{"abstract":"Counters exceed the true frequency and the error guarantee no longer holds.","category":"Probabilistic sketches","checks":7,"contract":"Input {k, stream} of [item, positive weight]. Keep at most k counters. A tracked item adds its weight; an untracked item takes a free counter. Otherwise dec = min(smallest counter, weight) is subtracted from every counter and from the incoming weight, counters reaching 0 are dropped, and a positive remainder is inserted. removed accumulates dec*(k+1), the discarded mass. Return [sorted [item, count] pairs, removed].","evaluation_group":"w2-probabilistic_sketches-misra-gries-weighted","failed_approach":"Inserting the remainder unconditionally creates zero-valued counters that occupy capacity.","family":"w2-probabilistic_sketches-misra-gries-weighted-remainder-insert","id":"FA-73091","implementations":{"attempt":{"sha256":"f20317f7c49009df56a6615911600b6f396ee8c8391cca4177d089326d8611a8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    k = x['k']\n    C = {}\n    removed = 0\n    for item, wt in x['stream']:\n        if item in C:\n            C[item] += wt\n        elif len(C) < k:\n            C[item] = wt\n        else:\n            dec = min(min(C.values()), wt)\n            for key in list(C):\n                C[key] -= dec\n                if C[key] == 0:\n                    del C[key]\n            wt -= dec\n            removed += dec * (k + 1)\n            C[item] = wt\n    return [sorted([key, v] for key, v in C.items()), removed]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 4],\n               ['c', 1],\n               ['a', 3],\n               ['d', 1],\n               ['d', 3],\n               ['a', 5],\n               ['e', 2],\n               ['d', 3],\n               ['d', 4],\n               ['a', 5],\n               ['a', 4]]},\n   [[['a', 14], ['d', 12]], 9]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['e', 5],\n               ['c', 5],\n               ['b', 3],\n               ['d', 2],\n               ['c', 2],\n               ['d', 2],\n               ['d', 1],\n               ['c', 3],\n               ['a', 4],\n               ['d', 4],\n               ['f', 1]]},\n   [[['a', 1], ['c', 4], ['d', 3]], 24]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['d', 2],\n               ['c', 2],\n               ['c', 1],\n               ['c', 4],\n               ['a', 1],\n               ['c', 4],\n               ['d', 4],\n               ['c', 5],\n               ['c', 3],\n               ['c', 4],\n               ['a', 1]]},\n   [[['c', 21], ['d', 4]], 6]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 5],\n               ['a', 5],\n               ['a', 2],\n               ['a', 3],\n               ['d', 4],\n               ['a', 3],\n               ['e', 4],\n               ['e', 1],\n               ['g', 4],\n               ['g', 1],\n               ['g', 3]]},\n   [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 7]]},\n   [[['b', 1], ['c', 5]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 1]]},\n   [[['a', 2], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 1],\n               ['e', 5],\n               ['d', 4],\n               ['e', 5],\n               ['b', 1],\n               ['e', 4],\n               ['a', 5],\n               ['b', 3],\n               ['d', 1],\n               ['d', 2],\n               ['e', 1],\n               ['d', 1]]},\n   [[['d', 2], ['e', 7]], 24]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['c', 2],\n               ['b', 5],\n               ['b', 5],\n               ['c', 1],\n               ['d', 1],\n               ['a', 5],\n               ['c', 2],\n               ['f', 4],\n               ['a', 2],\n               ['f', 5],\n               ['b', 2],\n               ['d', 4]]},\n   [[['b', 5], ['d', 2], ['f', 3]], 28]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['c', 2],\n               ['d', 2],\n               ['c', 4],\n               ['d', 5],\n               ['d', 1],\n               ['b', 2],\n               ['b', 5],\n               ['c', 3],\n               ['e', 4],\n               ['c', 5],\n               ['e', 3],\n               ['b', 2]]},\n   [[['c', 4], ['e', 4]], 30]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 2],\n               ['g', 1],\n               ['c', 5],\n               ['a', 3],\n               ['b', 2],\n               ['b', 1],\n               ['d', 3],\n               ['g', 2],\n               ['e', 3],\n               ['b', 4],\n               ['d', 2],\n               ['d', 4]]},\n   [[['b', 2], ['d', 4], ['e', 1]], 25]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 8]]},\n   [[['b', 