1. WANG Yanjin
  2. euler.py

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WANG Yanjin  committed 1acec9d

first commit, containing problems from 7th to 44th

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+#!/usr/bin/env pypy
+#Euler Project
+
+import time
+start = time.clock()
+
+
+def p7():
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1))))
+    n, i = 1, 2
+    while n < 10001:
+        i += 1
+        if isp(i):
+            n += 1
+    return i
+
+
+def p8():
+    a = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
+    rlist = []
+    for i in range(996):
+        b = [int(j) for j in a[i:i + 5]]
+        product = lambda x: x[0] * x[1] * x[2] * x[3] * x[4]
+        rlist.append(product(b))
+    return max(rlist)
+
+
+def p9():
+    for i in range(1, 1000):
+        for j in range(i + 1, 1000):
+            for k in range(j + 1, 1000):
+                if i * i + j * j == k * k and i + j + k == 1000:
+                    return i * j * k, i, j, k
+
+
+def p10():
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1))))
+    gen = (i for i in range(2, 2000000) if isp(i))
+    return sum(gen)
+
+
+def p11():
+    data = \
+    '08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\
+     49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\
+     81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\
+     52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\
+     22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\
+     24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\
+     32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\
+     67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\
+     24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\
+     21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\
+     78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\
+     16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\
+     86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\
+     19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\
+     04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\
+     88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\
+     04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\
+     20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\
+     20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\
+     01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48'
+    data = [int(i) for i in data.split()]
+    pick = lambda x, y: data[y * 20 + x]
+    seq = []
+    for i in range(20):
+        tseq1 = [pick(i, j) for j in range(20)]
+        tseq2 = [pick(j, i) for j in range(20)]
+        tseq3 = [pick(i + n, n) for n in range(25) if (i + n) < 20]
+        tseq4 = [pick(n, i + n) for n in range(25) if (i + n) < 20]
+        tseq5 = [pick(i + n, 19 - n) for n in range(25) \
+                if (19 - n) >= 0 and (i + n) < 20]
+        tseq6 = [pick(n, 19 - i - n) for n in range(25) \
+                if (19 - i - n) >= 0 and n < 20]
+        seq.append(tseq1)
+        seq.append(tseq2)
+        seq.append(tseq3)
+        seq.append(tseq4)
+        seq.append(tseq5)
+        seq.append(tseq6)
+
+    def max4(s):
+        if len(s) < 4:
+            return 0
+        rlist = []
+        for i in range(len(s) - 4 + 1):
+            ts = s[i:i + 4]
+            rlist.append(ts[0] * ts[1] * ts[2] * ts[3])
+        return max(rlist)
+
+    return max([max4(i) for i in seq])
+
+
+def p12():
+    import itertools
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1))))
+    product = lambda x: reduce(lambda y, z: y * z, x)
+
+    def primedivisors(n):
+        for i in range(2, n / 2 + 2):
+            t = n % i
+            if isp(i) and t == 0:
+                return [i] + (primedivisors(n / i))
+        return [n]
+
+    def divisors(n):
+        d = []
+        pd = primedivisors(n)
