From 9d4a08297e7b7485174904367741597b2d810990 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Tue, 23 Mar 2021 23:38:29 -0400
Subject: [PATCH] Solve problem 85

---
 python/e085.py | 52 +++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 49 insertions(+), 3 deletions(-)

diff --git a/python/e085.py b/python/e085.py
index ba42412..585d122 100644
--- a/python/e085.py
+++ b/python/e085.py
@@ -1,8 +1,54 @@
+from collections import namedtuple
+from collections import deque
+
+Rect = namedtuple("Rect", ["cols", "rows"])
+
+
+def sub_rectangles(rect):
+    r = [Rect(i, j)
+          for i in range(1, rect.cols + 1)
+          for j in range(1, rect.rows + 1)]
+    return r
+
+def flat_fit(n_inner, n_outer):
+    return n_outer - n_inner + 1
+
+def count_fits(sub_rect, main_rect):
+    row_fits = flat_fit(sub_rect.rows, main_rect.rows)
+    col_fits = flat_fit(sub_rect.cols, main_rect.cols)
+    return row_fits * col_fits
+
+
+def count_sub_rectangles(rect):
+    r = 0
+    for sub_rect in sub_rectangles(rect):
+        r += count_fits(sub_rect, rect)
+    return r
+
 
 def euler_085():
-    return 0
+    limit = 2 * 10**6
+    nearest = 0
+    canditate_rects = deque([Rect(1, 1)])
+
+    while canditate_rects:
+        rect = canditate_rects.popleft()
+        sub_count = count_sub_rectangles(rect)
+        # print(rect, sub_count)
+
+        if sub_count < limit and sub_count > nearest:
+            nearest = sub_count
+
+        if sub_count == 1999998:
+            return rect.cols * rect.rows
+        elif sub_count < limit:
+            canditate_rects.append(Rect(rect.cols + 0, rect.rows + 1))
+        else:
+            canditate_rects.append(Rect(rect.cols + 1, 1))
 
 
 if __name__ == "__main__":
-    print("e085.py: " + str(euler_085()))
-    assert(euler_085() == 0)
+    s = euler_085()
+    print("e085.py: " + str(s))
+    assert(s == 2772)
+