[メモ] Project Euler を Python で (Problem 1 ～ 22)

取り急ぎ忘れないようにメモとして残します。


```python
#probrem 1
sum = 0
for i in range(1000):
    if i % 3 == 0 or i % 5 == 0:
        sum += i
print(sum)
```

    233168



```python
# problem 2
num1 = 0
num2 = 1

MAX = 4000000
sum = 0

while(True):
    num_tmp = num2
    num2 += num1
    num1 = num_tmp
    if num2 > MAX:
        break
    if num2 % 2 == 0:
        sum += num2
print(sum)
```

    4613732



```python
# problem 3
# row method
# http://sucrose.hatenablog.com/entry/2014/10/10/235805

import math
import collections
num = 600851475143

def trial_division_sqrt(n):
#     prime_count = collections.Counter()
    prime_count = []
    for i in range(2, int(math.sqrt(n)) + 2):
        while n % i == 0:
            n /= i
#             prime_count[i] += 1
            prime_count.append(i)
    if n > 1:
#         prime_count[n] += 1
        prime_count.append(i)
    return prime_count

ans = trial_division_sqrt(num)
print(ans)
```

    [71, 839, 1471, 6857]



```python
# problem 4
max_num = 1000
max_ans = 0


for i in range(100, max_num):
    for j in range(i, max_num):
        num = i * j
        num_str = str(num)
        # str[::-1] で反転。str[i:j:k] は i to j step by k
        if num_str == num_str[::-1] and num > max_ans:
            max_ans = num
print(max_ans)
```

    906609



```python
# problem 5
# 1 から 20 までのすべての数の最小公倍数
# 1 から 10 までの場合は 2520
max_num = 20
ans = 1

# 最大公約数 を求める（ユークリッドの互除法）
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

# 最小公倍数 は a * b / gcd(a,b)
def lcm(a, b):
    return a * b // gcd(a, b)

# 指定の数まで、すべての最小公倍数を求める
for i in range(1, max_num + 1):
    ans = lcm(i, ans)

print(ans)
```

    232792560



```python
# problem 6
max_num = 100
sum = 0
for i in range(max_num):
    for j in range(i, max_num):
        if i != j:
            sum += (i + 1) * (j + 1)
sum *= 2
print(sum)
```

    25164150



```python
# problem 7
import math
indx_num = 10001
count = 0
num_tmp = 1
ans_prime = 0

# 素数判定
def is_prime(q):
    if q == 2: return True
    # 2 未満か 偶数ならFalse
    if q < 2 or q & 1 == 0: return False
    num_sqrt = int(math.sqrt(q))
    for i in range(3, num_sqrt + 1):
        if q % i == 0:
            # 素数ではない
            return False
    # 素数である
    return True

while(True):
    if is_prime(num_tmp):
        ans_prime = num_tmp
        count += 1
    if count > indx_num - 1:
        break
    num_tmp += 1
ans_prime
```




    104743




```python
# problem 8
max_num = 1
digit = 13
num_str = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'

for i in range(len(num_str) - digit):
    tmp_num = 1
    for j in range(digit):
        tmp_num *= int(num_str[i + j])
    if tmp_num > max_num:
        max_num = tmp_num
max_num
```




    23514624000




```python
# problem 9
obj_num = 1000 # 1000^2 / 2
max_num = 1000
ans_num = 0
# ごり押しサーチ
for i in range(1, max_num + 1):
    for j in range(1, max_num + 1 - i):
        k = max_num - i -j
        if (i**2 + j**2) == k**2:
            ans_num = i * j * k
ans_num
```




    31875000




```python
# problem 10
max_num = 2000000
ans_sum = 0

def is_prime(q):
    if q == 2: return True
    # 2 未満か 偶数ならFalse
    if q < 2 or q & 1 == 0: return False
    num_sqrt = int(math.sqrt(q))
    for i in range(3, num_sqrt + 1):
        if q % i == 0:
            # 素数ではない
            return False
    # 素数である
    return True

for i in range(max_num):
    if is_prime(i):
        ans_sum += i
ans_sum
```