+        for i in range(1, len(pd)):
+            d.extend([product(j) for j in itertools.combinations(pd, i)])
+        return set(d)
+
+    n = 1
+    while 1:
+        tn = sum(range(n + 1))
+        if len(divisors(tn)) > 500 - 2:
+            return tn
+        n += 1
+
+
+def p13():
+    data = """
+    37107287533902102798797998220837590246510135740250
+    46376937677490009712648124896970078050417018260538
+    74324986199524741059474233309513058123726617309629
+    91942213363574161572522430563301811072406154908250
+    23067588207539346171171980310421047513778063246676
+    89261670696623633820136378418383684178734361726757
+    28112879812849979408065481931592621691275889832738
+    44274228917432520321923589422876796487670272189318
+    47451445736001306439091167216856844588711603153276
+    70386486105843025439939619828917593665686757934951
+    62176457141856560629502157223196586755079324193331
+    64906352462741904929101432445813822663347944758178
+    92575867718337217661963751590579239728245598838407
+    58203565325359399008402633568948830189458628227828
+    80181199384826282014278194139940567587151170094390
+    35398664372827112653829987240784473053190104293586
+    86515506006295864861532075273371959191420517255829
+    71693888707715466499115593487603532921714970056938
+    54370070576826684624621495650076471787294438377604
+    53282654108756828443191190634694037855217779295145
+    36123272525000296071075082563815656710885258350721
+    45876576172410976447339110607218265236877223636045
+    17423706905851860660448207621209813287860733969412
+    81142660418086830619328460811191061556940512689692
+    51934325451728388641918047049293215058642563049483
+    62467221648435076201727918039944693004732956340691
+    15732444386908125794514089057706229429197107928209
+    55037687525678773091862540744969844508330393682126
+    18336384825330154686196124348767681297534375946515
+    80386287592878490201521685554828717201219257766954
+    78182833757993103614740356856449095527097864797581
+    16726320100436897842553539920931837441497806860984
+    48403098129077791799088218795327364475675590848030
+    87086987551392711854517078544161852424320693150332
+    59959406895756536782107074926966537676326235447210
+    69793950679652694742597709739166693763042633987085
+    41052684708299085211399427365734116182760315001271
+    65378607361501080857009149939512557028198746004375
+    35829035317434717326932123578154982629742552737307
+    94953759765105305946966067683156574377167401875275
+    88902802571733229619176668713819931811048770190271
+    25267680276078003013678680992525463401061632866526
+    36270218540497705585629946580636237993140746255962
+    24074486908231174977792365466257246923322810917141
+    91430288197103288597806669760892938638285025333403
+    34413065578016127815921815005561868836468420090470
+    23053081172816430487623791969842487255036638784583
+    11487696932154902810424020138335124462181441773470
+    63783299490636259666498587618221225225512486764533
+    67720186971698544312419572409913959008952310058822
+    95548255300263520781532296796249481641953868218774
+    76085327132285723110424803456124867697064507995236
+    37774242535411291684276865538926205024910326572967
+    23701913275725675285653248258265463092207058596522
+    29798860272258331913126375147341994889534765745501
+    18495701454879288984856827726077713721403798879715
+    38298203783031473527721580348144513491373226651381
+    34829543829199918180278916522431027392251122869539
+    40957953066405232632538044100059654939159879593635
+    29746152185502371307642255121183693803580388584903
+    41698116222072977186158236678424689157993532961922
+    62467957194401269043877107275048102390895523597457
+    23189706772547915061505504953922979530901129967519
+    86188088225875314529584099251203829009407770775672
