{ "id": "P085", "slug": "stock-chart", "key": "P085-stock-chart", "title": "Stock chart", "summary": "Daily prices in whole cents drawn as a chart: the best single buy and sell, which is the best run of daily changes (Kadane); every rise taken; and the best profit from at most k trades by dynamic programming, with the trades listed.", "entry": "main.eml", "ui": "terminal", "readme": "# P085 - Stock chart\n\nDaily prices in whole cents, drawn as a chart. The program finds the best\nsingle buy and sell, which is the same as the best run of daily changes;\nthe profit from taking every rise; and the best profit from at most k\ntrades, with the trades listed. It starts with 16 days of prices.\n\n- `main.eml` - the menu, reading prices, the chart and the reports\n- `market.eml` - the best trade, the best run, daily changes, every rise,\n and the best k trades\n\nHow each part works:\n\n- Best single trade, as in the corpus case `stock-buy-sell-profit`: one\n pass, keeping the cheapest price so far. Not trading is allowed, so when\n nothing rises the best is 0.\n- Best run, as in the corpus case `max-subarray-kadane`: the largest sum\n of consecutive daily changes, keeping where the run starts. A trade's\n profit is the sum of the changes it holds through, so with any rise the\n two are the same. When every change is a fall, Kadane gives the\n smallest fall, while the best trade is still 0.\n- Every rise: as many trades as you like means taking each day's rise.\n- At most k trades, one share at a time, by dynamic programming over the\n days: the most made by day d with at most j trades is either the most by\n the day before, or a sale on day d of a share bought on an earlier day\n b, after the most made with j - 1 trades by day b. The trades are read\n back from the choices made.\n- The chart scales each price to a bar of 1 to 40 # from the lowest to the\n highest, in whole numbers.\n\nWhat is checked: menu choices 1 to 5; 1 to 5 trades; 2 to 40 prices, each\nabove 0 and up to 99999.99, with at most two decimals, separated by\nspaces. An empty answer cancels.\n\nSessions: `sessions/basic.in` gives:\n- the chart, and the best trade: buy on day 3, sell on day 15, 5.20 a\n share, the same as the best run of changes;\n- at most 1, 2 and 5 trades: 5.20, 7.55 and 10.00, the last being every\n rise;\n- prices that only fall (no trade, the smallest fall as the best run) and\n prices that stay flat.\n\n`sessions/bad-input.in` gives:\n- menu choices 0 and x;\n- 0, 6 and abc trades;\n- one price, a word, a negative price, 0, three decimals, \"12.\" and 41\n prices - each refused, then cancelled.\n\nBuilt on the verified corpus cases `stock-buy-sell-profit` (the cheapest\nprice so far) and `max-subarray-kadane` (the best run, and why it differs\nwhen nothing rises).\n", "modules": [ { "name": "main.eml", "eml": "# P085 stock chart: daily prices drawn as a chart; the best single trade,\n# which is the best run of daily changes; and the best profit from up to k\n# trades, with the trades listed.\nimport market\n\ndef trim(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 cents_of(s):\n # \"12.40\", \"12.4\" or \"12\" as whole cents (up to 99999.99), or -1.\n 0 => k\n while k < len(s) and s[k] != \".