1], ['c', 6]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 2]]},\n   [[['a', 3], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['c', 3],\n               ['e', 5],\n               ['c', 1],\n               ['a', 2],\n               ['a', 2],\n               ['a', 4],\n               ['c', 3],\n               ['d', 5],\n               ['e', 3],\n               ['a', 1],\n               ['c', 1],\n               ['b', 5],\n               ['d', 1]]},\n   [[['b', 5], ['d', 1]], 30]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['a', 1],\n               ['e', 4],\n               ['e', 5],\n               ['b', 2],\n               ['f', 3],\n               ['d', 3],\n               ['b', 1],\n               ['b', 1],\n               ['f', 3],\n               ['d', 2],\n               ['c', 3],\n               ['f', 3],\n               ['c', 3]]},\n   [[['c', 4], ['e', 3], ['f', 3]], 24]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['e', 3],\n               ['a', 1],\n               ['c', 5],\n               ['b', 5],\n               ['c', 3],\n               ['e', 4],\n               ['b', 1],\n               ['a', 5],\n               ['e', 3],\n               ['d', 1],\n               ['e', 1],\n               ['e', 1],\n               ['e', 5]]},\n   [[['a', 3], ['e', 8]], 27]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 3],\n               ['f', 4],\n               ['e', 4],\n               ['b', 2],\n               ['c', 1],\n               ['g', 1],\n               ['f', 4],\n               ['e', 3],\n               ['a', 1],\n               ['e', 4],\n               ['e', 2],\n               ['b', 2],\n               ['f', 1]]},\n   [[['a', 2], ['b', 2], ['e', 11], ['f', 7]], 10]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 9]]},\n   [[['b', 1], ['c', 7]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 3]]},\n   [[['a', 4], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 3],\n               ['e', 1],\n               ['d', 3],\n               ['c', 1],\n               ['c', 4],\n               ['c', 3],\n               ['e', 5],\n               ['e', 2],\n               ['b', 5],\n               ['a', 2],\n               ['e', 5],\n               ['d', 3],\n               ['a', 1],\n               ['b', 4]]},\n   [[['b', 3]], 39]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['c', 2],\n               ['d', 1],\n               ['b', 2],\n               ['d', 3],\n               ['b', 3],\n               ['d', 4],\n               ['c', 1],\n               ['f', 5],\n               ['d', 1],\n               ['e', 5],\n               ['b', 2],\n               ['d', 3]]},\n   [[['d', 8], ['e', 3], ['f', 1]], 28]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['c', 5],\n               ['b', 5],\n               ['c', 2],\n               ['c', 5],\n               ['d', 4],\n               ['a', 4],\n               ['b', 4],\n               ['c', 5],\n               ['c', 1],\n               ['e', 2],\n               ['b', 3],\n               ['e', 2],\n               ['b', 3],\n               ['d', 5]]},\n   [[['c', 3], ['d', 2]], 45]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['b', 5],\n               ['d', 2],\n               ['a', 4],\n               ['f', 3],\n               ['a', 1],\n               ['b', 2],\n               ['g', 1],\n               ['c', 2],\n               ['d', 3],\n               ['d', 5],\n               ['d', 3],\n               ['e', 4],\n               ['c', 3],\n               ['g', 4]]},\n   [[['b', 1], ['d', 7], ['e', 1], ['g', 3]], 30]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 10]]},\n   [[['b', 1], ['c', 8]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 4]]},\n   [[['a', 5], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['b', 4],\n               ['d', 3],\n               ['d', 4],\n               ['e', 4],\n               ['c', 1],\n               ['a', 3],\n               ['b', 2],\n               ['b', 5],\n               ['e', 5],\n               ['e', 1],\n               ['d', 4],\n               ['e', 3],\n               ['c', 3],\n               ['d', 3],\n               ['e', 5]]},\n   [[['d', 1], ['e', 7]], 42]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['b', 5],\n               ['e', 3],\n               ['c', 4],\n               ['d', 4],\n               ['e', 4],\n               ['e', 2],\n               ['b', 4],\n               ['d', 1],\n               ['a', 4],\n               ['b', 3],\n               ['f', 1],\n               ['f', 2],\n               ['d', 4]]},\n   [[['b', 1], ['d', 4]], 44]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['a', 