    142913828922




```python
# problem 11
grid_size = 20 * 20
max_nums = [0 for i in range(4)]
grid = '\
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 \
'
max_num = 0
# grid 中の n　番目の数字を得る n は 0～399
def get_num(n):
    return int(grid[3*n:3*n+2])

# たて
for i in range(grid_size - 60):
    tmp_num = get_num(i) * get_num(i+20) * get_num(i+40) * get_num(i+60)
    if tmp_num > max_num:
        for j in range(4):
            max_nums[j] = get_num(i + j * 20)
        max_num = tmp_num

# 横。右端ではできないので注意
for i in range(grid_size - 2):
    if i % 20 > 16:
        # 右端に近いときはスキップ
        continue
    tmp_num = get_num(i) * get_num(i+1) * get_num(i+2) * get_num(i+3)
    if tmp_num > max_num:
        for j in range(4):
            max_nums[j] = get_num(i + j)
        max_num = tmp_num

# 右下斜め
for i in range(grid_size - 63):
    if i % 20 > 16:
        # 右端に近いときはスキップ
        continue
    tmp_num = get_num(i) * get_num(i+21) * get_num(i+42) * get_num(i+63)
    if tmp_num > max_num:
        for j in range(4):
            max_nums[j] = get_num(i + j * 21)
        max_num = tmp_num

# 左下斜め
for i in range(grid_size - 63):
    if i % 20 < 3:
        # 左端に近いときはスキップ
        continue
    tmp_num = get_num(i) * get_num(i+19) * get_num(i+38) * get_num(i+57)
    if tmp_num > max_num:
        for j in range(4):
            max_nums[j] = get_num(i + j * 19)
        max_num = tmp_num

print(max_num)
print(max_nums)
```

    70600674
    [89, 94, 97, 87]



```python
# problem 12
import collections

# 数字を素因数分解する
def trial_division_sqrt(n):
    prime_count = collections.Counter()
    for i in range(2, int(math.sqrt(n)) + 2):
        while n % i == 0:
            n /= i
            prime_count[i] += 1
    if n > 1:
        prime_count[int(n)] += 1
    return prime_count

# 約数の個数を求める
def count_divisor(num):
    ans_count = 1
    count_one = 0
    # 素因数分解して各素数の個数のリストを求める
    prime_count = trial_division_sqrt(num)
    
    # 各リスト内の個数をカウント
    for v in prime_count.values():
        if v == 1:
            count_one += 1
        else:
            # 同じ素数が複数個含まれている場合
            ans_count *= v + 1
    return ans_count * pow(2, count_one)

ans_num = 0
count = 0
divisors = 500

while(True):
    count += 1
    ans_num += count
    if count_divisor(ans_num) > divisors:
        break
ans_num
```




    76576500




```python
# problem 13
numbers = '''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'''

numbers_list = numbers.split("\n")
ans_sum = 0
for number_str in numbers_list:
    ans_sum += int(number_str)
ans_sum_str = str(ans_sum)
ans_sum_str[0:10]
```




    '5537376230'




```python
# problem 14
MAX_NUM =  1000000
ans_dict = {1:1}
(max_i, max_length) = (1, 1)

def next(n):
    if n % 2:
        return n * 3 + 1
    else:
        return n / 2

def calc_collats_seq(n1):
    # ある数が与えられたら数を求める
    n2 = next(n1)
    if not n2 in ans_dict:
        ans_dict[n2] = calc_collats_seq(n2)
    ans_dict[n1] = ans_dict[n2] + 1
    return ans_dict[n1]

for i in range(2, 10**6):
    if not i in ans_dict:
        ans_dict[i] = calc_collats_seq(i)
    if ans_dict[i] > max_length:
        (max_i, max_length) = (i, ans_dict[i])
print((max_i, max_length))
```

