From d43681b8798b3038b6612a412df884a18841d206 Mon Sep 17 00:00:00 2001
From: "Nour A." <me@nourthearab.com>
Date: Wed, 5 Mar 2025 23:28:34 -0500
Subject: [PATCH] Final version. Applied the 4 search algorithms and added the
report.
---
OUTPUT.txt | 1015 +++++++++++++++++
...n and Implementation Choices - Nour A..pdf | Bin 0 -> 201147 bytes
State.py | 130 +--
multiprize-small.txt | 13 +
4 files changed, 1079 insertions(+), 79 deletions(-)
create mode 100644 OUTPUT.txt
create mode 100644 State Space Representation and Implementation Choices - Nour A..pdf
create mode 100644 multiprize-small.txt
diff --git a/OUTPUT.txt b/OUTPUT.txt
new file mode 100644
index 0000000..da9f9dd
--- /dev/null
+++ b/OUTPUT.txt
@@ -0,0 +1,1015 @@
+Expanding: (3, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (3, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (2, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (1, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (3, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (3, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (3, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (3, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (2, 28) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (3, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 28) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (11, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 20) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
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+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
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+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
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+Moving to (3, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
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+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
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+Expanding: (11, 20) | Remaining rewards: frozenset({(10, 1), (3, 28)})
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+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (3, 28)})
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+Expanding: (9, 20) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 20) | Remaining rewards: frozenset({(10, 1), (3, 28)})
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+Moving to (7, 25) | New rewards left: frozenset({(10, 1), (5, 28)})
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+Moving to (10, 20) | New rewards left: frozenset({(10, 1), (5, 28)})
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+Moving to (9, 21) | New rewards left: frozenset({(10, 1), (5, 28)})
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+Expanding: (9, 24) | Remaining rewards: frozenset({(10, 1), (5, 28)})
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+Expanding: (9, 14) | Remaining rewards: frozenset({(10, 1)})
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+Moving to (8, 13) | New rewards left: frozenset({(10, 1)})
+Expanding: (9, 13) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (9, 13) | Remaining rewards: frozenset({(10, 1)})
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+Moving to (8, 10) | New rewards left: frozenset({(10, 1)})
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+Expanding: (10, 13) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (11, 12) | Remaining rewards: frozenset({(10, 1)})
+Moving to (10, 12) | New rewards left: frozenset({(10, 1)})
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+Expanding: (11, 12) | Remaining rewards: frozenset({(10, 1)})
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+Moving to (8, 11) | New rewards left: frozenset({(10, 1)})
+Expanding: (10, 12) | Remaining rewards: frozenset({(10, 1)})
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+Expanding: (1, 9) | Remaining rewards: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
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+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (3, 26) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (3, 26) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (3, 23) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (2, 23) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (4, 23) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (3, 24) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (4, 23) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (3, 23) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (2, 23) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 22) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 24) | New rewards left: frozenset({(10, 1), (3, 28)})
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+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (3, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (3, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(10, 1), (3, 28)})
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+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
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+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 19) | New rewards left: frozenset({(10, 1), (3, 28)})
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+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
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+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 20) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 21) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (5, 23) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (4, 23) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (6, 23) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (5, 24) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 23) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 25) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (8, 25) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (7, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 14) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (9, 14) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (9, 14) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 20) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 19) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 21) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 22) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (8, 19) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (9, 20) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 21) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 21) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 25) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 25) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (9, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (8, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (10, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (9, 14) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (10, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (9, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (11, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (10, 12) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (10, 12) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (11, 12) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (10, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (11, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (10, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (11, 12) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 6) | Remaining rewards: frozenset({(10, 1), (3, 28), (1, 14), (5, 28), (11, 28)})
+Expanding: (1, 8) | Remaining rewards: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Moving to (1, 7) | New rewards left: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Moving to (1, 9) | New rewards left: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Expanding: (1, 9) | Remaining rewards: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Expanding: (1, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (1, 20) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (1, 22) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (3, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 18) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (1, 23) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 24) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 25) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (4, 18) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (3, 18) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (4, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 23) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 28) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 24) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 28) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (2, 28) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (8, 18) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 25) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 18) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (11, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 28) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (3, 24) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (2, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 23) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 24) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 23) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 25) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 18) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 19) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (5, 24) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (4, 24) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (5, 23) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (5, 25) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (6, 23) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (7, 25) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (7, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (9, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 12) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 14) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (9, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 19) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 18) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 20) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 21) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 25) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 14) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (10, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (10, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (11, 12) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (10, 12) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (11, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (11, 12) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (7, 23) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 23) | New rewards left: frozenset({(10, 1)})
+Moving to (8, 23) | New rewards left: frozenset({(10, 1)})
+Expanding: (9, 25) | Remaining rewards: frozenset({(10, 1)})
+Moving to (8, 25) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 24) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 26) | New rewards left: frozenset({(10, 1)})
+Expanding: (8, 23) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 23) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (9, 24) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 22) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 21) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 20) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 18) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 14) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 13) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (7, 11) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 11) | New rewards left: frozenset({(10, 1)})
+Moving to (8, 11) | New rewards left: frozenset({(10, 1)})
+Expanding: (8, 12) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (11, 13) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 11) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 11) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (8, 10) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (6, 6) | Remaining rewards: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Moving to (6, 5) | New rewards left: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Moving to (6, 7) | New rewards left: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Expanding: (6, 7) | Remaining rewards: frozenset({(11, 28), (10, 1), (5, 28), (3, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (1, 28) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (1, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (1, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (1, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 20) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 22) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 23) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 25) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 24) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (4, 19) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 18) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 14) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (5, 23) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (5, 25) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (5, 24) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (5, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 25) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (6, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (7, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (7, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 12) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (8, 11) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 13) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 14) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 14) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 18) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 19) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 20) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (10, 12) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (11, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 3) | Remaining rewards: frozenset({(10, 1), (3, 28), (1, 14), (5, 28), (11, 28)})
+Expanding: (1, 5) | Remaining rewards: frozenset({(10, 1), (3, 28), (1, 14), (5, 28), (11, 28)})
+Expanding: (1, 20) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (1, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (1, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (1, 20) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (1, 22) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (4, 19) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (3, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (2, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (4, 19) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (3, 18) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 14) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (4, 19) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (3, 19) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (4, 18) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (8, 14) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 14) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 20) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 22) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (2, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (3, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (3, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (4, 19) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (4, 21) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 14) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (9, 15) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (8, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (8, 15) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (8, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(3, 28), (10, 1), (11, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (1, 25) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (1, 28) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (9, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (9, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (10, 15) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (10, 17) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 16) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Moving to (11, 18) | New rewards left: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (11, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (2, 23) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (1, 23) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (3, 23) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (3, 23) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (4, 19) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (3, 19) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (4, 18) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(10, 1), (5, 28), (11, 28)})
+Expanding: (4, 20) | Remaining rewards: frozenset({(10, 1), (5, 28), (3, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (1, 25) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (1, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (1, 20) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 19) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 21) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 22) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 24) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (1, 26) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 25) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (2, 26) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (3, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 26) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 27) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (3, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (3, 28) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (2, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (2, 27) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (1, 27) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (2, 28) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 27) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 26) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (3, 28) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+🆠Collected reward at (3, 28)!
