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3052288380
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-- Write a function which takes a limit and returns a list of every
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-- prime number below that limit. It is recommended that you use the
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-- "Sieve of Eratosthenes" algorithm, but you can try a different
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-- prime sieve algorithm if you want.
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--
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-- Solution --------------------------------------------------------------------
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function lesser_primes(limit)
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-- Your implementation here
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end
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-- Tests -----------------------------------------------------------------------
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local luaunit = require("luaunit.luaunit")
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function test_primes_below_2048()
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local primes = {
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
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73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
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157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
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239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
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331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
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421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
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509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
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613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
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709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
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821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
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919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
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1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097,
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1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201,
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1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291,
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1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409,
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1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487,
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1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579,
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1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
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1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777,
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1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
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1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
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1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039
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}
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luaunit.assertEquals(lesser_primes(2048), primes)
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end
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os.exit(luaunit.LuaUnit.run())
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-- Run length encoding is a simple data compression technique where a
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-- "run" of the same value is replaced with a count and a single copy.
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-- In this exercise we will use the notation "#<count>:<value>" to
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-- indicate such a run; however, this should only be put into the
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-- output if it is strictly shorter than the string it is replacing.
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-- The input will consist only of alphanumeric characters.
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--
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-- Solution --------------------------------------------------------------------
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function run_length_encode(input)
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-- Your implementation here
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end
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-- Tests -----------------------------------------------------------------------
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local luaunit = require("luaunit.luaunit")
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function test_encoding_of_aaaaaaaa22bbbbbbssssfffffff67eee66666asdfff()
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local input = "aaaaaaaa22bbbbbbssssfffffff67eee66666asdfff"
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local expected = "#8:a22#6:bssss#7:f67eee#5:6asdfff"
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luaunit.assertEquals(run_length_encode(input), expected)
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end
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function test_encoding_of_wwwwwfffff1223566666666bbbbbbbbbbb78b99asasdfbnfasdafffffff99()
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local input = "wwwwwfffff1223566666666bbbbbbbbbbb78b99asasdfbnfasdafffffff99"
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local expected = "#5:w#5:f12235#8:6#11:b78b99asasdfbnfasda#7:f99"
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luaunit.assertEquals(run_length_encode(input), expected)
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end
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os.exit(luaunit.LuaUnit.run())
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-- Postfix notation is an alternative to the normal "infix" notation
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-- used in mathematical expressions. Instead of writing the operator
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-- between the operands, the operator comes after them. For example,
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-- "1 + 2" is notated as "1 2 +". This removes the need for operator
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-- precedence and parentheses: rather than having to resolve the
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-- ambiguity of an expression like "1 + 2 * 3" with convention or
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-- parentheses, the evaluation order is explicit -- multiplication-
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-- first is "1 2 3 * +" and addition-first is "1 2 + 3 *".
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--
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-- As well as this notational convenience, postfix can be easily
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-- evaluated using a stack. Whenever an operand is encountered, the
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-- value is pushed onto the stack, and whenever an operator is
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-- encountered, two values are popped from the stack and the result of
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-- the operation is pushed on in their place. Finally, the value left
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-- on the top of the stack is the result of the operation.
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--
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-- Write a function that will evaluate a postfix expression and return
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-- the result. You can assume that the expression is valid, and not
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-- worry about handling error cases. The operators will be "+", "-",
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-- "*" and "/".
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--
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-- Solution --------------------------------------------------------------------
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function evaluate_postfix(expression)
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-- Your implementation here
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end
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-- Tests -----------------------------------------------------------------------
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local luaunit = require("luaunit.luaunit")
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function test_1_2_plus_3_times_is_9()
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luaunit.assertEquals(evaluate_postfix("1 2 + 3 *"), 9)
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end
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function test_1_2_3_times_plus_is_7()
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luaunit.assertEquals(evaluate_postfix("1 2 3 * +"), 7)
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end
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function test_4_6_plus_5_divide_2_1_minus_minus_is_1()
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luaunit.assertEquals(evaluate_postfix("4 6 + 5 / 2 1 - -"), 1)
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end
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function test_12_2_times_6_divide_10_times_2_plus_is_42()
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luaunit.assertEquals(evaluate_postfix("12 2 * 6 / 10 * 2 +"), 42)
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end
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os.exit(luaunit.LuaUnit.run())
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