I am wondering why my code does not work. I am new to the code world so if anyone can break this problem down for me and how would be best to solve it thanks!
I am trying to create a program which will indicate the prime numbers from a list of numbers that I specify.
Please tell my why these two codes do not work! I am confused as to what the second code is trying to do as I found it as someone else's solution to my problem. I am new to coding but I love it so bear with me!
Here is my simple code:
def is_prime?(*nums)
i = 2
nums.each do |num|
while i < num
if num % i == 0
puts "#{num} is not a prime"
else
puts "#{num} is a prime"
end
i += 1
end
end
end
....Why does this not work? How can I get it to work? It keeps giving me a weird answer in that it gets stuck on my first number and doesnt seem to process the next numbers I insert when I put:
puts is_prime?(21, 23, 17)
Here is a second code that I wasnt able to run correctly either. Can someone break down what is going on here? How can I get it to work?
def is_prime?(*nums)
nums.each_with_object({}) do |num, hsh|
hsh[num] = num > 1 && 2.upto(num - 1).none? {|i| num % i == 0}
end
end
puts is_prime?(27, 13, 42)
Anyways, I know this question is kind of confusing but if anyone cares to input their 2 cents I would appreciate it! Oh and lastly how do I post code on question board this correctly? I am so new and so confused without a mentor!
You have a few problems. One was identified earlier: the location of the statement i = 2. Here is your code with that fixed.
def is_prime?(*nums)
nums.each do |num|
i = 2
while i < num
if num % i == 0
puts "#{num} is not a prime"
else
puts "#{num} is a prime"
end
i += 1
end
end
end
When num % i == 0 you've determined the number is not prime, and print a message to that effect, but then you continue checking to see if it is divisible all larger numbers less than num. Each time num % i == 0 you print out that it's not prime. The point is that you don't need to keep checking once you determine a number is not prime.
Another problem is whenever num % i != 0 you print that the number is prime. That's premature, however. You can't draw that conclusion until you determine that num % i != 0 for all integers less than num.
Let's see how to fix these problems. I think the easiest ways is to write a separate method that determines if a single number is prime. I've called that method is_prime? and renamed the main method is_each_prime?.
def is_each_prime?(*nums)
nums.each { |num|
puts "#{num} is #{ is_prime?(num) ? '' : "not " }a prime" }
end
def is_prime?(num)
(2...Math.sqrt(num)).all? { |i| num % i != 0 }
end
puts is_each_prime?(21, 23, 17)
#=> 21 is not a prime
# 23 is a prime
# 17 is a prime
One advantage of creating a separate method is_prime? is that you can test it separately, to make sure it is working properly.
Prime numbers exclude evens (except 2 of course), so you can skip them in outer and inner loops. Once you found out number is prime, break the loop. Two those techniques speed up algorithm dramatically, with my experiments from 3.9sec downto 0.2sec on 10000 array.
Standard inneficient algorithm first:
class PrimeNumbers
def initialize(size)
@array = (2..size).to_a
@prime = []
raise ArgumentError if size < 2
end
def process
@array.each do |i|
@prime.push(i) if inner_loop(i)
end
@prime
end
private
def inner_loop(e)
is_prime = true
e.downto(2) do |k|
next if k == e
if e % k == 0
is_prime = false
break
end
end
is_prime
end
end
Next step is to ask these questions:
- Where to skip even numbers?
- why to even iterate through even numbers?
- why to iterate beyond a certain point?
- Is there any chance to have prime number once you pass half of array?