+    11306739708304724483816533873502340845647058077308
+    82959174767140363198008187129011875491310547126581
+    97623331044818386269515456334926366572897563400500
+    42846280183517070527831839425882145521227251250327
+    55121603546981200581762165212827652751691296897789
+    32238195734329339946437501907836945765883352399886
+    75506164965184775180738168837861091527357929701337
+    62177842752192623401942399639168044983993173312731
+    32924185707147349566916674687634660915035914677504
+    99518671430235219628894890102423325116913619626622
+    73267460800591547471830798392868535206946944540724
+    76841822524674417161514036427982273348055556214818
+    97142617910342598647204516893989422179826088076852
+    87783646182799346313767754307809363333018982642090
+    10848802521674670883215120185883543223812876952786
+    71329612474782464538636993009049310363619763878039
+    62184073572399794223406235393808339651327408011116
+    66627891981488087797941876876144230030984490851411
+    60661826293682836764744779239180335110989069790714
+    85786944089552990653640447425576083659976645795096
+    66024396409905389607120198219976047599490197230297
+    64913982680032973156037120041377903785566085089252
+    16730939319872750275468906903707539413042652315011
+    94809377245048795150954100921645863754710598436791
+    78639167021187492431995700641917969777599028300699
+    15368713711936614952811305876380278410754449733078
+    40789923115535562561142322423255033685442488917353
+    44889911501440648020369068063960672322193204149535
+    41503128880339536053299340368006977710650566631954
+    81234880673210146739058568557934581403627822703280
+    82616570773948327592232845941706525094512325230608
+    22918802058777319719839450180888072429661980811197
+    77158542502016545090413245809786882778948721859617
+    72107838435069186155435662884062257473692284509516
+    20849603980134001723930671666823555245252804609722
+    53503534226472524250874054075591789781264330331690
+    """
+    data = [int(i) for i in data.split()]
+    s = sum(data)
+    return str(s)[:10]
+
+
+def p14_():
+    even = lambda x: x // 2
+    odd = lambda x: x * 3 + 1
+    collatz_next = lambda x: None if x == 1 else (odd(x) if x % 2 else even(x))
+
+    def collatz(n, cl=[]):
+        if not cl:
+            cl.append([2, 1])
+        if n == 1:
+            return [1]
+
+        remainder = n % 2
+        if remainder == 0:
+            for i in cl:
+                if n in i:
+                    index = i.index(n)
+                    n_list = [n] + i[index:]
+            cl.append(n_list)
+            return n_list
+
+        n_list = []
+        while 1:
+            if len(n_list) > 0 and n > n_list[0]:
+                n_list.append(n)
+                n = collatz_next(n)
+                continue
+            for i, j in enumerate(cl):
+                if n in j:
+                    index = j.index(n)
+                    if n_list == []:  # n_list is contained in existing list
+                        return j[index:]
+                    n_list += j[index:]
+                    if index == 0:  # n_list overwrite an existing list
+                        cl[i] = n_list
+                    else:  # n_list is a new independent list
+                        cl.append(n_list)
+                    return n_list
+
+            n_list.append(n)
+            n = collatz_next(n)
+
+    i = 3
+    cl = []
+    ml = 0
+    while 1:
+        l = len(collatz(i, cl))
+        if l > 200:
+            break
+        if l > ml:
+            ml = l
+            print("{0} @ {1}".format(ml, i))
+        i += 1
+    print(cl, len(cl))
+    return i
+
+
+def p14():
+    even = lambda x: x // 2
+    odd = lambda x: x * 3 + 1
+    collatz_next = lambda x: None if x == 1 else (odd(x) if x % 2 else even(x))
+
+    def collatz(n, cl=[]):