5],\n               ['e', 3],\n               ['b', 4],\n               ['c', 4],\n               ['a', 2],\n               ['e', 1],\n               ['e', 2],\n               ['a', 5],\n               ['e', 1],\n               ['c', 3],\n               ['c', 4],\n               ['c', 1],\n               ['c', 3]]},\n   [[['a', 6], ['c', 7]], 33]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['b', 1],\n               ['g', 4],\n               ['f', 3],\n               ['g', 1],\n               ['f', 1],\n               ['e', 1],\n               ['g', 3],\n               ['g', 5],\n               ['g', 2],\n               ['a', 4],\n               ['d', 2],\n               ['e', 2],\n               ['d', 3],\n               ['d', 3],\n               ['e', 5]]},\n   [[['d', 5], ['e', 4], ['g', 11]], 20]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 11]]},\n   [[['b', 1], ['c', 9]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 5]]},\n   [[['a', 6], ['b', 1], ['c', 1]], 0]]]]\nfor label, args, expected in cases[N - 1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"5fc9fd00f956c7b620370d2669a3c1ff4f84244786f70ccfed9c0d6c5dcb0ead","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    k = x['k']\n    C = {}\n    removed = 0\n    for item, wt in x['stream']:\n        if item in C:\n            C[item] += wt\n        elif len(C) < k:\n            C[item] = wt\n        else:\n            dec = min(min(C.values()), wt)\n            for key in list(C):\n                C[key] -= dec\n                if C[key] == 0:\n                    del C[key]\n            wt -= dec\n            removed += dec * (k + 1)\n            C[item] = wt + dec\n    return [sorted([key, v] for key, v in C.items()), removed]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 4],\n               ['c', 1],\n               ['a', 3],\n               ['d', 1],\n               ['d', 3],\n               ['a', 5],\n               ['e', 2],\n               ['d', 3],\n               ['d', 4],\n               ['a', 5],\n               ['a', 4]]},\n   [[['a', 14], ['d', 12]], 9]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['e', 5],\n               ['c', 5],\n               ['b', 3],\n               ['d', 2],\n               ['c', 2],\n               ['d', 2],\n               ['d', 1],\n               ['c', 3],\n               ['a', 4],\n               ['d', 4],\n               ['f', 1]]},\n   [[['a', 1], ['c', 4], ['d', 3]], 24]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['d', 2],\n               ['c', 2],\n               ['c', 1],\n               ['c', 4],\n               ['a', 1],\n               ['c', 4],\n               ['d', 4],\n               ['c', 5],\n               ['c', 3],\n               ['c', 4],\n               ['a', 1]]},\n   [[['c', 21], ['d', 4]], 6]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 5],\n               ['a', 5],\n               ['a', 2],\n               ['a', 3],\n               ['d', 4],\n               ['a', 3],\n               ['e', 4],\n               ['e', 1],\n               ['g', 4],\n               ['g', 1],\n               ['g', 3]]},\n   [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 7]]},\n   [[['b', 1], ['c', 5]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 1]]},\n   [[['a', 2], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 1],\n               ['e', 5],\n               ['d', 4],\n               ['e', 5],\n               ['b', 1],\n               ['e', 4],\n               ['a', 5],\n               ['b', 3],\n               ['d', 1],\n               ['d', 2],\n               ['e', 1],\n               ['d', 1]]},\n   [[['d', 2], ['e', 7]], 24]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['c', 2],\n               ['b', 5],\n               ['b', 5],\n               ['c', 1],\n               ['d', 1],\n               ['a', 5],\n               ['c', 2],\n               ['f', 4],\n               ['a', 2],\n               ['f', 5],\n               ['b', 2],\n               ['d', 4]]},\n   [[['b', 5], ['d', 2], ['f', 3]], 28]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['c', 2],\n               ['d', 2],\n               ['c', 4],\n               ['d', 5],\n               ['d', 1],\n               ['b', 2],\n               ['b', 5],\n               ['c', 3],\n               ['e', 4],\n               ['c', 5],\n               ['e', 3],\n               ['b', 2]]},\n   [[['c', 4], ['e', 4]], 30]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 2],\n               ['g', 1],\n               ['c', 5],\n               ['a', 3],\n               ['b', 2],\n               ['b', 1],\n               ['d', 3],\n               ['g', 