{ "id": "P132", "slug": "fair-share", "key": "P132-fair-share", "title": "Fair share", "summary": "One worker and one-slot jobs from a heavy tenant and light ones, first come first served or tenants in turn: the light tenants' worst wait changes a lot, the mean per job not at all.", "entry": "main.eml", "ui": "terminal", "readme": "# P132 - Fair share\n\nOne worker, jobs of one slot each, from one heavy tenant and several light\nones, run first come first served or taking the tenants in turn.\n\n- `main.eml` - the menu, the tenants, the comparison slot by slot and per\n tenant, and the settings\n- `fair.eml` - the jobs, the two schedules, and the counts per tenant and\n per job\n\nHow each part works:\n\n- Tenant H sends its jobs at slot 0; each light tenant sends one at a\n later slot. The worker runs one job a slot and is never idle while a\n job waits. In turn, it takes the next waiting job of the next tenant\n that has one.\n- As in the corpus case `fair-share-vs-fifo`, first come is fair to jobs\n and in turn is fair to tenants. With 20 jobs from H and one each from a\n to e at slot 1, the light tenants' worst completion is 25 first come and\n 6 in turn; H's last job moves from 20 to 25.\n- Per job the two are the same: the worker is busy in the same slots\n either way, so the mean completion and the mean wait per job do not\n move at all. Taking turns never makes a light tenant's worst completion\n later.\n\nWhat is checked: menu choices 1 to 4; 1 to 30 jobs for H, 1 to 8 light\ntenants, and a slot from 0 to 30 for their jobs. An empty answer cancels.\n\nSessions: `sessions/basic.in` gives:\n- the tenants and the comparison;\n- the light jobs at slot 25, after H's are done: the two run alike, the\n worker idle in between;\n- 6 jobs from H and 3 light tenants at slot 0.\n\n`sessions/bad-input.in` gives:\n- menu choices 0 and x;\n- settings: a cancel, 0, 31 and x for H, then 5 with a cancel and 9\n light tenants, and 5 and 2 with a cancel and slot 31;\n- the most of everything: 30 jobs from H and 8 light tenants at slot 0.\n\nBuilt on the verified corpus case `fair-share-vs-fifo` (the same jobs in\ntwo orders, fair to requests or fair to tenants).\n", "modules": [ { "name": "main.eml", "eml": "# P132 fair share: one heavy tenant and several light ones through first\n# come first served and through taking tenants in turn, slot by slot and\n# per tenant.\nimport fair\n\ndef plain(s):\n 0 => i\n len(s) => j\n while i < j and s[i] == \" \":\n i + 1 => i\n while j > i and s[j - 1] == \" \":\n j - 1 => j\n return s[i:j]\n\ndef pad(s, n):\n s => out\n while len(out) < n:\n out + \" \" => out\n return out\n\ndef lpad(s, n):\n s => out\n while len(out) < n:\n \" \" + out => out\n return out\n\ndef letter(t):\n \"Habcdefgh\" => ls\n return ls[t]\n\ndef tenths(p, q):\n # p / q to one decimal, rounded half up\n int((20 * p + q) / (2 * q)) => t\n while t * 2 * q > 20 * p + q:\n t - 1 => t\n while (t + 1) * 2 * q <= 20 * p + q:\n t + 1 => t\n return str(int(t / 10)) + \".\" + str(t % 10)\n\ndef show(heavy, light, late):\n (\"Tenant H sends \" + str(heavy) + \" jobs at slot 0; tenants a to \" + letter(light) + \" send one each at slot \" + str(late) + \". Every job takes one slot.