+        if not cl:
+            cl.extend([0, 1, 2])
+        if n < 2:
+            return n
+
+        tn = 0
+        remainder = n % 2
+        if remainder == 0:
+            tn = n // 2
+            nn = cl[tn] + 1
+            cl.append(nn)
+            return nn
+        else:
+            nn = 1
+            tn = collatz_next(n)
+            while tn >= n:
+                nn += 1
+                tn = collatz_next(tn)
+            nn += cl[tn]
+            cl.append(nn)
+            return nn
+    i = 3
+    ml = 0
+    while i < 1000 * 1000:
+        l = collatz(i)
+        if l > ml:
+            ml = l
+            print("{0} @ {1}".format(ml, i))
+        i += 1
+
+
+def p15():
+    def perm(n):
+        return n * perm(n - 1) if n > 1 else 1
+
+    def ways_count(n):
+        return perm(2 * n) / perm(n) / perm(n)
+
+    n = 20
+    print(ways_count(n), n)
+
+
+def p16():
+    n = 2 ** 1000
+    print(sum((int(i) for i in str(n))))
+
+
+def p17():
+    names = {1: "one", 2: "two", 3: "three", 4: "four", 5: "five",\
+             6: "six", 7: "seven", 8: "eight", 9: "nine", 10: "ten",\
+             11: "eleven", 12: "twelve", 13: "thirteen", 14: "fourteen",\
+             15: "fifteen", 16: "sixteen", 17: "seventeen", 18: "eighteen",\
+             19: "nineteen", 20: "twenty", 30: "thirty", 40: "forty",\
+             50: "fifty", 60: "sixty", 70: "seventy", 80: "eighty",\
+             90: "ninety"}
+
+    def get_name(n):
+        assert 0 < n < 1000
+
+        hs = n // 100
+        ts = (n % 100) // 10
+        ons = n % 10
+
+        name = ''
+        if hs:
+            name += names[hs] + ' hundred'
+        if (ts or ons) and hs:
+            name += ' and'
+        if ts or ons:
+            if ts >= 2:
+                name += ' ' + names[ts * 10]
+                if ons:
+                    name += '-' + names[ons]
+            else:
+                name += ' ' + names[ts * 10 + ons]
+        return name
+
+    l = 0
+    for i in range(1, 1000):
+        name = get_name(i)
+        name = name.replace(' ', '')
+        name = name.replace('-', '')
+        l += len(name)
+    print(l + 11)
+
+
+def p18():
+    text = """         75
+                     95 64
+                   17 47 82
+                  18 35 87 10
+                20 04 82 47 65
+              19 01 23 75 03 34
+             88 02 77 73 07 63 67
+            99 65 04 28 06 16 70 92
+          41 41 26 56 83 40 80 70 33
+        41 48 72 33 47 32 37 16 94 29
+       53 71 44 65 25 43 91 52 97 51 14
+     70 11 33 28 77 73 17 78 39 68 17 57
+    91 71 52 38 17 14 91 43 58 50 27 29 48
+   63 66 04 68 89 53 67 30 73 16 69 87 40 31
+  04 62 98 27 23 09 70 98 73 93 38 53 60 04 23"""
+    tri = []
+    for i in text.split('\n'):
+        tri.append([int(j) for j in i.split()])
+    dev_m = [max(i) - min(i) for i in tri]
+    m = [sum(dev_m[i + 1:]) for i in range(len(dev_m))]
+    print(m)
+
+    def f(n):
+        if n == 1:
+            yield [0, 0]
+            yield [0, 1]
+        else:
+            _max = 0
+            for i in f(n - 1):
+                for j in [0, 1]:
+                    _i = i + [j]
+                    cur = 0
+                    ns = []
+                    for s, t in enumerate(_i):
+                        cur += t
+                        ns.append(tri[s][cur])
+                    _sum = sum(ns)
+                    if _max > _sum and (_max - _sum > m[n]):
+                        pass
+                    elif _sum > _max:
+                        _max = _sum
+                        print("_max = " + str(_max))
+                        yield _i
+                    else:
+                        yield _i
+
+    n = 0
+    for i in f(14):
+        n += 1
+    print(n)
+
+
+def p19():
+    import datetime
+    d = datetime.date(1901, 1, 1)
+    day = datetime.timedelta(days=1)