\":\n k + 1 => k\n s[0:k] => whole\n \"\" => part\n if k < len(s):\n s[k + 1:len(s)] => part\n if len(whole) == 0 or len(whole) > 5 or len(part) > 2 or (k < len(s) and len(part) == 0):\n return -1\n 0 => n\n for c in whole + part:\n if not (c >= \"0\" and c <= \"9\"):\n return -1\n n * 10 + int(c) => n\n if len(part) == 0:\n return n * 100\n if len(part) == 1:\n return n * 10\n return n\n\ndef money(c):\n if c < 0:\n return \"-\" + money(0 - c)\n 0 => w\n c => r\n while r >= 100:\n r - 100 => r\n w + 1 => w\n if r < 10:\n return str(w) + \".0\" + str(r)\n return str(w) + \".\" + str(r)\n\ndef prices_of(s):\n [] => out\n \"\" => w\n for c in s + \" \":\n if c == \" \" or c == \",\":\n if w != \"\":\n cents_of(w) => v\n if v <= 0:\n return []\n out + [v] => out\n \"\" => w\n else:\n w + c => w\n return out\n\ndef chart(ps):\n # One row per day, a bar of up to 40 # from the lowest price to the\n # highest.\n ps[0] => lo\n ps[0] => hi\n for p in ps:\n if p < lo:\n p => lo\n if p > hi:\n p => hi\n for d in [0:len(ps) - 1]:\n 1 => n\n if hi > lo:\n # 1 + floor((price - lowest) x 39 / (highest - lowest)), in\n # whole numbers\n (ps[d] - lo) * 39 => r\n while r >= hi - lo:\n r - (hi - lo) => r\n n + 1 => n\n \"\" => bar\n for i in [1:n]:\n bar + \"#\" => bar\n \"\" => day\n if d + 1 < 10:\n \" \" => day\n (\" day \" + day + str(d + 1) + \" \" + money(ps[d]) + \" \" + bar) ^0\n\ndef best(ps):\n market.best_trade(ps) => t\n if t[0] == 0:\n \"No single trade makes money: the price only falls (or stays). Not trading is the best.\" ^0\n else:\n (\"Best single trade: buy on day \" + str(t[1] + 1) + \" at \" + money(ps[t[1]]) + \", sell on day \" + str(t[2] + 1) + \" at \" + money(ps[t[2]]) + \" - \" + money(t[0]) + \" a share.\") ^0\n market.changes(ps) => cs\n market.best_run(cs) => r\n (\"The best run of daily changes is days \" + str(r[1] + 1) + \" to \" + str(r[2] + 2) + \", adding up to \" + money(r[0]) + \".\") ^0\n if r[0] > 0:\n \"The same thing: a trade's profit is the sum of the daily changes it holds through.\" ^0\n elif r[0] == 0:\n \"No day rises, so the best run adds up to nothing - and the best trade is not to trade.\" ^0\n else:\n \"Every daily change is a fall, so the best run is the smallest fall - while the best trade is not to trade.\" ^0\n (\"Trading every rise, as often as you like: \" + money(market.every_rise(ps)) + \".\") ^0\n\ndef trades(ps):\n while True:\n trim(input(\"at most how many trades (1 to 5)> \")) => s\n if s == \"\":\n \"Cancelled.\" ^0\n return\n if s == \"1\" or s == \"2\" or s == \"3\" or s == \"4\" or s == \"5\":\n int(s) => k\n market.best_k(ps, k) => r\n if len(r[1]) == 0:\n \"No trade makes money.\" ^0\n return\n for t in r[1]:\n (\" buy day \" + str(t[0] + 1) + \" at \" + money(ps[t[0]]) + \", sell day \" + str(t[1] + 1) + \" at \" + money(ps[t[1]]) + \": \" + money(ps[t[1]] - ps[t[0]])) ^0\n \"trades\" => word\n if k == 1:\n \"trade\" => word\n (\"At most \" + str(k) + \" \" + word + \", one share at a time: \" + money(r[0]) + \" in all.\") ^0\n return\n \"Type a whole number from 1 to 5.\" ^0\n\ndef new_prices(ps):\n while True:\n trim(input(\"prices, oldest first (2 to 40, like 12.40 13 11.85)> \")) => s\n if s == \"\":\n \"Cancelled.\" ^0\n return ps\n prices_of(s) => out\n if len(out) >= 2 and len(out) <= 40:\n (str(len(out)) + \" days of prices.\") ^0\n return out\n \"Type 2 to 40 prices above 0, up to 99999.99, separated by spaces.\" ^0\n\n[1250, 1310, 1180, 1225, 1405, 1390, 1530, 1480, 1295, 1350, 1610, 1575, 1440, 1520, 1700, 1655] => prices\n\n\"== Stock chart ==\" ^0\n\"Daily prices: the best single trade, the best run of changes, and the best k trades.