+Moving to (2, 28) | New rewards left: frozenset({(10, 1)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1)})
+Expanding: (4, 19) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (3, 19) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (4, 18) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (4, 20) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (4, 21) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (4, 23) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (3, 23) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (5, 23) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (4, 24) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (5, 23) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 14) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 14) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Moving to (8, 14) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 13) | New rewards left: frozenset({(10, 1), (3, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(10, 1), (3, 28)})
+Expanding: (11, 16) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 16) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (11, 18) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (3, 27) | Remaining rewards: frozenset({(10, 1)})
+Moving to (2, 27) | New rewards left: frozenset({(10, 1)})
+Moving to (3, 26) | New rewards left: frozenset({(10, 1)})
+Moving to (3, 28) | New rewards left: frozenset({(10, 1)})
+Expanding: (3, 26) | Remaining rewards: frozenset({(10, 1)})
+Moving to (2, 26) | New rewards left: frozenset({(10, 1)})
+Moving to (3, 27) | New rewards left: frozenset({(10, 1)})
+Expanding: (5, 24) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (5, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (5, 25) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (5, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (6, 27) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (5, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (7, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (6, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 26) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (7, 28) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (6, 28) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (7, 27) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 11) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Moving to (7, 11) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 10) | New rewards left: frozenset({(10, 1), (11, 28)})
+Moving to (8, 12) | New rewards left: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 13) | Remaining rewards: frozenset({(10, 1), (11, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (8, 18) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (8, 19) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (8, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (9, 17) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (9, 16) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 15) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Moving to (9, 15) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (11, 15) | New rewards left: frozenset({(10, 1), (5, 28)})
+Moving to (10, 16) | New rewards left: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (10, 17) | Remaining rewards: frozenset({(10, 1), (5, 28)})
+Expanding: (6, 23) | Remaining rewards: frozenset({(10, 1)})
+Moving to (5, 23) | New rewards left: frozenset({(10, 1)})
+Moving to (7, 23) | New rewards left: frozenset({(10, 1)})
+Expanding: (8, 25) | Remaining rewards: frozenset({(10, 1)})
+Moving to (7, 25) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 25) | New rewards left: frozenset({(10, 1)})
+Expanding: (9, 26) | Remaining rewards: frozenset({(10, 1)})
+Moving to (9, 25) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 27) | New rewards left: frozenset({(10, 1)})
+Expanding: (7, 23) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (9, 25) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (9, 25) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (6, 11) | Remaining rewards: frozenset({(10, 1)})
+Moving to (7, 11) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 10) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 12) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 10) | Remaining rewards: frozenset({(10, 1)})
+Moving to (5, 10) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 9) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 11) | New rewards left: frozenset({(10, 1)})
+Expanding: (7, 11) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (6, 9) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 8) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 10) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 8) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 7) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 9) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 7) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 6) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 8) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 6) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 5) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 7) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 5) | Remaining rewards: frozenset({(10, 1)})
+Moving to (5, 5) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 4) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 6) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 4) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 3) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 5) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 3) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 2) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 4) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 2) | Remaining rewards: frozenset({(10, 1)})
+Moving to (7, 2) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 1) | New rewards left: frozenset({(10, 1)})
+Moving to (6, 3) | New rewards left: frozenset({(10, 1)})
+Expanding: (6, 1) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 2) | New rewards left: frozenset({(10, 1)})
+Expanding: (7, 2) | Remaining rewards: frozenset({(10, 1)})
+Moving to (6, 2) | New rewards left: frozenset({(10, 1)})
+Moving to (8, 2) | New rewards left: frozenset({(10, 1)})
+Expanding: (8, 2) | Remaining rewards: frozenset({(10, 1)})
+Moving to (7, 2) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 2) | New rewards left: frozenset({(10, 1)})
+Moving to (8, 1) | New rewards left: frozenset({(10, 1)})
+Moving to (8, 3) | New rewards left: frozenset({(10, 1)})
+Expanding: (8, 1) | Remaining rewards: frozenset({(10, 1)})
+Moving to (9, 1) | New rewards left: frozenset({(10, 1)})
+Moving to (8, 2) | New rewards left: frozenset({(10, 1)})
+Expanding: (9, 2) | Remaining rewards: frozenset({(10, 1)})
+Moving to (8, 2) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 1) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 3) | New rewards left: frozenset({(10, 1)})
+Expanding: (9, 1) | Remaining rewards: frozenset({(10, 1)})
+Moving to (8, 1) | New rewards left: frozenset({(10, 1)})
+Moving to (10, 1) | New rewards left: frozenset({(10, 1)})
+Moving to (9, 2) | New rewards left: frozenset({(10, 1)})
+Expanding: (9, 1) | Remaining rewards: frozenset({(10, 1)})
+Expanding: (10, 1) | Remaining rewards: frozenset({(10, 1)})
+🆠Collected reward at (10, 1)!