+    week = datetime.timedelta(days=7)
+    while d.weekday() != 6:
+        d += day
+    n = 0
+    eday = datetime.date(2000, 12, 31)
+    while d < eday:
+        if d.day == 1:
+            n += 1
+        d += week
+    print(n)
+
+
+def p20():
+    fab = lambda n: n * fab(n - 1) if n > 1 else 1
+    f100 = fab(100)
+    print(sum([int(i) for i in str(f100)]))
+
+
+def p21():
+    pd = lambda n: [i for i in range(1, n) if n % i == 0]
+
+    def isamicable(n):
+        s = sum(pd(n))
+        if s != n and sum(pd(s)) == n:
+            return True
+
+    n = 0
+    for i in range(2, 10000):
+        if isamicable(i):
+            n += i
+
+    print(n)
+
+
+def p22():
+    with open('names.txt') as f:
+        names = f.read()
+    names = names.split(',')
+    names = [eval(i) for i in names]
+    names = sorted(names)
+    v = lambda c: ord(c) - 64
+    n = 0
+    for i, k in enumerate(names):
+        m = 0
+        for j in k:
+            m += v(j)
+        n += (i + 1) * m
+    print(n)
+
+
+def p23():
+    import itertools
+    n = 28124
+    pd = lambda n: [i for i in range(1, n) if n % i == 0]
+    abundant_numbers = [i for i in range(n) if sum(pd(i)) > i]
+    t_numbers = [s for s in (sum(i) for i in itertools.product(abundant_numbers, abundant_numbers)) if s < n]
+    print(sum(range(n)) - sum(set(t_numbers)))
+
+
+def p24():
+    import itertools
+    a = list(itertools.permutations(list(range(10))))
+    a.sort()
+    print(a[999999])
+
+
+def p25():
+
+    def fib():
+        n1 = 0
+        n2 = 1
+        while 1:
+            yield n2
+            n1, n2 = n2, n1 + n2
+
+    n = 0
+    for i in fib():
+        n += 1
+        if len(str(i)) == 1000:
+            print(n)
+            break
+
+
+def p26():
+
+    def d(n1, n2):
+        r1, r2 = [], []
+        while 1:
+            yield n1
+            if n1 < n2:
+                n1 *= 10
+            else:
+                if n1 % n2 == 0:
+                    yield None
+                    break
+                else:
+                    n1 = n1 % n2 * 10
+
+    def cn(n):
+        tlist = []
+        for i in d(1, n):
+            if i and i in tlist:
+                return len(tlist) - tlist.index(i)
+            elif i:
+                tlist.append(i)
+            else:
+                return 0
+
+    cn_dict = {cn(i): i for i in range(1, 1000)}
+    max_cn_dict = max(cn_dict)
+    print(cn_dict[max_cn_dict])
+
+
+def p27():
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1))))
+
+    def prime_count(a, b):
+        for i in range(81):
+            n = i * i + a * i + b
+            if n < 0 or not isp(n):
+                return i
+
+    print(prime_count(-79, 1601))
+    import itertools
+    r = range(-999, 1000)
+    ma, mb, mr = 0, 0, 0
+    for i in itertools.product(r, r):
+        n = prime_count(*i)
+        if n > mr:
+            mr = n
+            ma, mb = i
+
+    print(ma, mb, mr, ma * mb)
+
+
+def p28():
+
+    def table(n):
+        assert n % 2 == 1
+        if n == 1:
+            return [[1]]
+        else:
+            import copy
+            n0 = [0] * n
+            tb = [copy.deepcopy(n0) for i in range(n)]
+            for i, j in enumerate(table(n - 2)):
+                tb[1 + i][1: -1] = j
+
+            m = (n - 2) ** 2
+            for i in range(1, n - 1):
+                tb[i][-1] = m + i
+            tb[-1] = list(reversed(list(range(m + n - 1, m + 2 * n - 1))))
+            for i in range(1, n - 1):
+                tb[n - i - 1][0] = m + 2 * n - 2 + i
+            tb[0] = list(range(m + 3 * n - 3, m + 4 * n - 3))
+
+            return tb
+
+    n = 1001
+    tb = table(n)
+    s = 0
+    for i in range(n):
+        s += tb[i][i] + tb[n - 1 - i][i]
+    s -= 1
+    print(s)
+
+
+def p29():
+    import itertools
+    r = range(2, 101)
+    tlist = []
+    for a, b in itertools.product(r, r):