\" ^0\nTrue => running\nwhile running:\n \"\" ^0\n \"1) chart 2) best trade 3) best k trades 4) new prices 5) quit\" ^0\n trim(input(\"choice> \")) => choice\n if choice == \"1\":\n chart(prices)\n elif choice == \"2\":\n best(prices)\n elif choice == \"3\":\n trades(prices)\n elif choice == \"4\":\n new_prices(prices) => prices\n elif choice == \"5\":\n False => running\n else:\n \"Pick a number from 1 to 5.\" ^0\n\"Bye.\" ^0\n", "python": "import market\n\ndef trim(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 cents_of(s):\n k = 0\n while k < len(s) and s[k] != \".\":\n k = k + 1\n whole = s[0:k]\n part = \"\"\n if k < len(s):\n part = s[k + 1:len(s)]\n if len(whole) == 0 or len(whole) > 5 or len(part) > 2 or k < len(s) and len(part) == 0:\n return -1\n n = 0\n for c in whole + part:\n if not (c >= \"0\" and c <= \"9\"):\n return -1\n n = n * 10 + int(c)\n if len(part) == 0:\n return n * 100\n if len(part) == 1:\n return n * 10\n return n\n\ndef money(c):\n if c < 0:\n return \"-\" + money(0 - c)\n w = 0\n r = c\n while r >= 100:\n r = r - 100\n w = w + 1\n if r < 10:\n return str(w) + \".0\" + str(r)\n return str(w) + \".\" + str(r)\n\ndef prices_of(s):\n out = []\n w = \"\"\n for c in s + \" \":\n if c == \" \" or c == \",\":\n if w != \"\":\n v = cents_of(w)\n if v <= 0:\n return []\n out = out + [v]\n w = \"\"\n else:\n w = w + c\n return out\n\ndef chart(ps):\n lo = ps[0]\n hi = ps[0]\n for p in ps:\n if p < lo:\n lo = p\n if p > hi:\n hi = p\n for d in range(0, len(ps)):\n n = 1\n if hi > lo:\n r = (ps[d] - lo) * 39\n while r >= hi - lo:\n r = r - (hi - lo)\n n = n + 1\n bar = \"\"\n for i in range(1, n+1):\n bar = bar + \"#\"\n day = \"\"\n if d + 1 < 10:\n day = \" \"\n print(\" day \" + day + str(d + 1) + \" \" + money(ps[d]) + \" \" + bar)\n\ndef best(ps):\n t = market.best_trade(ps)\n if t[0] == 0:\n print(\"No single trade makes money: the price only falls (or stays). Not trading is the best.\")\n else:\n print(\"Best single trade: buy on day \" + str(t[1] + 1) + \" at \" + money(ps[t[1]]) + \", sell on day \" + str(t[2] + 1) + \" at \" + money(ps[t[2]]) + \" - \" + money(t[0]) + \" a share.\")\n cs = market.changes(ps)\n r = market.best_run(cs)\n print(\"The best run of daily changes is days \" + str(r[1] + 1) + \" to \" + str(r[2] + 2) + \", adding up to \" + money(r[0]) + \".\")\n if r[0] > 0:\n print(\"The same thing: a trade's profit is the sum of the daily changes it holds through.\")\n elif r[0] == 0:\n print(\"No day rises, so the best run adds up to nothing - and the best trade is not to trade.\")\n else:\n print(\"Every daily change is a fall, so the best run is the smallest fall - while the best trade is not to trade.\")\n print(\"Trading every rise, as often as you like: \" + money(market.every_rise(ps)) + \".\")\n\ndef trades(ps):\n while True:\n s = trim(input(\"at most how many trades (1 to 5)> \"))\n if s == \"\":\n print(\"Cancelled.\")\n return\n if s == \"1\" or s == \"2\" or s == \"3\" or s == \"4\" or s == \"5\":\n k = int(s)\n r = market.best_k(ps, k)\n if len(r[1]) == 0:\n print(\"No trade makes money.\")\n return\n for t in r[1]:\n print(\" buy day \" + str(t[0] + 1) + \" at \" + money(ps[t[0]]) + \", sell day \" + str(t[1] + 1) + \" at \" + money(ps[t[1]]) + \": \" + money(ps[t[1]] - ps[t[0]]))\n word = \"trades\"\n if k == 1:\n word = \"trade\"\n print(\"At most \" + str(k) + \" \" + word + \", one share at a time: \" + money(r[0]) + \" in all.\")\n return\n print(\"Type a whole number from 1 to 5.