2],\n               ['e', 3],\n               ['b', 4],\n               ['d', 2],\n               ['d', 4]]},\n   [[['b', 2], ['d', 4], ['e', 1]], 25]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 8]]},\n   [[['b', 1], ['c', 6]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 2]]},\n   [[['a', 3], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['c', 3],\n               ['e', 5],\n               ['c', 1],\n               ['a', 2],\n               ['a', 2],\n               ['a', 4],\n               ['c', 3],\n               ['d', 5],\n               ['e', 3],\n               ['a', 1],\n               ['c', 1],\n               ['b', 5],\n               ['d', 1]]},\n   [[['b', 5], ['d', 1]], 30]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['a', 1],\n               ['e', 4],\n               ['e', 5],\n               ['b', 2],\n               ['f', 3],\n               ['d', 3],\n               ['b', 1],\n               ['b', 1],\n               ['f', 3],\n               ['d', 2],\n               ['c', 3],\n               ['f', 3],\n               ['c', 3]]},\n   [[['c', 4], ['e', 3], ['f', 3]], 24]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['e', 3],\n               ['a', 1],\n               ['c', 5],\n               ['b', 5],\n               ['c', 3],\n               ['e', 4],\n               ['b', 1],\n               ['a', 5],\n               ['e', 3],\n               ['d', 1],\n               ['e', 1],\n               ['e', 1],\n               ['e', 5]]},\n   [[['a', 3], ['e', 8]], 27]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 3],\n               ['f', 4],\n               ['e', 4],\n               ['b', 2],\n               ['c', 1],\n               ['g', 1],\n               ['f', 4],\n               ['e', 3],\n               ['a', 1],\n               ['e', 4],\n               ['e', 2],\n               ['b', 2],\n               ['f', 1]]},\n   [[['a', 2], ['b', 2], ['e', 11], ['f', 7]], 10]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 9]]},\n   [[['b', 1], ['c', 7]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 3]]},\n   [[['a', 4], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 3],\n               ['e', 1],\n               ['d', 3],\n               ['c', 1],\n               ['c', 4],\n               ['c', 3],\n               ['e', 5],\n               ['e', 2],\n               ['b', 5],\n               ['a', 2],\n               ['e', 5],\n               ['d', 3],\n               ['a', 1],\n               ['b', 4]]},\n   [[['b', 3]], 39]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['c', 2],\n               ['d', 1],\n               ['b', 2],\n               ['d', 3],\n               ['b', 3],\n               ['d', 4],\n               ['c', 1],\n               ['f', 5],\n               ['d', 1],\n               ['e', 5],\n               ['b', 2],\n               ['d', 3]]},\n   [[['d', 8], ['e', 3], ['f', 1]], 28]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['c', 5],\n               ['b', 5],\n               ['c', 2],\n               ['c', 5],\n               ['d', 4],\n               ['a', 4],\n               ['b', 4],\n               ['c', 5],\n               ['c', 1],\n               ['e', 2],\n               ['b', 3],\n               ['e', 2],\n               ['b', 3],\n               ['d', 5]]},\n   [[['c', 3], ['d', 2]], 45]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['b', 5],\n               ['d', 2],\n               ['a', 4],\n               ['f', 3],\n               ['a', 1],\n               ['b', 2],\n               ['g', 1],\n               ['c', 2],\n               ['d', 3],\n               ['d', 5],\n               ['d', 3],\n               ['e', 4],\n               ['c', 3],\n               ['g', 4]]},\n   [[['b', 1], ['d', 7], ['e', 1], ['g', 3]], 30]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 10]]},\n   [[['b', 1], ['c', 8]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 4]]},\n   [[['a', 5], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['b', 4],\n               ['d', 3],\n               ['d', 4],\n               ['e', 4],\n               ['c', 1],\n               ['a', 3],\n               ['b', 2],\n               ['b', 5],\n               ['e', 5],\n               ['e', 1],\n               ['d', 4],\n               ['e', 3],\n               ['c', 3],\n               ['d', 3],\n               ['e', 5]]},\n   [[['d', 1], ['e', 7]], 42]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['b', 5],\n               ['e', 3],\n               ['c', 4],\n               ['d', 4],\n               ['e', 4],\n               ['e', 2],\n               ['b', 4],\n               ['d', 