+        tlist.append(a ** b)
+    print(len(set(tlist)))
+
+
+def p30():
+
+    def fifth():
+        for i in range(10, 1000 * 1000):
+            ns = (int(j) for j in str(i))
+            s = sum((k ** 5 for k in ns))
+            if s == i:
+                yield i
+
+    print(sum((i for i in fifth())))
+
+
+def p31():
+
+    def combs(n, tl, el=[]):
+        if len(tl) > 2:
+            cs = sorted(combs(n, tl[1:], el), key=lambda s: s[-1])
+            for i in range(n / tl[0] + 1):
+                for j in cs:
+                    _nsum = i + j[-1]
+                    if _nsum <= n / tl[0]:
+                        _sum = i * tl[0] + j[-2]
+                        if _sum < n:
+                            k = [i] + j[:-2] + [_sum, _nsum]
+                            yield k
+                        elif _sum == n:
+                            k = [i] + j[:-2] + [_sum, _nsum]
+                            el.append(k)
+                    else:
+                        break
+        else:
+            for i in range(n / tl[0] + 1):
+                for j in range(n / tl[1] + 1):
+                    _nsum = i + j
+                    _sum = i * tl[0] + j * tl[1]
+                    if _nsum <= n / tl[0]:
+                        if _sum < n:
+                            k = [i, j, _sum, _nsum]
+                            yield k
+                        elif _sum == n:
+                            k = [i, j, _sum, _nsum]
+                            el.append(k)
+
+    n = 0
+    el = []
+    for n_p1, n_p2, n_p5, n_p10, n_p20, n_p50, n_p100, n_p200, _s, _ns in combs(200, [1, 2, 5, 10, 20, 50, 100, 200], el):
+        if n_p1 + 2 * n_p2 + 5 * n_p5 + 10 * n_p10 + 20 * n_p20 + 50 * n_p50 + 100 * n_p100 + 200 * n_p200 == 200:
+            n += 1
+            print(n)
+    print(len(el) + n)
+
+
+def p32():
+    r = []
+    for i in range(10, 100):
+        si = str(i)
+        if '0' not in si and len(set(si)) == 2:
+            for j in range(100, 1000):
+                sj = str(j)
+                if '0' not in sj and len(set(sj)) == 3:
+                    k = i * j
+                    if k < 10000:
+                        s = si + sj + str(k)
+                        if '0' not in s and len(set(s)) == 9:
+                            print(i, j, k)
+                            r.append(k)
+    for i in range(1, 10):
+        for j in range(1000, 10000):
+            sj = str(j)
+            if '0' not in sj and len(set(sj)) == 4:
+                k = i * j
+                if k < 10000:
+                    s = str(i) + sj + str(k)
+                    if '0' not in s and len(set(s)) == 9:
+                        print(i, j, k)
+                        r.append(k)
+    sr = set(r)
+    print(sum(sr))
+
+
+def p33():
+
+    def gcd(a, b):
+        a, b = sorted([a, b])
+        r = b % a
+        if r:
+            return gcd(r, a)
+        else:
+            return a
+
+    def reduce_fraction(numerator, denominator):
+        _gcd = gcd(numerator, denominator)
+        return numerator / _gcd, denominator / _gcd
+
+    r = [1, 1]
+    for i in range(10, 100):
+        for j in range(i + 1, 100):
+            if i % 10 == j // 10:
+                frac = (i // 10, j % 10)
+                if 0 in frac:
+                    continue
+                if reduce_fraction(i, j) == reduce_fraction(*frac):
+                    r[0] *= i
+                    r[1] *= j
+    print(reduce_fraction(*r))
+
+
+def p34():
+
+    import math
+    d10 = {str(i): math.factorial(i) for i in range(10)}
+
+    r = []
+    for i in range(10, 3 * 1000 * 1000):
+        fac = (d10[j] for j in str(i))
+        if i == sum(fac):
+            r.append(i)
+    print(r, sum(r))
+
+
+def p35():
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1))))
+
+    def circular(n):
+        sn = str(n)
+        l = len(sn)
+        sn2 = sn * 2