\")\n\ndef new_prices(ps):\n while True:\n s = trim(input(\"prices, oldest first (2 to 40, like 12.40 13 11.85)> \"))\n if s == \"\":\n print(\"Cancelled.\")\n return ps\n out = prices_of(s)\n if len(out) >= 2 and len(out) <= 40:\n print(str(len(out)) + \" days of prices.\")\n return out\n print(\"Type 2 to 40 prices above 0, up to 99999.99, separated by spaces.\")\n\nprices = [1250, 1310, 1180, 1225, 1405, 1390, 1530, 1480, 1295, 1350, 1610, 1575, 1440, 1520, 1700, 1655]\nprint(\"== Stock chart ==\")\nprint(\"Daily prices: the best single trade, the best run of changes, and the best k trades.\")\nrunning = True\nwhile running:\n print(\"\")\n print(\"1) chart 2) best trade 3) best k trades 4) new prices 5) quit\")\n choice = trim(input(\"choice> \"))\n if choice == \"1\":\n chart(prices)\n elif choice == \"2\":\n best(prices)\n elif choice == \"3\":\n trades(prices)\n elif choice == \"4\":\n prices = new_prices(prices)\n elif choice == \"5\":\n running = False\n else:\n print(\"Pick a number from 1 to 5.\")\nprint(\"Bye.\")\n" }, { "name": "market.eml", "eml": "# P085 stock chart - a run of daily prices in whole cents: the best single\n# buy and sell, the best run of daily changes, and the best profit from up\n# to k trades, each holding at most one share at a time.\n\ndef best_trade(prices):\n # The corpus case stock-buy-sell-profit: one pass keeping the cheapest\n # price so far. Returns [profit, buy day, sell day] (days from 0), or\n # [0, -1, -1] when no trade makes money - not trading is allowed.\n 0 => best\n -1 => buy\n -1 => sell\n 0 => low\n for d in [1:len(prices) - 1]:\n if prices[d] - prices[low] > best:\n prices[d] - prices[low] => best\n low => buy\n d => sell\n if prices[d] < prices[low]:\n d => low\n return [best, buy, sell]\n\ndef best_run(xs):\n # The corpus case max-subarray-kadane, keeping where the run starts:\n # the largest sum of consecutive numbers (at least one), and its first\n # and last index. With every number negative it is the least negative.\n xs[0] => best\n 0 => bs\n 0 => be\n xs[0] => cur\n 0 => cs\n for i in [1:len(xs) - 1]:\n if cur + xs[i] < xs[i]:\n xs[i] => cur\n i => cs\n else:\n cur + xs[i] => cur\n if cur > best:\n cur => best\n cs => bs\n i => be\n return [best, bs, be]\n\ndef changes(prices):\n [0] * (len(prices) - 1) => out\n for d in [1:len(prices) - 1]:\n prices[d] - prices[d - 1] => out[d - 1]\n return out\n\ndef every_rise(prices):\n # As many trades as you like: take every rise from one day to the next.\n 0 => s\n for c in changes(prices):\n if c > 0:\n s + c => s\n return s\n\ndef best_k(prices, k):\n # At most k trades, by dynamic programming over the days. best[j][d] is\n # the most that can be made by day d with at most j trades: either day\n # d does nothing, or it sells a share bought on an earlier day b, with\n # best[j - 1][b] made before buying. `hold` keeps the best of\n # best[j - 1][b] - price[b] so far. Returns [profit, trades as [buy day,\n # sell day]], the trades read back from the choices made.