1],\n               ['a', 4],\n               ['b', 3],\n               ['f', 1],\n               ['f', 2],\n               ['d', 4]]},\n   [[['b', 1], ['d', 4]], 44]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['a', 5],\n               ['e', 3],\n               ['b', 4],\n               ['c', 4],\n               ['a', 2],\n               ['e', 1],\n               ['e', 2],\n               ['a', 5],\n               ['e', 1],\n               ['c', 3],\n               ['c', 4],\n               ['c', 1],\n               ['c', 3]]},\n   [[['a', 6], ['c', 7]], 33]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['b', 1],\n               ['g', 4],\n               ['f', 3],\n               ['g', 1],\n               ['f', 1],\n               ['e', 1],\n               ['g', 3],\n               ['g', 5],\n               ['g', 2],\n               ['a', 4],\n               ['d', 2],\n               ['e', 2],\n               ['d', 3],\n               ['d', 3],\n               ['e', 5]]},\n   [[['d', 5], ['e', 4], ['g', 11]], 20]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 11]]},\n   [[['b', 1], ['c', 9]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 5]]},\n   [[['a', 6], ['b', 1], ['c', 1]], 0]]]]\nfor label, args, expected in cases[N - 1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"0fdc29d94abd088a6de46b49563bf7ebe69dd686782c706b06e1f15ed32c8be9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    k = x['k']\n    C = {}\n    removed = 0\n    for item, wt in x['stream']:\n        if item in C:\n            C[item] += wt\n        elif len(C) < k:\n            C[item] = wt\n        else:\n            dec = min(min(C.values()), wt)\n            for key in list(C):\n                C[key] -= dec\n                if C[key] == 0:\n                    del C[key]\n            wt -= dec\n            removed += dec * (k + 1)\n            if wt > 0:\n                C[item] = wt\n    return [sorted([key, v] for key, v in C.items()), removed]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 4],\n               ['c', 1],\n               ['a', 3],\n               ['d', 1],\n               ['d', 3],\n               ['a', 5],\n               ['e', 2],\n               ['d', 3],\n               ['d', 4],\n               ['a', 5],\n               ['a', 4]]},\n   [[['a', 14], ['d', 12]], 9]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['e', 5],\n               ['c', 5],\n               ['b', 3],\n               ['d', 2],\n               ['c', 2],\n               ['d', 2],\n               ['d', 1],\n               ['c', 3],\n               ['a', 4],\n               ['d', 4],\n               ['f', 1]]},\n   [[['a', 1], ['c', 4], ['d', 3]], 24]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['d', 2],\n               ['c', 2],\n               ['c', 1],\n               ['c', 4],\n               ['a', 1],\n               ['c', 4],\n               ['d', 4],\n               ['c', 5],\n               ['c', 3],\n               ['c', 4],\n               ['a', 1]]},\n   [[['c', 21], ['d', 4]], 6]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 5],\n               ['a', 5],\n               ['a', 2],\n               ['a', 3],\n               ['d', 4],\n               ['a', 3],\n               ['e', 4],\n               ['e', 1],\n               ['g', 4],\n               ['g', 1],\n               ['g', 3]]},\n   [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 7]]},\n   [[['b', 1], ['c', 5]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 1]]},\n   [[['a', 2], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 1],\n               ['e', 5],\n               ['d', 4],\n               ['e', 5],\n               ['b', 1],\n               ['e', 4],\n               ['a', 5],\n               ['b', 3],\n               ['d', 1],\n               ['d', 2],\n               ['e', 1],\n               ['d', 1]]},\n   [[['d', 2], ['e', 7]], 24]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['c', 2],\n               ['b', 5],\n               ['b', 5],\n               ['c', 1],\n               ['d', 1],\n               ['a', 5],\n               ['c', 2],\n               ['f', 4],\n               ['a', 2],\n               ['f', 5],\n               ['b', 2],\n               ['d', 4]]},\n   [[['b', 5], ['d', 2], ['f', 3]], 28]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['c', 2],\n               ['d', 2],\n               ['c', 4],\n               ['d', 5],\n               ['d', 1],\n               ['b', 2],\n               ['b', 5],\n               ['c', 3],\n               ['e', 4],\n               ['c', 5],\n               ['e', 3],\n               ['b', 2]]},\n   [[['c', 4], ['e', 