\") ^0\n\ndef compare(heavy, light, late):\n fair.jobs(heavy, light, late) => js\n light + 1 => tenants\n \"Slot by slot (H the heavy tenant, a letter each light one):\" ^0\n [] => orders\n for plan in [\"fifo\", \"fair\"]:\n fair.schedule(js, tenants, plan) => o\n orders + [o] => orders\n \"\" => line\n for e in o:\n line + letter(js[e[0]][0]) => line\n \"first come\" => label\n if plan == \"fair\":\n \"in turn\" => label\n (\" \" + pad(label, 11) + line) ^0\n \" tenant jobs first come: worst mean in turn: worst mean\" ^0\n fair.per_tenant(js, tenants, orders[0]) => a\n fair.per_tenant(js, tenants, orders[1]) => b\n 0 => worst_a\n 0 => worst_b\n for t in [0:tenants - 1]:\n (\" \" + pad(letter(t), 7) + lpad(str(a[t][0]), 6) + lpad(str(a[t][1]), 19) + lpad(tenths(a[t][2], a[t][0]), 6) + lpad(str(b[t][1]), 16) + lpad(tenths(b[t][2], b[t][0]), 6)) ^0\n if t > 0:\n if a[t][1] > worst_a:\n a[t][1] => worst_a\n if b[t][1] > worst_b:\n b[t][1] => worst_b\n fair.per_job(js, orders[0]) => ja\n fair.per_job(js, orders[1]) => jb\n (\"Worst completion among the light tenants: \" + str(worst_a) + \" first come, \" + str(worst_b) + \" in turn; tenant H's: \" + str(a[0][1]) + \" and \" + str(b[0][1]) + \".\") ^0\n (\"Mean completion per job: \" + tenths(ja[0], len(js)) + \" first come, \" + tenths(jb[0], len(js)) + \" in turn; mean wait per job: \" + tenths(ja[1], len(js)) + \" and \" + tenths(jb[1], len(js)) + \".\") ^0\n if ja[0] == jb[0]:\n \"Per job the two are the same: the worker is busy in the same slots either way, and only who goes first changes.\" ^0\n\ndef ask_int(prompt, low, high):\n plain(input(prompt)) => t\n if t == \"\":\n \"Cancelled.\" ^0\n return 0 - 1\n if len(t) > 2:\n (\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\") ^0\n return 0 - 1\n for c in t:\n if c < \"0\" or c > \"9\":\n (\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\") ^0\n return 0 - 1\n if int(t) < low or int(t) > high:\n (\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\") ^0\n return 0 - 1\n return int(t)\n\ndef settings(heavy, light, late):\n ask_int(\"tenant H's jobs (1 to 30)> \", 1, 30) => h\n if h < 0:\n return [heavy, light, late]\n ask_int(\"light tenants (1 to 8)> \", 1, 8) => l\n if l < 0:\n return [heavy, light, late]\n ask_int(\"slot the light tenants send at (0 to 30)> \", 0, 30) => s\n if s < 0:\n return [heavy, light, late]\n show(h, l, s)\n return [h, l, s]\n\n20 => heavy\n5 => light\n1 => late\n\n\"== Fair share ==\" ^0\n\"One worker, jobs of one slot each, from one heavy tenant and several light ones.\" ^0\nTrue => running\nwhile running:\n \"\" ^0\n \"1) the tenants 2) compare 3) settings 4) quit\" ^0\n plain(input(\"choice> \")) => choice\n if choice == \"1\":\n show(heavy, light, late)\n elif choice == \"2\":\n compare(heavy, light, late)\n elif choice == \"3\":\n settings(heavy, light, late) => s\n s[0] => heavy\n s[1] => light\n s[2] => late\n elif choice == \"4\":\n False => running\n else:\n \"Pick a number from 1 to 4.\" ^0\n\"Bye.\" ^0\n", "python": "import fair\n\ndef plain(s):\n i = 0\n j = len(s)\n while i < j and s[i] == \" \":\n i = i + 1\n while j > i and s[j - 1] == \" \":\n j = j - 1\n return s[i:j]\n\ndef pad(s, n):\n out = s\n while len(out) < n:\n out = out + \" \"\n return out\n\ndef lpad(s, n):\n out = s\n while len(out) < n:\n out = \" \" + out\n return out\n\ndef letter(t):\n ls = \"Habcdefgh\"\n return ls[t]\n\ndef tenths(p, q):\n t = int((20 * p + q) / (2 * q))\n while t * 2 * q > 20 * p + q:\n t = t - 1\n while (t + 1) * 2 * q <= 20 * p + q:\n t = t + 1\n return str(int(t / 10)) + \".\" + str(t % 10)\n\ndef show(heavy, light, late):\n print(\"Tenant H sends \" + str(heavy) + \" jobs at slot 0; tenants a to \" + letter(light) + \" send one each at slot \" + str(late) + \". Every job takes one slot.