Checkpoint experiments through SWE pilot v2

results/board-muse-sept8/artifact-replays/episode-008/func.py

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+def expected_black_ball_position(N: int, K: int) -> int:
+    """ There are N-1 white balls and one black ball arranged in a row, with the black ball
+    initially at the leftmost position. Takahashi performs K operations, where each operation
+    consists of:
+    - Choose two integers a and b uniformly at random between 1 and N, inclusive
+    - If a ≠ b, swap the a-th and b-th balls from the left
+    
+    Find the expected position of the black ball after K operations, modulo 998244353.
+    
+    The result is returned as an integer R where R × Q ≡ P (mod 998244353), where P/Q is
+    the expected value expressed as an irreducible fraction.
+    
+    Args:
+        N: Total number of balls (1 ≤ N ≤ 998244352)
+        K: Number of operations (1 ≤ K ≤ 10^5)
+    
+    Returns:
+        The expected position modulo 998244353
+    
+    >>> expected_black_ball_position(2, 1)
+    499122178
+    >>> expected_black_ball_position(3, 2)
+    554580198
+    >>> expected_black_ball_position(4, 4)
+    592707587
+    """
+    MOD = 998244353
+    inv2 = (MOD + 1) // 2  # 499122177
+    # Expected value: ((N+1) - (N-1)*((N-2)/N)^K) / 2
+    # Derived from symmetry: q_K = 1/N + ((N-2)/N)^K * (N-1)/N
+    # E_K = (N+1)/2 - (N-1)/2 * ((N-2)/N)^K ... actually
+    # E_K = (N+1)/2 - (N-1)/2 * r^K with r=(N-2)/N
+    # Equivalent to ((N+1) - (N-1)*r^K)/2
+    n_mod = N % MOD
+    inv_n = pow(n_mod, MOD - 2, MOD)
+    r = (n_mod - 2) % MOD * inv_n % MOD
+    p = pow(r, K, MOD)
+    return ((n_mod + 1 - (n_mod - 1) * p) % MOD) * inv2 % MOD

results/board-muse-sept8/artifact-replays/episode-008/probe.py

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+import runpy
+runpy.run_path('/workspace/test.py', run_name='__main__')
+print('REPLAY_COMPLETED')

results/board-muse-sept8/artifact-replays/episode-008/result.json

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+{
+  "create_command": [
+    "docker",
+    "create",
+    "--name",
+    "board-artifact-validation-999c2cdda9c4",
+    "--network",
+    "none",
+    "--memory",
+    "512m",
+    "--pids-limit",
+    "64",
+    "--cap-drop",
+    "ALL",
+    "--security-opt",
+    "no-new-privileges",
+    "--user",
+    "65534:65534",
+    "--workdir",
+    "/workspace",
+    "aisiuk/inspect-tool-support",
+    "python3",
+    "-B",
+    "/workspace/probe.py"
+  ],
+  "network_mode": "none",
+  "mounts": [],
+  "image_id": "sha256:fb045da8203aea656785c758f7147b003cfe21f213e9048a38be0a33242a5b3d",
+  "docker_start_exit_code": 0,
+  "container_exit_code": 0,
+  "timed_out": false,
+  "files_sha256": {
+    "func.py": "83c3ade25cb0564639539d95374214e996ba1281c65c64529ae17d21a3115053",
+    "test.py": "f4361d7e31aef9f46f42b030037702ffb2dc505511aa6a99fdd93d1316607678",
+    "probe.py": "010f28d35c16feb589ee22de82f1b579e04fc1f3f415862e2db86598e230b5ef"
+  }
+}

results/board-muse-sept8/artifact-replays/episode-008/stdout.txt

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+All tests passed!
+REPLAY_COMPLETED

results/board-muse-sept8/artifact-replays/episode-008/test.py

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+from func import expected_black_ball_position
+
+def test_func(candidate):
+    # Sample test cases
+    assert candidate(2, 1) == 499122178
+    assert candidate(3, 2) == 554580198
+    assert candidate(4, 4) == 592707587
+    
+    # Additional test cases
+    assert candidate(92724482, 8713) == 397187210
+    assert candidate(42952, 42770) == 3846140
+    assert candidate(998244352, 100000) == 296595689
+    assert candidate(87868, 84659) == 469774635
+    assert candidate(1, 1) == 1
+    assert candidate(73, 2890) == 757452161
+    assert candidate(84789430, 17447) == 571416630
+    assert candidate(324383216, 75454) == 492179107
+    assert candidate(11655411, 67422) == 90043236
+    assert candidate(159870726, 60658) == 686981596
+    assert candidate(9, 89855) == 3867007
+    assert candidate(85, 39232) == 566906027
+    assert candidate(1, 100000) == 1
+    assert candidate(48020, 79364) == 191000302
+    assert candidate(795705262, 33277) == 6449814
+    assert candidate(82330, 30021) == 205041562
+    assert candidate(95, 82089) == 603320441
+    assert candidate(164026938, 72649) == 390346149
+    assert candidate(3492853, 52547) == 341797331
+    assert candidate(196203458, 63938) == 743047251
+
+if __name__ == "__main__":
+    test_func(expected_black_ball_position)
+    print("All tests passed!")