4]], 30]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 2],\n               ['g', 1],\n               ['c', 5],\n               ['a', 3],\n               ['b', 2],\n               ['b', 1],\n               ['d', 3],\n               ['g', 2],\n               ['e', 3],\n               ['b', 4],\n               ['d', 2],\n               ['d', 4]]},\n   [[['b', 2], ['d', 4], ['e', 1]], 25]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 8]]},\n   [[['b', 1], ['c', 6]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 2]]},\n   [[['a', 3], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['c', 3],\n               ['e', 5],\n               ['c', 1],\n               ['a', 2],\n               ['a', 2],\n               ['a', 4],\n               ['c', 3],\n               ['d', 5],\n               ['e', 3],\n               ['a', 1],\n               ['c', 1],\n               ['b', 5],\n               ['d', 1]]},\n   [[['b', 5], ['d', 1]], 30]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['a', 1],\n               ['e', 4],\n               ['e', 5],\n               ['b', 2],\n               ['f', 3],\n               ['d', 3],\n               ['b', 1],\n               ['b', 1],\n               ['f', 3],\n               ['d', 2],\n               ['c', 3],\n               ['f', 3],\n               ['c', 3]]},\n   [[['c', 4], ['e', 3], ['f', 3]], 24]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['e', 3],\n               ['a', 1],\n               ['c', 5],\n               ['b', 5],\n               ['c', 3],\n               ['e', 4],\n               ['b', 1],\n               ['a', 5],\n               ['e', 3],\n               ['d', 1],\n               ['e', 1],\n               ['e', 1],\n               ['e', 5]]},\n   [[['a', 3], ['e', 8]], 27]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['a', 3],\n               ['f', 4],\n               ['e', 4],\n               ['b', 2],\n               ['c', 1],\n               ['g', 1],\n               ['f', 4],\n               ['e', 3],\n               ['a', 1],\n               ['e', 4],\n               ['e', 2],\n               ['b', 2],\n               ['f', 1]]},\n   [[['a', 2], ['b', 2], ['e', 11], ['f', 7]], 10]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 9]]},\n   [[['b', 1], ['c', 7]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 3]]},\n   [[['a', 4], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['d', 3],\n               ['e', 1],\n               ['d', 3],\n               ['c', 1],\n               ['c', 4],\n               ['c', 3],\n               ['e', 5],\n               ['e', 2],\n               ['b', 5],\n               ['a', 2],\n               ['e', 5],\n               ['d', 3],\n               ['a', 1],\n               ['b', 4]]},\n   [[['b', 3]], 39]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['c', 2],\n               ['d', 1],\n               ['b', 2],\n               ['d', 3],\n               ['b', 3],\n               ['d', 4],\n               ['c', 1],\n               ['f', 5],\n               ['d', 1],\n               ['e', 5],\n               ['b', 2],\n               ['d', 3]]},\n   [[['d', 8], ['e', 3], ['f', 1]], 28]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['c', 5],\n               ['b', 5],\n               ['c', 2],\n               ['c', 5],\n               ['d', 4],\n               ['a', 4],\n               ['b', 4],\n               ['c', 5],\n               ['c', 1],\n               ['e', 2],\n               ['b', 3],\n               ['e', 2],\n               ['b', 3],\n               ['d', 5]]},\n   [[['c', 3], ['d', 2]], 45]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['b', 5],\n               ['d', 2],\n               ['a', 4],\n               ['f', 3],\n               ['a', 1],\n               ['b', 2],\n               ['g', 1],\n               ['c', 2],\n               ['d', 3],\n               ['d', 5],\n               ['d', 3],\n               ['e', 4],\n               ['c', 3],\n               ['g', 4]]},\n   [[['b', 1], ['d', 7], ['e', 1], ['g', 3]], 30]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 10]]},\n   [[['b', 1], ['c', 8]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 4]]},\n   [[['a', 5], ['b', 1], ['c', 1]], 0]]],\n [['weighted stream 0 k=2',\n   {'k': 2,\n    'stream': [['b', 4],\n               ['d', 3],\n               ['d', 4],\n               ['e', 4],\n               ['c', 1],\n               ['a', 3],\n               ['b', 2],\n               ['b', 5],\n               ['e', 5],\n               ['e', 1],\n               ['d', 4],\n               ['e', 3],\n               ['c', 3],\n               ['d', 3],\n               ['e', 5]]},\n   [[['d', 1], ['e', 7]], 42]],\n  ['weighted stream 1 k=3',\n   {'k': 3,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['b', 5],\n               ['e', 3],\n               ['c', 4],\n               ['d', 4],\n               ['e', 4],\n               ['e', 2],\n               ['b', 4],\n               ['d', 1],\n               ['a', 4],\n               ['b', 3],\n               ['f', 1],\n               ['f', 2],\n               ['d', 4]]},\n   [[['b', 1], ['d', 4]], 44]],\n  ['weighted stream 2 k=2',\n   {'k': 2,\n    'stream': [['d', 3],\n               ['a', 5],\n               ['a', 5],\n               ['e', 3],\n               ['b', 4],\n               ['c', 4],\n               ['a', 2],\n               ['e', 1],\n               ['e', 2],\n               ['a', 5],\n               ['e', 1],\n               ['c', 3],\n               ['c', 4],\n               ['c', 1],\n               ['c', 3]]},\n   [[['a', 6], ['c', 7]], 33]],\n  ['weighted stream 3 k=4',\n   {'k': 4,\n    'stream': [['b', 1],\n               ['g', 4],\n               ['f', 3],\n               ['g', 1],\n               ['f', 1],\n               ['e', 1],\n               ['g', 3],\n               ['g', 5],\n               ['g', 2],\n               ['a', 4],\n               ['d', 2],\n               ['e', 2],\n               ['d', 3],\n               ['d', 3],\n               ['e', 5]]},\n   [[['d', 5], ['e', 4], ['g', 11]], 20]],\n  ['newcomer fully absorbed',\n   {'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},\n   [[['a', 2], ['b', 1]], 9]],\n  ['newcomer survives decrement',\n   {'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 11]]},\n   [[['b', 1], ['c', 9]], 6]],\n  ['exact capacity',\n   {'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 5]]},\n   [[['a', 6], ['b', 1], ['c', 1]], 0]]]]\nfor label, args, expected in cases[N - 1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic, bounded teaching model with stipulated constants and pre-hashed or explicitly hashed inputs; it is not a production implementation and makes no claim of conformance to any library or paper beyond the stated contract. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-probabilistic_sketches-misra-gries-weighted-remainder-insert","generated_at":"2026-09-29T14:48:44.290397+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Heavy-hitter detection over weighted traffic (bytes per flow, spend per account) relies on the deterministic Misra-Gries error bound removed/(k+1).","repair":"Insert the incoming item only with its positive remainder.","root_cause":"After decrementing, the incoming item is inserted with its original weight instead of the remainder.","sha256":"939a5ec850fc3cd9f5a5f90495997f6c37f456fdcc5e6b820b43e583f10ccb32","title":"Weighted Misra-Gries frequent items: newcomer inserted with its full weight · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.948,"exit_code":1,"observations":[{"actual":[[["a",14],["d",12],["e",0]],9],"check":"weighted stream 0 k=2","expected":[[["a",14],["d",12]],9],"passed":false},{"actual":[[["a",2],["c",6],["d",5],["e",1],["f",0]],16],"check":"weighted stream 1 k=3","expected":[[["a",1],["c",4],["d",3]],24],"passed":false},{"actual":[[["a",1],["c",22],["d",5]],3],"check":"weighted stream 2 k=2","expected":[[["c",21],["d",4]],6],"passed":false},{"actual":[[["a",18],["d",4],["e",5],["g",8]],0],"check":"weighted stream 3 k=4","expected":[[["a",18],["d",4],["e",5],["g",8]],0],"passed":true},{"actual":[[["a",2],["b",1],["c",0]],9],"check":"newcomer fully absorbed","expected":[[["a",2],["b",1]],9],"passed":false},{"actual":[[["b",1],["c",5]],6],"check":"newcomer survives decrement","expected":[[["b",1],["c",5]],6],"passed":true},{"actual":[[["a",2],["b",1],["c",1]],0],"check":"exact capacity","expected":[[["a",2],["b",1],["c",1]],0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"weighted stream 0 k=2\", \"actual\": [[[\"a\", 14], [\"d\", 12], [\"e\", 0]], 9], \"expected\": [[[\"a\", 14], [\"d\", 12]], 9], \"passed\": false}, {\"check\": \"weighted stream 1 k=3\", \"actual\": [[[\"a\", 2], [\"c\", 6], [\"d\", 5], [\"e\", 1], [\"f\", 0]], 16], \"expected\": [[[\"a\", 1], [\"c\", 4], [\"d\", 3]], 24], \"passed\": false}, {\"check\": \"weighted stream 2 k=2\", \"actual\": [[[\"a\", 1], [\"c\", 22], [\"d\", 5]], 3], \"expected\": [[[\"c\", 21], [\"d\", 4]], 6], \"passed\": false}, {\"check\": \"weighted stream 3 k=4\", \"actual\": [[[\"a\", 18], [\"d\", 4], [\"e\", 5], [\"g\", 8]], 0], \"expected\": [[[\"a\", 18], [\"d\", 4], [\"e\", 5], [\"g\", 8]], 0], \"passed\": true}, {\"check\": \"newcomer fully absorbed\", \"actual\": [[[\"a\", 2], [\"b\", 1], [\"c\", 0]], 