\")\n\ndef compare(heavy, light, late):\n js = fair.jobs(heavy, light, late)\n tenants = light + 1\n print(\"Slot by slot (H the heavy tenant, a letter each light one):\")\n orders = []\n for plan in [\"fifo\", \"fair\"]:\n o = fair.schedule(js, tenants, plan)\n orders = orders + [o]\n line = \"\"\n for e in o:\n line = line + letter(js[e[0]][0])\n label = \"first come\"\n if plan == \"fair\":\n label = \"in turn\"\n print(\" \" + pad(label, 11) + line)\n print(\" tenant jobs first come: worst mean in turn: worst mean\")\n a = fair.per_tenant(js, tenants, orders[0])\n b = fair.per_tenant(js, tenants, orders[1])\n worst_a = 0\n worst_b = 0\n for t in range(0, tenants):\n print(\" \" + pad(letter(t), 7) + lpad(str(a[t][0]), 6) + lpad(str(a[t][1]), 19) + lpad(tenths(a[t][2], a[t][0]), 6) + lpad(str(b[t][1]), 16) + lpad(tenths(b[t][2], b[t][0]), 6))\n if t > 0:\n if a[t][1] > worst_a:\n worst_a = a[t][1]\n if b[t][1] > worst_b:\n worst_b = b[t][1]\n ja = fair.per_job(js, orders[0])\n jb = fair.per_job(js, orders[1])\n print(\"Worst completion among the light tenants: \" + str(worst_a) + \" first come, \" + str(worst_b) + \" in turn; tenant H's: \" + str(a[0][1]) + \" and \" + str(b[0][1]) + \".\")\n print(\"Mean completion per job: \" + tenths(ja[0], len(js)) + \" first come, \" + tenths(jb[0], len(js)) + \" in turn; mean wait per job: \" + tenths(ja[1], len(js)) + \" and \" + tenths(jb[1], len(js)) + \".\")\n if ja[0] == jb[0]:\n print(\"Per job the two are the same: the worker is busy in the same slots either way, and only who goes first changes.\")\n\ndef ask_int(prompt, low, high):\n t = plain(input(prompt))\n if t == \"\":\n print(\"Cancelled.\")\n return 0 - 1\n if len(t) > 2:\n print(\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\")\n return 0 - 1\n for c in t:\n if c < \"0\" or c > \"9\":\n print(\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\")\n return 0 - 1\n if int(t) < low or int(t) > high:\n print(\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\")\n return 0 - 1\n return int(t)\n\ndef settings(heavy, light, late):\n h = ask_int(\"tenant H's jobs (1 to 30)> \", 1, 30)\n if h < 0:\n return [heavy, light, late]\n l = ask_int(\"light tenants (1 to 8)> \", 1, 8)\n if l < 0:\n return [heavy, light, late]\n s = ask_int(\"slot the light tenants send at (0 to 30)> \", 0, 30)\n if s < 0:\n return [heavy, light, late]\n show(h, l, s)\n return [h, l, s]\n\nheavy = 20\nlight = 5\nlate = 1\nprint(\"== Fair share ==\")\nprint(\"One worker, jobs of one slot each, from one heavy tenant and several light ones.\")\nrunning = True\nwhile running:\n print(\"\")\n print(\"1) the tenants 2) compare 3) settings 4) quit\")\n choice = plain(input(\"choice> \"))\n if choice == \"1\":\n show(heavy, light, late)\n elif choice == \"2\":\n compare(heavy, light, late)\n elif choice == \"3\":\n s = settings(heavy, light, late)\n heavy = s[0]\n light = s[1]\n late = s[2]\n elif choice == \"4\":\n running = False\n else:\n print(\"Pick a number from 1 to 4.\")\nprint(\"Bye.\")\n" }, { "name": "fair.eml", "eml": "# P132 fair share - one worker, jobs of one slot each from several tenants.\n# As in the corpus case fair-share-vs-fifo, first come first served is fair\n# to jobs, and taking the tenants in turn is fair to tenants. Each job is\n# [tenant, arrival slot]; the worker runs one job a slot, never idle while a\n# job is waiting.\n\ndef jobs(heavy, light, late):\n # tenant 0 sends heavy jobs at slot 0; tenants 1 to light one each at\n # slot late\n [] => out\n for k in [1:heavy]:\n out + [[0, 0]] => out\n for t in [1:light]:\n out + [[t, late]] => out\n return out\n\ndef schedule(js, tenants, plan):\n # the order the jobs run in, as [job index, start slot]\n [] => done\n for j in js:\n done + [False] => done\n [] => out\n 0 => slot\n 0 => turn\n while len(out) < len(js):\n 0 - 1 => pick\n if plan == \"fifo\":\n for i in [0:len(js) - 1]:\n if pick < 0 and not done[i] and js[i][1] <= slot:\n i => pick\n else:\n for step in [0:tenants - 1]:\n (turn + step) % tenants => t\n if pick < 