So let's see 30x faster algorithm (input 50000 size, took 3sec instead of 98sec compare to first algorithm version):
class PrimeNumbers
def initialize(size)
raise ArgumentError if size < 2
@array = 1.step(size,2).to_a
@array.shift
@prime = [2]
end
def process
@array.each do |i|
@prime.push(i) if inner_loop(i)
end
@prime
end
private
def inner_loop(e, is_prime = true)
3.step(e/3, 2) do |k|
if e % k == 0
is_prime = false
break
end
end
is_prime
end
end
Depends on algorithm efficiency time results can be as following (original array 50000 size):
96.824695s (loop through all array)
92.385227s (loop through all array, skip even numbers in inner loop)
9.251714s (loop through all array, skip even numbers in outer loop)
5.901579s (loop through outer loop odds only)
3.480197s (loop through outer loop odds only, cut half)
2.329469s (loop through outer loop odds only, cut two thirds)
Why to cut half? Because 67/51 can not be Integer. Why to cut third? There is strong dependency. Look the delimiters for odd numbers:
UPDATE:
Diving deeper into algorithm I've find out that no need to loop through half or even third size of initial array. At the end you can iterate through less than 10% of array to reject composite numbers.
It is relevantly easy to cut 1/2 or 1/3, but to cut 4/5 you have to exclude 9, to cut 7/8 - 9,15,25 etc. It helps to loop through only small set of data ignoring the rest of array. See more details on graph below:
0.398072s (loop through odds only, cut selective block depend on initial size)
What selective block is? Let's choose Array size, for instance 8000 and see through the variables:
size = 8000
@loop_end = 19
@denominators = [9, 15, 21, 27, 33, 39, 45, 51, 25, 35, 45, 55, 65, 75, 85, 49, 63, 77, 91, 105, 119, 81, 99, 117, 135, 153, 121, 143, 165, 187, 169, 195, 221, 225, 255, 289]
Maximum number of values you need to loop through is 5% (19/20)! So to compare a given value no need to loop more than first 5-10% of values.
For the algorithm it is enough to loop through 421 elements to select prime numbers. In case of bigger input @loop_end will adapt. On smaller data set (1000 values) the variables are:
size = 1000
@loop_end = 9
@denominators = [9, 15, 21, 25, 35, 49]
Loop through 111 elements helps to find out prime numbers from 1000 elements array. Although @denominators array is bigger than actual denominators (see spreadsheet above) but it doesn't affect correctness of the algorithm. We reject @denominators and loop up to element/@loop_end with step 2 to avoid even numbers.
The optimization to speed algorithm up 320x is really impressive. See the code down below:
class PrimeNumbers
def initialize(size)
raise ArgumentError if size < 2
prepare_vars(size)
end
def process
@array.each do |i|
next if @denominators.include?(i)
@prime.push(i) if test_of_prime(i)
end
@prime
end
private
def prepare_vars(size)
@prime = [2]
@array = 1.step(size,2).to_a
@array.shift
@loop_end = (size**(1/3.0)).to_i
@loop_end += 1 if (@loop_end % 2 == 0)
@denominators = []
3.step(@loop_end-2,2).each do |i|
i.step(@loop_end-2,2).each do |k|
@denominators << i * k
end
end
end
def test_of_prime(e, is_prime = true)
3.step(e/@loop_end, 2) do |k|
if e % k == 0
is_prime = false
break
end
end
is_prime
end
end
Unit tests are available down below:
require 'minitest/autorun'
class PrimeNumbersTest < Minitest::Unit::TestCase
def test_valid_1
assert_equal [2], PrimeNumbers.new(2).process
end
def test_valid_2
assert_equal [2, 3, 5, 7, 11], PrimeNumbers.new(11).process
end
def test_valid_3
assert_equal [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47], PrimeNumbers.new(50).process
end
def test_valid_4
assert_equal [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97], PrimeNumbers.new(100).process
end
def test_valid_5
assert_equal [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797], PrimeNumbers.new(800).process
end
def test_valid_6
assert_equal [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499], PrimeNumbers.new(1500).process
end
def test_valid_7
assert_equal [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993], PrimeNumbers.new(8000).process
end
def test_invalid_8
assert_raises( ArgumentError ) { PrimeNumbers.new(1) }
end
end
UPDATE2
Sieve of Eratosthenes algorithm is a way faster.
You initialized i outside your loop, so subsequent numbers start by testing with an i already set to some high value.
来源：https://stackoverflow.com/questions/26792960/why-doesnt-my-ruby-coding-for-finding-prime-numbers-work