9], \"expected\": [[[\"a\", 2], [\"b\", 1]], 9], \"passed\": false}, {\"check\": \"newcomer survives decrement\", \"actual\": [[[\"b\", 1], [\"c\", 5]], 6], \"expected\": [[[\"b\", 1], [\"c\", 5]], 6], \"passed\": true}, {\"check\": \"exact capacity\", \"actual\": [[[\"a\", 2], [\"b\", 1], [\"c\", 1]], 0], \"expected\": [[[\"a\", 2], [\"b\", 1], [\"c\", 1]], 0], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.752,"exit_code":1,"observations":[{"actual":[[["a",15],["d",12],["e",2]],9],"check":"weighted stream 0 k=2","expected":[[["a",14],["d",12]],9],"passed":false},{"actual":[[["a",3],["c",6],["d",7],["e",1],["f",1]],16],"check":"weighted stream 1 k=3","expected":[[["a",1],["c",4],["d",3]],24],"passed":false},{"actual":[[["a",2],["c",22],["d",5]],3],"check":"weighted stream 2 k=2","expected":[[["c",21],["d",4]],6],"passed":false},{"actual":[[["a",18],["d",4],["e",5],["g",8]],0],"check":"weighted stream 3 k=4","expected":[[["a",18],["d",4],["e",5],["g",8]],0],"passed":true},{"actual":[[["a",2],["b",1],["c",3]],9],"check":"newcomer fully absorbed","expected":[[["a",2],["b",1]],9],"passed":false},{"actual":[[["b",1],["c",7]],6],"check":"newcomer survives decrement","expected":[[["b",1],["c",5]],6],"passed":false},{"actual":[[["a",2],["b",1],["c",1]],0],"check":"exact capacity","expected":[[["a",2],["b",1],["c",1]],0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"weighted stream 0 k=2\", \"actual\": [[[\"a\", 15], [\"d\", 12], [\"e\", 2]], 9], \"expected\": [[[\"a\", 14], [\"d\", 12]], 9], \"passed\": false}, {\"check\": \"weighted stream 1 k=3\", \"actual\": [[[\"a\", 3], [\"c\", 6], [\"d\", 7], [\"e\", 1], [\"f\", 1]], 16], \"expected\": [[[\"a\", 1], [\"c\", 4], [\"d\", 3]], 24], \"passed\": false}, {\"check\": \"weighted stream 2 k=2\", \"actual\": [[[\"a\", 2], [\"c\", 22], [\"d\", 5]], 3], \"expected\": [[[\"c\", 21], [\"d\", 4]], 6], \"passed\": false}, {\"check\": \"weighted stream 3 k=4\", \"actual\": [[[\"a\", 18], [\"d\", 4], [\"e\", 5], [\"g\", 8]], 0], \"expected\": [[[\"a\", 18], [\"d\", 4], [\"e\", 5], [\"g\", 8]], 0], \"passed\": true}, {\"check\": \"newcomer fully absorbed\", \"actual\": [[[\"a\", 2], [\"b\", 1], [\"c\", 3]], 9], \"expected\": [[[\"a\", 2], [\"b\", 1]], 9], \"passed\": false}, {\"check\": \"newcomer survives decrement\", \"actual\": [[[\"b\", 1], [\"c\", 7]], 6], \"expected\": [[[\"b\", 1], [\"c\", 5]], 6], \"passed\": false}, {\"check\": \"exact capacity\", \"actual\": [[[\"a\", 2], [\"b\", 1], [\"c\", 1]], 0], \"expected\": [[[\"a\", 2], [\"b\", 1], [\"c\", 1]], 0], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.845,"exit_code":0,"observations":[{"actual":[[["a",14],["d",12]],9],"check":"weighted stream 0 k=2","expected":[[["a",14],["d",12]],9],"passed":true},{"actual":[[["a",1],["c",4],["d",3]],24],"check":"weighted stream 1 k=3","expected":[[["a",1],["c",4],["d",3]],24],"passed":true},{"actual":[[["c",21],["d",4]],6],"check":"weighted stream 2 k=2","expected":[[["c",21],["d",4]],6],"passed":true},{"actual":[[["a",18],["d",4],["e",5],["g",8]],0],"check":"weighted stream 3 k=4","expected":[[["a",18],["d",4],["e",5],["g",8]],0],"passed":true},{"actual":[[["a",2],["b",1]],9],"check":"newcomer fully absorbed","expected":[[["a",2],["b",1]],9],"passed":true},{"actual":[[["b",1],["c",5]],6],"check":"newcomer survives decrement","expected":[[["b",1],["c",5]],6],"passed":true},{"actual":[[["a",2],["b",1],["c",1]],0],"check":"exact capacity","expected":[[["a",2],["b",1],["c",1]],0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"weighted stream 0 k=2\", \"actual\": [[[\"a\", 14], [\"d\", 12]], 9], \"expected\": [[[\"a\", 14], [\"d\", 12]], 9], \"passed\": true}, {\"check\": \"weighted stream 1 k=3\", \"actual\": [[[\"a\", 1], [\"c\", 4], [\"d\", 3]], 24], \"expected\": [[[\"a\", 1], [\"c\", 4], [\"d\", 3]], 24], \"passed\": true}, {\"check\": \"weighted stream 2 k=2\", \"actual\": [[[\"c\", 21], [\"d\", 4]], 6], \"expected\": [[[\"c\", 21], [\"d\", 4]], 6], \"passed\": true}, {\"check\": \"weighted stream 3 k=4\", \"actual\": [[[\"a\", 18], [\"d\", 4], [\"e\", 5], [\"g\", 8]], 0], \"expected\": [[[\"a\", 18], [\"d\", 4], [\"e\", 5], [\"g\", 8]], 0], \"passed\": true}, {\"check\": \"newcomer fully absorbed\", \"actual\": [[[\"a\", 2], [\"b\", 1]], 9], \"expected\": [[[\"a\", 2], [\"b\", 1]], 9], \"passed\": true}, {\"check\": \"newcomer survives decrement\", \"actual\": [[[\"b\", 1], [\"c\", 5]], 6], \"expected\": [[[\"b\", 1], [\"c\", 5]], 6], \"passed\": true}, {\"check\": \"exact capacity\", \"actual\": [[[\"a\", 2], [\"b\", 1], [\"c\", 1]], 0], \"expected\": [[[\"a\", 2], [\"b\", 1], [\"c\", 1]], 0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}