\n len(prices) => n\n # best[j][d]: the most made by day d with at most j trades closed\n [0] * (k + 1) => best\n for j in [0:k]:\n [0] * n => best[j]\n # came[j][d]: the buy day of the trade closing on day d, or -1 if day d\n # closed none\n [0] * (k + 1) => came\n for j in [0:k]:\n [-1] * n => came[j]\n for j in [1:k]:\n 0 - prices[0] => hold\n 0 => hold_day\n for d in [1:n - 1]:\n best[j][d - 1] => keep\n prices[d] + hold => sell\n if sell > keep:\n sell => best[j][d]\n hold_day => came[j][d]\n else:\n keep => best[j][d]\n if best[j - 1][d] - prices[d] > hold:\n best[j - 1][d] - prices[d] => hold\n d => hold_day\n [] => trades\n k => j\n n - 1 => d\n while j > 0 and d > 0:\n if came[j][d] == -1:\n d - 1 => d\n else:\n [[came[j][d], d]] + trades => trades\n came[j][d] => d\n j - 1 => j\n return [best[k][n - 1], trades]\n", "python": "def best_trade(prices):\n best = 0\n buy = -1\n sell = -1\n low = 0\n for d in range(1, len(prices)):\n if prices[d] - prices[low] > best:\n best = prices[d] - prices[low]\n buy = low\n sell = d\n if prices[d] < prices[low]:\n low = d\n return [best, buy, sell]\n\ndef best_run(xs):\n best = xs[0]\n bs = 0\n be = 0\n cur = xs[0]\n cs = 0\n for i in range(1, len(xs)):\n if cur + xs[i] < xs[i]:\n cur = xs[i]\n cs = i\n else:\n cur = cur + xs[i]\n if cur > best:\n best = cur\n bs = cs\n be = i\n return [best, bs, be]\n\ndef changes(prices):\n out = [0] * (len(prices) - 1)\n for d in range(1, len(prices)):\n out[d - 1] = prices[d] - prices[d - 1]\n return out\n\ndef every_rise(prices):\n s = 0\n for c in changes(prices):\n if c > 0:\n s = s + c\n return s\n\ndef best_k(prices, k):\n n = len(prices)\n best = [0] * (k + 1)\n for j in range(0, k+1):\n best[j] = [0] * n\n came = [0] * (k + 1)\n for j in range(0, k+1):\n came[j] = [-1] * n\n for j in range(1, k+1):\n hold = 0 - prices[0]\n hold_day = 0\n for d in range(1, n):\n keep = best[j][d - 1]\n sell = prices[d] + hold\n if sell > keep:\n best[j][d] = sell\n came[j][d] = hold_day\n else:\n best[j][d] = keep\n if best[j - 1][d] - prices[d] > hold:\n hold = best[j - 1][d] - prices[d]\n hold_day = d\n trades = []\n j = k\n d = n - 1\n while j > 0 and d > 0:\n if came[j][d] == -1:\n d = d - 1\n else:\n trades = [[came[j][d], d]] + trades\n d = came[j][d]\n j = j - 1\n return [best[k][n - 1], trades]\n" } ], "sessions": [ { "name": "bad-input", "input": "0\nx\n3\n0\n6\nabc\n\n4\n12\n12 abc\n12 -3\n12 0\n12.345 13\n12. 13\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n\n5\n", "screen": "== Stock chart ==\nDaily prices: the best single trade, the best run of changes, and the best k trades.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 0\nPick a number from 1 to 5.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> x\nPick a number from 1 to 5.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 3\nat most how many trades (1 to 5)> 0\nType a whole number from 1 to 5.\nat most how many trades (1 to 5)> 6\nType a whole number from 1 to 5.\nat most how many trades (1 to 5)> abc\nType a whole number from 1 to 5.\nat most how many trades (1 to 5)> \nCancelled.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 4\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 12\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 12 abc\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 12 -3\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 12 0\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 12.345 13\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 12. 13\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\nType 2 to 40 prices above 0, up to 99999.99, separated by spaces.\nprices, oldest first (2 to 40, like 12.40 13 11.85)> \nCancelled.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" }, { "name": "basic", "input": "1\n2\n3\n1\n3\n2\n3\n5\n4\n10 9 8.5 7\n2\n3\n2\n4\n5 5 5\n2\n1\n5\n", "screen": "== Stock chart ==\nDaily prices: the best single trade, the best run of changes, and the best k trades.