0:\n for i in [0:len(js) - 1]:\n if pick < 0 and not done[i] and js[i][0] == t and js[i][1] <= slot:\n i => pick\n if pick >= 0:\n (t + 1) % tenants => turn\n if pick >= 0:\n True => done[pick]\n out + [[pick, slot]] => out\n slot + 1 => slot\n return out\n\ndef per_tenant(js, tenants, order):\n # per tenant [jobs, worst completion, total completion]; completion is the\n # slot after the job's slot\n [] => out\n for t in [0:tenants - 1]:\n out + [[0, 0, 0]] => out\n for e in order:\n js[e[0]][0] => t\n e[1] + 1 => c\n out[t][0] + 1 => out[t][0]\n if c > out[t][1]:\n c => out[t][1]\n out[t][2] + c => out[t][2]\n return out\n\ndef per_job(js, order):\n # [total completion, total wait] over all jobs\n 0 => c\n 0 => w\n for e in order:\n c + e[1] + 1 => c\n w + e[1] - js[e[0]][1] => w\n return [c, w]\n", "python": "def jobs(heavy, light, late):\n out = []\n for k in range(1, heavy+1):\n out = out + [[0, 0]]\n for t in range(1, light+1):\n out = out + [[t, late]]\n return out\n\ndef schedule(js, tenants, plan):\n done = []\n for j in js:\n done = done + [False]\n out = []\n slot = 0\n turn = 0\n while len(out) < len(js):\n pick = 0 - 1\n if plan == \"fifo\":\n for i in range(0, len(js)):\n if pick < 0 and not done[i] and js[i][1] <= slot:\n pick = i\n else:\n for step in range(0, tenants):\n t = (turn + step) % tenants\n if pick < 0:\n for i in range(0, len(js)):\n if pick < 0 and not done[i] and js[i][0] == t and js[i][1] <= slot:\n pick = i\n if pick >= 0:\n turn = (t + 1) % tenants\n if pick >= 0:\n done[pick] = True\n out = out + [[pick, slot]]\n slot = slot + 1\n return out\n\ndef per_tenant(js, tenants, order):\n out = []\n for t in range(0, tenants):\n out = out + [[0, 0, 0]]\n for e in order:\n t = js[e[0]][0]\n c = e[1] + 1\n out[t][0] = out[t][0] + 1\n if c > out[t][1]:\n out[t][1] = c\n out[t][2] = out[t][2] + c\n return out\n\ndef per_job(js, order):\n c = 0\n w = 0\n for e in order:\n c = c + e[1] + 1\n w = w + e[1] - js[e[0]][1]\n return [c, w]\n" } ], "sessions": [ { "name": "bad-input", "input": "0\nx\n3\n\n3\n0\n3\n31\n3\nx\n3\n5\n\n3\n5\n9\n3\n5\n2\n\n3\n5\n2\n31\n3\n30\n8\n0\n2\n4\n", "screen": "== Fair share ==\nOne worker, jobs of one slot each, from one heavy tenant and several light ones.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 0\nPick a number from 1 to 4.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> x\nPick a number from 1 to 4.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> \nCancelled.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 0\nType a whole number from 1 to 30.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 31\nType a whole number from 1 to 30.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> x\nType a whole number from 1 to 30.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 5\nlight tenants (1 to 8)> \nCancelled.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 5\nlight tenants (1 to 8)> 9\nType a whole number from 1 to 8.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 5\nlight tenants (1 to 8)> 2\nslot the light tenants send at (0 to 30)> \nCancelled.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 5\nlight tenants (1 to 8)> 2\nslot the light tenants send at (0 to 30)> 31\nType a whole number from 0 to 30.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 30\nlight tenants (1 to 8)> 8\nslot the light tenants send at (0 to 30)> 0\nTenant H sends 30 jobs at slot 0; tenants a to h send one each at slot 0. Every job takes one slot.