f5e4f14ac47bd2c519efe7512178b2e7 Mon Sep 17 00:00:00 2001
From: William Carroll <wpcarro@gmail.com>
Date: Fri, 13 Nov 2020 16:57:47 +0000
Subject: Solve box-stacking problem

Write a function to compute the highest stack of boxes that can be created from
a list of boxes.
---
 scratch/facebook/stacking-boxes.py | 50 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 scratch/facebook/stacking-boxes.py

(limited to 'scratch/facebook/stacking-boxes.py')

diff --git a/scratch/facebook/stacking-boxes.py b/scratch/facebook/stacking-boxes.py
new file mode 100644
index 000000000000..7a3304bc51b9
--- /dev/null
+++ b/scratch/facebook/stacking-boxes.py
@@ -0,0 +1,50 @@
+from random import randint
+
+class Box(object):
+    def __init__(self, w, h, d):
+        self.width  = w
+        self.depth  = d
+        self.height = h
+
+    def __repr__(self):
+        return "{}x{}x{}".format(self.width, self.depth, self.height)
+
+    def lt(self, b):
+        return all([
+            self.width  < b.width,
+            self.height < b.height,
+            self.depth  < b.depth,
+        ])
+
+    def gt(self, b):
+        return all([
+            self.width  > b.width,
+            self.height > b.height,
+            self.depth  > b.depth,
+        ])
+
+def random_box():
+    return Box(
+        randint(1, 10),
+        randint(1, 10),
+        randint(1, 10),
+    )
+
+xs = [random_box() for _ in range(5)]
+
+def highest_stack(xs, cache={}):
+    if not xs:
+        return 0
+    heights = []
+    for i in range(len(xs)):
+        x, rest = xs[i], xs[0:i] + xs[i+1:]
+        if cache and x in cache:
+            height = cache[x]
+        else:
+            height = x.height + highest_stack([b for b in rest if x.gt(b)], cache)
+            cache[x] = height
+        heights += [height]
+    return max(heights)
+
+print(xs)
+print(highest_stack(xs))
-- 
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