655 lines
17 KiB
Julia
655 lines
17 KiB
Julia
# This file is a part of Julia. License is MIT: https://julialang.org/license
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## Project Euler
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#
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# problems: http://projecteuler.net/problems
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# solutions: https://code.google.com/p/projecteuler-solutions/wiki/ProjectEulerSolutions
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#1: 233168
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@test sum(filter(n->(n%3==0)|(n%5==0),1:999)) == 233168
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#2: 4613732
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function euler2(n)
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t, i, j = 0, 1, 2
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while j <= n
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t += j
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i, j = j, i+j
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i, j = j, i+j
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i, j = j, i+j
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end
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return t
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end
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@test euler2(4000000) == 4613732
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#4: 906609
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function euler4(n)
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m = 1
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for a = 10^n-1:-1:10^(n-1)
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for b = 10^n-1:-1:max(a,-fld(-m,a))
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p = a*b
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d = digits(p)
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if d == reverse(d) && p > m
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m = p
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b < -fld(-m,a) && break
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end
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end
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end
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return m
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end
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@test euler4(3) == 906609
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#5: 232792560
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@test lcm(1:20) == 232792560
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#6: 25164150
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@test sum(1:100)^2 - sum((1:100).^2) == 25164150
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#8: 40824
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function euler8(n,m)
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d = digits(n)
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maximum([prod(d[k:k+m-1]) for k=1:length(d)-m+1])
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end
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let n = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450
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@test euler8(n,5) == 40824
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end
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#9: 31875000
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function euler9(n)
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for a = 1:n, b = 1:n-a, c = n-a-b
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a^2 + b^2 == c^2 && return a*b*c
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end
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end
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@test euler9(1000) == 31875000
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#11: 70600674
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function euler11(grid,n)
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m = typemin(eltype(grid))
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for i = n:size(grid,1)-n+1,
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j = n:size(grid,2)-n+1,
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di = -1:1, dj = -1:1
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di == dj == 0 && continue
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idx = sub2ind(size(grid),
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di==0 ? fill(i,n) : range(i,di,n),
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dj==0 ? fill(j,n) : range(j,dj,n))
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m = max(m,prod(grid[idx]))
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end
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return m
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end
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let grid = [
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08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
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49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
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81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
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52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
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22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
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24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
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32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
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67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
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24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
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21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
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78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
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16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
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86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
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19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
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04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
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88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
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04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
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20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
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20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
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01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
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]
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@test euler11(grid,4) == 70600674
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end
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#12: 76576500
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#13: 5537376230
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let nums = [
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37107287533902102798797998220837590246510135740250
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46376937677490009712648124896970078050417018260538
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74324986199524741059474233309513058123726617309629
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91942213363574161572522430563301811072406154908250
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23067588207539346171171980310421047513778063246676
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89261670696623633820136378418383684178734361726757
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28112879812849979408065481931592621691275889832738
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44274228917432520321923589422876796487670272189318
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47451445736001306439091167216856844588711603153276
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70386486105843025439939619828917593665686757934951
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62176457141856560629502157223196586755079324193331
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64906352462741904929101432445813822663347944758178
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92575867718337217661963751590579239728245598838407
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58203565325359399008402633568948830189458628227828
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80181199384826282014278194139940567587151170094390
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35398664372827112653829987240784473053190104293586
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86515506006295864861532075273371959191420517255829
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71693888707715466499115593487603532921714970056938
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54370070576826684624621495650076471787294438377604
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53282654108756828443191190634694037855217779295145
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36123272525000296071075082563815656710885258350721
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45876576172410976447339110607218265236877223636045
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17423706905851860660448207621209813287860733969412
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81142660418086830619328460811191061556940512689692
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51934325451728388641918047049293215058642563049483
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62467221648435076201727918039944693004732956340691
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15732444386908125794514089057706229429197107928209