+        for i in range(l):
+            yield int(sn2[i: i + l])
+
+    n = 0
+    for i in range(2, 1000 * 1000):
+        if not isp(i):
+            continue
+        if i < 10:
+            print(i)
+            n += 1
+        else:
+            si = str(i)
+            sp = [int(j) for j in si]
+            if all(j % 2 != 0 and j != 5 for j in sp) and sum(sp) % 3 != 0:
+                if all((isp(x) for x in circular(i))):
+                    print(i)
+                    n += 1
+
+    print(n)
+
+
+def p36():
+
+    def ispld(s):
+        return all(i == j for i, j in zip(s, reversed(s)))
+
+    n = 0
+    for i in range(1000 * 1000):
+        di = str(i)
+        bi = bin(i)[2:]
+        if ispld(di) and ispld(bi):
+            print(i)
+            n += i
+
+    print(n)
+
+
+def p37():
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1)))) if x > 1 else False
+
+    def combs(n, s=[], sc=[]):
+        sc = [(i, s.count(i)) for i in set(s)] if s else sc
+        if n < 1 or sum(i[1] for i in sc) < n:
+            yield
+            raise StopIteration
+        if len(sc) > 1:
+            i, c = sc[0]
+            c = n if c > n else c
+            for j in range(c + 1):
+                for k in combs(n - j, sc=sc[1:]):
+                    if j or k:
+                        k = () if not k else k
+                        yield (i,) * j + k
+        else:
+            yield (sc[0][0],) * n
+
+    def ins(c1, c2):
+        if c1 == 0:
+            yield (c2,)
+            raise StopIteration
+        for i in range(c2 + 1):
+            for j in ins(c1 - 1, c2 - i):
+                yield (i,) + j
+
+    def perm2(s1, c1, i2, c2, insl):
+        for i in insl:
+            k = 0
+            a = []
+            for k in range(len(s1)):
+                a.extend([i2] * i[k])
+                a.append(s1[k])
+            a.extend([i2] * i[k + 1])
+            yield tuple(a)
+
+    def perms(n=[], s=[], sc=[]):
+        sc = [(i, s.count(i)) for i in set(s)] if s else (sc or [(i, 1) for i in range(n)])
+        sc = sorted(sc, key=lambda x: x[1], reverse=True)
+        if len(sc) == 1:
+            yield (sc[0][0],) * sc[0][1]
+        elif len(sc) == 2:
+            insl = [i for i in ins(sc[0][1], sc[1][1])]
+            for i in perm2([sc[0][0]] * sc[0][1], sc[0][1], sc[1][0], sc[1][1], insl):
+                yield i
+        else:
+            sc1 = sc[1:]
+            for i in perms(sc=sc1):
+                c1 = sum(j[1] for j in sc1)
+                insl = [j for j in ins(c1, sc[0][1])]
+                for j in perm2(i, c1, sc[0][0], sc[0][1], insl):
+                    yield j
+
+    dcl = {1:[(1,)]}
+    dcr = {1:[(1,)]}
+    def ng(n):
+        a = [1, 2, 3, 5, 7, 9] * n
+        for i in combs(n, a):
+            for j in perms(s=i):
+                yf = 1
+                for k in dcl:
+                    t = j[:k]
+                    if t in dcl[k]:
+                        yf = 0
+                        break
+                if yf == 1:
+                    for k in dcr:
+                        t = j[n - k:]
+                        if t in dcr[k]:
+                            yf = 0
+                            break
+                if yf:
+                    yield j
+
+    def rml(j):
+        l = len(j)
+        for i in range(l):
+            yield j[i:]
+
+    def rmr(j):
+        l = len(j)
+        for i in range(l):
+            yield j[:l - i]
+
+    s = 0
+    n = 0
+    i = 2
+    set_n = set()
+    while n < 11 and i < 14:
+        print('i = %s' % i)
+        for j in ng(i):
+            if not all(isp(int(''.join(str(k_) for k_ in k))) for k in rml(j)):
+                l = len(j)
+                if not l in dcr:
+                    dcr[l] = [j]
+                else:
+                    dcr[l].append(j)
+                continue
