ass3: handin

assignment3/Makefile

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+all: report.pdf handin.zip
+report.pdf: report.md
+	pandoc $< -o $@ --pdf-engine typst
+handin.zip: *.py report.pdf
+	zip $@ $^

assignment3/report.md

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+---
+title: assignment 3
+date: 2025-10-21
+author: Fredrik Robertsen, Erlend Ulvund Skaarberg
+---
+
+## (a) code output
+
+### halving game output
+
+```
+The number is 5 and it is P1's turn
+P1's action: --
+The number is 4 and it is P2's turn
+P2's action: --
+The number is 3 and it is P1's turn
+P1's action: /2
+The number is 1 and it is P2's turn
+P2's action: --
+The number is 0 and P1 won
+```
+
+this is as expected (provided by the example code)
+
+### bucket game output
+
+```
+The state is (0, ['A', 'B', 'C']) and it is P1's turn
+P1's action: B
+The state is (1, [3, 1]) and it is P2's turn
+P2's action: 1
+The state is (0, [1]) and P1's utility is 1
+```
+
+the results follow the expected run-through of the minimax algorithm
+
+### tic tac toe output
+
+```
+   |   |
+---+---+---
+   |   |
+---+---+---
+   |   |
+
+It is P1's turn to move
+P1's action: (0, 0)
+
+ x |   |
+---+---+---
+   |   |
+---+---+---
+   |   |
+
+It is P2's turn to move
+P2's action: (0, 1)
+
+ x | o |
+---+---+---
+   |   |
+---+---+---
+   |   |
+
+It is P1's turn to move
+P1's action: (0, 2)
+
+ x | o | x
+---+---+---
+   |   |
+---+---+---
+   |   |
+
+It is P2's turn to move
+P2's action: (1, 1)
+
+ x | o | x
+---+---+---
+   | o |
+---+---+---
+   |   |
+
+It is P1's turn to move
+P1's action: (1, 0)
+
+ x | o | x
+---+---+---
+ x | o |
+---+---+---
+   |   |
+
+It is P2's turn to move
+P2's action: (2, 0)
+
+ x | o | x
+---+---+---
+ x | o |
+---+---+---
+ o |   |
+
+It is P1's turn to move
+P1's action: (2, 1)
+
+ x | o | x
+---+---+---
+ x | o |
+---+---+---
+ o | x |
+
+It is P2's turn to move
+P2's action: (1, 2)
+
+ x | o | x
+---+---+---
+ x | o | o
+---+---+---
+ o | x |
+
+It is P1's turn to move
+P1's action: (2, 2)
+
+ x | o | x
+---+---+---
+ x | o | o
+---+---+---
+ o | x | x
+
+The game is a draw
+```
+
+this is an optimal game, ending in a draw
+
+## (b) runtime improvement with alpha-beta pruning
+
+### results of our benchmarks
+
+- 8.7112 seconds without alpha-beta pruning
+
+- 0.0001 seconds with alpha-beta pruning
+
+the results are measured at the first step of the algorithms
+
+we can see a clear speed-up from using the alpha-beta pruning
+
+### benchmarking code
+
+```
+game = Game()
+state = game.initial_state()
+game.print(state)
+record = False
+while not game.is_terminal(state):
+    player = game.to_move(state)
+    start_time = time.time()
+    action = minimax_search(game, state) # The player whose turn it is is the MAX player
+    if not record:
+        print(f"Elapsed time (minimax): {time.time() - start_time:.4f} seconds")
+        record = True
+    print(f'P{player+1}\'s action: {action}')
+    assert action is not None
+    state = game.result(state, action)
+    game.print(state)
+    print()
+
+game = Game()
+state = game.initial_state()
+game.print(state)
+record = False
+while not game.is_terminal(state):
+    start_time = time.time()
+    player = game.to_move(state)
+    action = alpha_beta_search(game, state) # The player whose turn it is is the MAX player
+    if not record:
+        print(f"Elapsed time (alpha-beta-pruning): {time.time() - start_time:.9f} seconds")
+        record = False
+    print(f'P{player+1}\'s action: {action}')
+    assert action is not None
+    state = game.result(state, action)
+    game.print(state)
+    print()
+```
+
+## non-mandatory
+
+in the provided game state
+
+```
+ x | o | o
+---+---+---
+ x |   |
+---+---+---
+   |   |
+```
+
+the minimax algorithm will choose the path that leads to victory, which could be
+the middle point, or the lower left one. although, due to our implementation, it
+will always pick the middle point because it sees it first (it is on a higher
+row). this path also provides two paths to win. it is in such a sense even more
+optimal than greedily choosing the lower left option, but both options lead to
+a win and are as such considered equal.
+
+to make the algorithm choose the immediate path on the lower left, we can for
+example have it greedily scan the board for such an option every recursive call
+so as to discover the option of a quicke win. though this may not be more
+performant due to the overhead of checking for this condition all the time, but
+on this rare occasion we will at least avoid performing unecessary minimax
+calls.
+
+another way to achieve this, which could also improve the performance, would be
+to keep track of path lengths. this would also let it discover such an option.
+
+yet another way would be to implement the algorithm differently, as a BFS
+algorithm that checks for the winning state before expanding it.