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55037687525678773091862540744969844508330393682126
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18336384825330154686196124348767681297534375946515
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80386287592878490201521685554828717201219257766954
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78182833757993103614740356856449095527097864797581
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16726320100436897842553539920931837441497806860984
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48403098129077791799088218795327364475675590848030
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87086987551392711854517078544161852424320693150332
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59959406895756536782107074926966537676326235447210
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69793950679652694742597709739166693763042633987085
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41052684708299085211399427365734116182760315001271
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65378607361501080857009149939512557028198746004375
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35829035317434717326932123578154982629742552737307
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94953759765105305946966067683156574377167401875275
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88902802571733229619176668713819931811048770190271
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25267680276078003013678680992525463401061632866526
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36270218540497705585629946580636237993140746255962
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24074486908231174977792365466257246923322810917141
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91430288197103288597806669760892938638285025333403
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34413065578016127815921815005561868836468420090470
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23053081172816430487623791969842487255036638784583
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11487696932154902810424020138335124462181441773470
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63783299490636259666498587618221225225512486764533
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67720186971698544312419572409913959008952310058822
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95548255300263520781532296796249481641953868218774
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76085327132285723110424803456124867697064507995236
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37774242535411291684276865538926205024910326572967
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23701913275725675285653248258265463092207058596522
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29798860272258331913126375147341994889534765745501
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18495701454879288984856827726077713721403798879715
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38298203783031473527721580348144513491373226651381
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34829543829199918180278916522431027392251122869539
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40957953066405232632538044100059654939159879593635
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29746152185502371307642255121183693803580388584903
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41698116222072977186158236678424689157993532961922
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62467957194401269043877107275048102390895523597457
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23189706772547915061505504953922979530901129967519
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86188088225875314529584099251203829009407770775672
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11306739708304724483816533873502340845647058077308
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82959174767140363198008187129011875491310547126581
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97623331044818386269515456334926366572897563400500
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42846280183517070527831839425882145521227251250327
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55121603546981200581762165212827652751691296897789
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32238195734329339946437501907836945765883352399886
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75506164965184775180738168837861091527357929701337
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62177842752192623401942399639168044983993173312731
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32924185707147349566916674687634660915035914677504
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99518671430235219628894890102423325116913619626622
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73267460800591547471830798392868535206946944540724
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76841822524674417161514036427982273348055556214818
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97142617910342598647204516893989422179826088076852
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87783646182799346313767754307809363333018982642090
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10848802521674670883215120185883543223812876952786
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71329612474782464538636993009049310363619763878039
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62184073572399794223406235393808339651327408011116
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66627891981488087797941876876144230030984490851411
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60661826293682836764744779239180335110989069790714
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85786944089552990653640447425576083659976645795096
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66024396409905389607120198219976047599490197230297
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64913982680032973156037120041377903785566085089252
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16730939319872750275468906903707539413042652315011
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94809377245048795150954100921645863754710598436791
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78639167021187492431995700641917969777599028300699
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15368713711936614952811305876380278410754449733078
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40789923115535562561142322423255033685442488917353
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44889911501440648020369068063960672322193204149535
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41503128880339536053299340368006977710650566631954
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81234880673210146739058568557934581403627822703280
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82616570773948327592232845941706525094512325230608
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22918802058777319719839450180888072429661980811197
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77158542502016545090413245809786882778948721859617
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72107838435069186155435662884062257473692284509516
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20849603980134001723930671666823555245252804609722
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53503534226472524250874054075591789781264330331690
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]
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@test sum(digits(sum(nums))[end-9:end].*Int64(10).^(0:9)) == 5537376230
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end
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#14: 837799
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function euler14(m)
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c = zeros(Int,m)
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c[1] = 1
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for n::Int64 = 2:m
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nʹ, d = n, 0
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while nʹ > length(c) || c[nʹ] == 0
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nʹ = iseven(nʹ) ? nʹ>>1 : 3nʹ+1
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d += 1
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end
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d += c[nʹ]
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while n > length(c) || c[n] == 0
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n <= length(c) && (c[n] = d)
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n = iseven(n) ? n>>1 : 3n+1
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d -= 1
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end
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end
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indmax(c)
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end
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@test euler14(999999) == 837799
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#15: 137846528820
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#16: 1366
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@test sum(digits(big(2)^1000)) == 1366
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#17: 21124
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#18: 1074
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#19: 171
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#20: 648
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@test sum(digits(factorial(big(100)))) == 648
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#21: 31626
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#22: 871198282
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#23: 4179871
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#24: 2783915460
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#25: 4782
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#26: 983
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#27: -59231
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#28: 669171001
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#29: 9183