+✅ Goal reached! All rewards collected!
+
+Solution:
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+%.% %%% % #% ##%% %%#%%%%%%
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+Path cost: 207
+Nodes expanded: 6324
\ No newline at end of file
diff --git a/State Space Representation and Implementation Choices - Nour A..pdf b/State Space Representation and Implementation Choices - Nour A..pdf
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HcmV?d00001
diff --git a/State.py b/State.py
index 7850d7f..4bfec39 100644
--- a/State.py
+++ b/State.py
@@ -1,22 +1,30 @@
+#Nour A. - Lab A
from collections import deque
import heapq
class State:
def __init__(self, position, remaining_rewards):
self.position = position # (x, y)
- self.remaining_rewards = frozenset(remaining_rewards) # {(x1, y1), (x2, y2), ...}
-
+ self.remaining_rewards = frozenset(remaining_rewards)
+
def __lt__(self, other):
- return self.position < other.position
+ return self.position < other.position #comparisons needed
def get_neighbors(state, maze):
x, y = state.position
+ rows, cols = len(maze), len(maze[0])
possible_moves = [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]
- valid_moves = [pos for pos in possible_moves if maze[pos[0]][pos[1]] != '%']
+ valid_moves = [
+ (nx, ny) for nx, ny in possible_moves
+ if 0 <= nx < rows and 0 <= ny < cols and maze[nx][ny] != '%'
+ ]
return valid_moves
def is_goal(state):
- return len(state.remaining_rewards) == 0
+ if len(state.remaining_rewards) == 0:
+ print("Goal reached: The mouse is happy.")
+ return True
+ return False
def read_maze(file_path):
with open(file_path, 'r') as file:
@@ -34,34 +42,8 @@ def read_maze(file_path):
return maze, State(start, rewards)
-def single_dfs(file_path):
- maze, initial_state = read_maze(file_path)
- stack = [(initial_state, [])] # (current state, path taken)
- visited = set()
-
- while stack:
- state, path = stack.pop()
-
- if state.position in visited:
- continue
- visited.add(state.position)
-
- if is_goal(state):
- print_maze_solution(maze, path)
- print(f"Path cost: {len(path)}")
- print(f"Nodes expanded: {len(visited)}")
- return path
-
- for move in get_neighbors(state, maze):
- new_rewards = state.remaining_rewards - {move} if move in state.remaining_rewards else state.remaining_rewards
- new_state = State(move, new_rewards)
- stack.append((new_state, path + [move]))
-
- print("No solution found.")