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 2\nSlot by slot (H the heavy tenant, a letter each light one):\n first come HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHabcdefgh\n in turn HabcdefghHHHHHHHHHHHHHHHHHHHHHHHHHHHHH\n tenant jobs first come: worst mean in turn: worst mean\n H 30 30 15.5 38 23.2\n a 1 31 31.0 2 2.0\n b 1 32 32.0 3 3.0\n c 1 33 33.0 4 4.0\n d 1 34 34.0 5 5.0\n e 1 35 35.0 6 6.0\n f 1 36 36.0 7 7.0\n g 1 37 37.0 8 8.0\n h 1 38 38.0 9 9.0\nWorst completion among the light tenants: 38 first come, 9 in turn; tenant H's: 30 and 38.\nMean completion per job: 19.5 first come, 19.5 in turn; mean wait per job: 18.5 and 18.5.\nPer job the two are the same: the worker is busy in the same slots either way, and only who goes first changes.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 4\nBye.\n", "interpreter": "equal" }, { "name": "basic", "input": "1\n2\n3\n20\n5\n25\n2\n3\n6\n3\n0\n2\n4\n", "screen": "== Fair share ==\nOne worker, jobs of one slot each, from one heavy tenant and several light ones.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 1\nTenant H sends 20 jobs at slot 0; tenants a to e send one each at slot 1. Every job takes one slot.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 2\nSlot by slot (H the heavy tenant, a letter each light one):\n first come HHHHHHHHHHHHHHHHHHHHabcde\n in turn HabcdeHHHHHHHHHHHHHHHHHHH\n tenant jobs first come: worst mean in turn: worst mean\n H 20 20 10.5 25 15.3\n a 1 21 21.0 2 2.0\n b 1 22 22.0 3 3.0\n c 1 23 23.0 4 4.0\n d 1 24 24.0 5 5.0\n e 1 25 25.0 6 6.0\nWorst completion among the light tenants: 25 first come, 6 in turn; tenant H's: 20 and 25.\nMean completion per job: 13.0 first come, 13.0 in turn; mean wait per job: 11.8 and 11.8.\nPer job the two are the same: the worker is busy in the same slots either way, and only who goes first changes.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 20\nlight tenants (1 to 8)> 5\nslot the light tenants send at (0 to 30)> 25\nTenant H sends 20 jobs at slot 0; tenants a to e send one each at slot 25. Every job takes one slot.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 2\nSlot by slot (H the heavy tenant, a letter each light one):\n first come HHHHHHHHHHHHHHHHHHHHabcde\n in turn HHHHHHHHHHHHHHHHHHHHabcde\n tenant jobs first come: worst mean in turn: worst mean\n H 20 20 10.5 20 10.5\n a 1 26 26.0 26 26.0\n b 1 27 27.0 27 27.0\n c 1 28 28.0 28 28.0\n d 1 29 29.0 29 29.0\n e 1 30 30.0 30 30.0\nWorst completion among the light tenants: 30 first come, 30 in turn; tenant H's: 20 and 20.\nMean completion per job: 14.0 first come, 14.0 in turn; mean wait per job: 8.0 and 8.0.\nPer job the two are the same: the worker is busy in the same slots either way, and only who goes first changes.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 3\ntenant H's jobs (1 to 30)> 6\nlight tenants (1 to 8)> 3\nslot the light tenants send at (0 to 30)> 0\nTenant H sends 6 jobs at slot 0; tenants a to c send one each at slot 0. Every job takes one slot.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 2\nSlot by slot (H the heavy tenant, a letter each light one):\n first come HHHHHHabc\n in turn HabcHHHHH\n tenant jobs first come: worst mean in turn: worst mean\n H 6 6 3.5 9 6.0\n a 1 7 7.0 2 2.0\n b 1 8 8.0 3 3.0\n c 1 9 9.0 4 4.0\nWorst completion among the light tenants: 9 first come, 4 in turn; tenant H's: 6 and 9.\nMean completion per job: 5.0 first come, 5.0 in turn; mean wait per job: 4.0 and 4.0.\nPer job the two are the same: the worker is busy in the same slots either way, and only who goes first changes.\n\n1) the tenants 2) compare 3) settings 4) quit\nchoice> 4\nBye.\n", "interpreter": "equal" } ], "builtOn": [ { "slug": "fair-share-vs-fifo", "caseId": "278-fair-share-vs-fifo", "title": "Fair share vs FIFO — a queue discipline picks who it is fair to" } ], "updated": "2026-10-17" }