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#30: 443839
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#31: 73682
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#32: 45228
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#33: 100
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#34: 40730
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#35: 55
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#36: 872187
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#37: 748317
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#38: 932718654
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#39: 840
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#40: 210
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#41: 7652413
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#42: 162
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#43: 16695334890
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#44: 5482660
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#45: 1533776805
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#46: 5777
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#47: 134043
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#48: 9110846700
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#49: 296962999629
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#50: 997651
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#51: 121313
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#52: 142857
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#53: 4075
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#54: 376
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#55: 249
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#56: 972
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#57: 153
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#58: 26241
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#59: 107359
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#60: 26033
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#61: 28684
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#62: 127035954683
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#63: 49
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#64: 1322
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#65: 272
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#66: 661
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#67: 7273
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#68: 6531031914842725
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#69: 510510
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#70: 8319823
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#71: 428570
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#72: 303963552391
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#73: 7295372
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#74: 402
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#75: 161667
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#76: 190569291
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#77: 71
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#78: 55374
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#79: 73162890
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#80: 40886
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#81: 427337
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#82: 260324
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#83: 425185
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#84: 101524
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#85: 2772
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#86: 1818
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#87: 1097343
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#88: 7587457
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#89: 743
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#90: 1217
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#91: 14234
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#92: 8581146
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#93: 1258
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#94: 518408346
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#95: 14316
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#96: 24702
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#97: 8739992577
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#98: 18769
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#99: 709
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#100: 756872327473
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#101: 37076114526
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#102: 228
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#103: 20313839404245
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#104: 329468
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#105: 73702
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#106: 21384
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#107: 259679
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#108: 180180
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#109: 38182
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#110: 9350130049860600
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#111: 612407567715
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#112: 1587000
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#113: 51161058134250
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#114: 16475640049
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#115: 168
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#116: 20492570929
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#117: 100808458960497
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#118: 44680
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#119: 248155780267521
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#120: 333082500
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#121: 2269
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#122: 1582
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#123: 21035
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#124: 21417
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#125: 2906969179
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#126: 18522
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#127: 18407904
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#128: 14516824220
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#129: 1000023
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#130: 149253
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#131: 173
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#132: 843296
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#133: 453647705
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#134: 18613426663617118
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#135: 4989
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#136: 2544559
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#137: 1120149658760
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#138: 1118049290473932
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#139: 10057761
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#140: 5673835352990
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#141: 878454337159
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#142: 1006193
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#143: 30758397
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#144: 354
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#145: 608720
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#146: 676333270
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#147: 846910284
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#148: 2129970655314432
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#149: 52852124
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#150: -271248680
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#151: 0.464399
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#152: 301
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#153: 17971254122360635
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#154: 479742450
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#155: 3857447
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#156: 21295121502550
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#157: 53490
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#158: 409511334375
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#159: 14489159
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#160: 16576
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#161: 20574308184277971
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#162: 3D58725572C62302
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#163: 343047
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#164: 378158756814587
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#165: 2868868
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#166: 7130034
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#167: 3916160068885
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#168: 59206
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#169: 178653872807
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#170: 9857164023
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#171: 142989277
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#172: 227485267000992000
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#173: 1572729
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#174: 209566
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#175: 1,13717420,8
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#176: 96818198400000
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#177: 129325
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#178: 126461847755
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#179: 986262
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#180: 285196020571078987
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#181: 83735848679360680
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#182: 399788195976
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#183: 48861552
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#184: 1725323624056
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