- return None
-
def print_maze_solution(maze, path):
- maze_copy = [row[:] for row in maze] # Make a copy of the maze
+ maze_copy = [row[:] for row in maze] # copy maze
for x, y in path:
if maze_copy[x][y] != '.': # Keep rewards visible
maze_copy[x][y] = '#'
@@ -69,66 +51,56 @@ def print_maze_solution(maze, path):
print("\nSolution:")
for row in maze_copy:
print("".join(row))
-single_dfs('test_maze.txt')
-
-def single_bfs(file_path):
- maze, initial_state = read_maze(file_path)
- queue = deque([(initial_state, [])]) # (current state, path)
- visited = set()
-
- while queue:
- state, path = queue.popleft()
-
- if state.position in visited:
- continue
- visited.add(state.position)
-
- if is_goal(state):
- print_maze_solution(maze, path)
- print(f"Path cost: {len(path)}")
- print(f"Nodes passed: {len(visited)}")
- return path
-
- for move in get_neighbors(state, maze):
- new_rewards = state.remaining_rewards - {move} if move in state.remaining_rewards else state.remaining_rewards
- new_state = State(move, new_rewards)
- queue.append((new_state, path + [move]))
-
- print("Sadly, the mouse is dead :(")
- return None
def manhattan_distance(pos1, pos2):
return abs(pos1[0] - pos2[0]) + abs(pos1[1] - pos2[1])
-def single_gbfs(file_path):
+def multi_astar(file_path):
maze, initial_state = read_maze(file_path)
- goal = next(iter(initial_state.remaining_rewards)) # 1prize,1goal
-
- priority_queue = [(manhattan_distance(initial_state.position, goal), initial_state, [])]
- visited = set()
+ priority_queue = [(0, 0, initial_state, [])] # (f, g, state, path)
+ visited = {} # keys are (position, remaining_rewards)
while priority_queue:
- _, state, path = heapq.heappop(priority_queue)
-
-
- if state.position in visited:
+ _, g, state, path = heapq.heappop(priority_queue)
+ print(f"Expanding: {state.position} | Remaining rewards: {state.remaining_rewards}")
+
+ if (state.position, state.remaining_rewards) in visited and visited[(state.position, state.remaining_rewards)] <= g:
continue
- visited.add(state.position)
+ visited[(state.position, state.remaining_rewards)] = g
- if is_goal(state):
+ # if the reward gets collected, remove it (so no loop)
+ new_rewards = set(state.remaining_rewards)
+ if state.position in new_rewards:
+ print(f"Collected reward at {state.position}!")
+ new_rewards.remove(state.position)
+
+ if not new_rewards: # stop when all rewards are collected
+ print("Goal reached! The mouse is happy.")
print_maze_solution(maze, path)
print(f"Path cost: {len(path)}")
- print(f"Nodes passed: {len(visited)}")
+ print(f"Nodes expanded: {len(visited)}")
return path
for move in get_neighbors(state, maze):
- new_rewards = state.remaining_rewards - {move} if move in state.remaining_rewards else state.remaining_rewards
- new_state = State(move, new_rewards)
- heapq.heappush(priority_queue, (manhattan_distance(move, goal), new_state, path + [move]))
-
-
-
- print("Sadly, the mouse is dead :(")
+ updated_rewards = frozenset(new_rewards) # Convert back to frozenset
+ new_state = State(move, updated_rewards)
+ print(f"Moving to {move} | New rewards left: {updated_rewards}")
+ heuristic = sum(manhattan_distance(move, reward) for reward in updated_rewards)
+ new_g = g + 1
+ f = new_g + heuristic
+ heapq.heappush(priority_queue, (f, new_g, new_state, path + [move]))
+
+ print("The mouse is dead.")
return None
-single_gbfs('test_maze.txt')
+if __name__ == "__main__":
+ while True:
+ file_name = input("Which maze do you want to throw the mouse at? Write the name: ")
+ if file_name.lower() == "q":
+ print("Quitting. The mouse escapes!")
+ break
+ try:
+ multi_astar(file_name) #so that I don't have a hardcoded file.
+ break
+ except FileNotFoundError:
+ print(f"Hmmmm..not sure that '{file_name}' is a correct maze name. Please try again or press 'q' to quit.")
diff --git a/multiprize-small.txt b/multiprize-small.txt
new file mode 100644
index 0000000..4f67525
--- /dev/null
+++ b/multiprize-small.txt
@@ -0,0 +1,13 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% P .% . . %
+% %%%%% %%%%%% % % % %% %
+% %. % % % % % % .%
+%. % . %. % %%%%%
+%%%%% %%%% %%% %%%%%%% .%
+%. . % %%% %
+%% %%%%%%%% %%%%%%%%%%% % %
+% % % %%%%
+% %%%%% %. %
+%.% %%% % % %% %% %%%%%%
+% % .% .%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--
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