+            if all(isp(int(''.join(str(k_) for k_ in k))) for k in rmr(j)):
+                set_n.add(j)
+                n += 1
+                _s = int(''.join(str(k) for k in j))
+                s += _s
+                print(_s)
+                if n == 11:
+                    break
+            else:
+                l = len(j)
+                if not l in dcl:
+                    dcl[l] = [j]
+                else:
+                    dcl[l].append(j)
+        i += 1
+    print("Sum: ", s)
+
+
+def p38():
+    import itertools
+    nums = tuple(reversed(range(1, 10)))
+    _max = 0
+    for i in range(9, 0, -1):
+        print(i)
+        for j in itertools.permutations(nums, i):
+            sj = [str(x) for x in j]
+            n = int(''.join(sj))
+            list_n = []
+            for _i in range(1, 10):
+                _n = n * _i
+                _sn = [int(x) for x in str(_n)]
+                if 0 in _sn or len(set(_sn)) < len(_sn) or any(x in list_n for x in _sn):
+                    break
+                else:
+                    for _j in _sn:
+                        list_n.append(_j)
+                    if len(list_n) == 9:
+                        if _i > 1:
+                            print(n)
+                            k = int(''.join(str(x) for x in list_n))
+                            if k > _max:
+                                print('New max', k)
+                                _max = k
+                        else:
+                            break
+
+
+def p39():
+    import math
+    _max = 0
+    for i in range(5, 1001):
+        a = []
+        onethird = int(math.ceil(i / 3.0))
+        half = int(math.ceil(i / 2.0))
+        for j in range(onethird, half + 1):
+            for x in range(1, j):
+                y = i - j - x
+                if j * j == x * x + y * y:
+                    if set([x, y, j]) not in a:
+                        a.append(set([x, y, j]))
+        if len(a) > _max:
+            _max = len(a)
+            print(i, a)
+        elif len(a) == _max > 0:
+            print("Equal", _max, "at", i)
+
+
+def p40():
+    from functools import reduce
+    s = []
+    i = 1
+    while len(s) < 1000 * 1000:
+        _s = [int(k) for k in str(i)]
+        s.extend(_s)
+        i += 1
+    ns = [s[k - 1] for k in (1, 10, 100, 1000, 10000, 100000, 1000000)]
+    print(ns)
+    print(reduce(lambda x, y: x * y, ns))
+
+
+def p41():
+    import itertools
+    isp = lambda x: all((x % j != 0 for j in range(2, int(x ** 0.5 + 1)))) if x > 1 else False
+
+    for i in range(9, 0, -1):
+        print('i = ', i)
+        if sum(range(i + 1)) % 3 == 0:
+            continue
+        for sn in itertools.permutations(range(i, 0, -1)):
+            n = int(''.join(str(k) for k in sn))
+            if isp(n):
+                print(n)
+                return n
+
+
+def p42():
+    from functools import reduce
+    tn = lambda n: n * (n + 1) // 2
+
+    ltn = [0]
+    with open('words.txt') as f:
+        c = f.read()
+    c = eval(c)
+    n = 0
+    for i in c:
+        j = reduce(lambda x, y: x + y, (ord(k) - 64 for k in i))
+        while ltn[-1] < j:
+            _len = len(ltn)
+            ltn.append(tn(_len))
+        if j in ltn:
+            print(j)
+            n += 1
+    print('n: ', n)
+
+
+def p43():
+    import itertools
+    ps = [2, 3, 5, 7, 11, 13, 17]
+    ns = tuple(range(10))
+    _sum = 0
+    for i in itertools.permutations(ns):
+        if i[0] == 0:
+            continue
+        if all((i[j + 1] * 100 + i[j + 2] * 10 + i[j + 3]) % ps[j] == 0 for j in range(7)):
+            n = int(''.join(str(j) for j in i))
+            print(n)
+            _sum += n
+    print('Sum: ', _sum)
+
+
+p43()
+print("Seconds:", time.clock() - start)

File names.txt

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File words.txt

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