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 1\n day 1 12.50 ######\n day 2 13.10 ##########\n day 3 11.80 #\n day 4 12.25 ####\n day 5 14.05 #################\n day 6 13.90 ################\n day 7 15.30 ###########################\n day 8 14.80 #######################\n day 9 12.95 #########\n day 10 13.50 #############\n day 11 16.10 #################################\n day 12 15.75 ##############################\n day 13 14.40 ####################\n day 14 15.20 ##########################\n day 15 17.00 ########################################\n day 16 16.55 ####################################\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 2\nBest single trade: buy on day 3 at 11.80, sell on day 15 at 17.00 - 5.20 a share.\nThe best run of daily changes is days 3 to 15, adding up to 5.20.\nThe same thing: a trade's profit is the sum of the daily changes it holds through.\nTrading every rise, as often as you like: 10.00.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 3\nat most how many trades (1 to 5)> 1\n buy day 3 at 11.80, sell day 15 at 17.00: 5.20\nAt most 1 trade, one share at a time: 5.20 in all.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 3\nat most how many trades (1 to 5)> 2\n buy day 3 at 11.80, sell day 7 at 15.30: 3.50\n buy day 9 at 12.95, sell day 15 at 17.00: 4.05\nAt most 2 trades, one share at a time: 7.55 in all.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 3\nat most how many trades (1 to 5)> 5\n buy day 1 at 12.50, sell day 2 at 13.10: 0.60\n buy day 3 at 11.80, sell day 5 at 14.05: 2.25\n buy day 6 at 13.90, sell day 7 at 15.30: 1.40\n buy day 9 at 12.95, sell day 11 at 16.10: 3.15\n buy day 13 at 14.40, sell day 15 at 17.00: 2.60\nAt most 5 trades, one share at a time: 10.00 in all.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 4\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 10 9 8.5 7\n4 days of prices.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 2\nNo single trade makes money: the price only falls (or stays). Not trading is the best.\nThe best run of daily changes is days 2 to 3, adding up to -0.50.\nEvery daily change is a fall, so the best run is the smallest fall - while the best trade is not to trade.\nTrading every rise, as often as you like: 0.00.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 3\nat most how many trades (1 to 5)> 2\nNo trade makes money.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 4\nprices, oldest first (2 to 40, like 12.40 13 11.85)> 5 5 5\n3 days of prices.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 2\nNo single trade makes money: the price only falls (or stays). Not trading is the best.\nThe best run of daily changes is days 1 to 2, adding up to 0.00.\nNo day rises, so the best run adds up to nothing - and the best trade is not to trade.\nTrading every rise, as often as you like: 0.00.\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 1\n day 1 5.00 #\n day 2 5.00 #\n day 3 5.00 #\n\n1) chart 2) best trade 3) best k trades 4) new prices 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" } ], "builtOn": [ { "slug": "stock-buy-sell-profit", "caseId": "105-stock-buy-sell-profit", "title": "Best single buy/sell profit" }, { "slug": "max-subarray-kadane", "caseId": "091-max-subarray-kadane", "title": "Maximum subarray (Kadane's algorithm)" } ], "updated": "2026-10-15" }