    (837799, 525)



```python
# problem 15
# 階乗計算
def calc_fact(n):
    if n == 1:
        return 1
    else:
        return n * calc_fact(n - 1)

print(calc_fact(40) // (calc_fact(20) * calc_fact(20)))

# ライブラリ使う
import math
print(math.factorial(40)//(math.factorial(20) * math.factorial(20)))
```

    137846528820
    137846528820



```python
# problem 16
num_str = str(pow(2, 10**3))
sum = 0
for i in num_str:
    sum += int(i)
print(sum)
```

    1366



```python
# problem 17
# 下二けたについて
num_dict = {
    0:'',
    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'
    }

ans = 0 #  length
ans += len('onethousand')

for i in range(1000):
    # 3 桁目の話
    if i > 99:
        ans += len(num_dict[i // 100])
        ans += len('hundred')
        if i % 100 > 0:
            ans += len('and')
    # 2 桁目の話
    tmp_i = i % 100
    if tmp_i in num_dict:
        ans += len(num_dict[tmp_i])
    else:
        ans += len(num_dict[(tmp_i // 10) * 10])
        ans += len(num_dict[tmp_i % 10])
ans
```




    21124




```python
# problem 18
# 方針
# 下から積み上げる。下から最大値となるルートを保存していって上にもっていく

triangle = '''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'''

nums = triangle.split('\n')
nums = [line.split(' ') for line in nums]

# 各地点での、最大となるルートを選んだ際の合計値を格納する
max_piramid = [[0 for j in range(len(i))] for i in nums]

# 逆順に検索していく
for i in reversed(range(len(nums))):
    if i == len(nums) - 1:
        # 一番下の層はそのまま代入する
        max_piramid[i] = [int(num) for num in nums[i]]
    else:
        # 左下の値と、右下の値を比べて、大きい方を加える
        for j in range(len(nums[i])):
            tmp_max = 0
            if max_piramid[i+1][j] > max_piramid[i+1][j+1]:
                tmp_max = max_piramid[i+1][j]
            else:
                tmp_max = max_piramid[i+1][j+1]
            max_piramid[i][j] = int(nums[i][j]) + tmp_max
max_piramid
```




    [[1074],
     [995, 999],
     [818, 900, 935],
     [704, 801, 853, 792],
     [686, 640, 766, 731, 782],
     [666, 614, 636, 684, 660, 717],
     [647, 501, 613, 609, 533, 657, 683],
     [559, 499, 479, 536, 514, 526, 594, 616],
     [460, 434, 419, 475, 508, 470, 510, 524, 487],
     [419, 365, 393, 387, 419, 425, 430, 376, 454, 322],
     [378, 317, 231, 321, 354, 372, 393, 354, 360, 293, 247],
     [325, 246, 187, 178, 256, 329, 273, 302, 263, 242, 193, 233],
     [255, 235, 154, 150, 140, 179, 256, 209, 224, 172, 174, 176, 148],
     [125, 164, 102, 95, 112, 123, 165, 128, 166, 109, 122, 147, 100, 54],
     [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]]




```python
# problem 22
# [chr(i) for i in range(ord('a'), ord('z')+1)]
# alphabets = [chr(i) for i in range(97, 97+26)]

# [chr(i) for i in range(ord('A'), ord('Z')+1)]
alphabets = [chr(i) for i in range(65, 65+26)]
indx = [i + 1 for i in range(len(alphabets))]
alphabets_score = dict(zip(alphabets, indx))
alphabets_score['"'] = 0  #  各名前の両端についているのは無視

# [chr(i) for i in range(ord('ぁ'), ord('ん')+1)]
hiragana = [chr(i) for i in range(12353, 12436)]

# というかstring で定義されているものもある
# import string
# help(string) で確認できる

# file read
f = open('p022_names.txt', 'r')
str_names = f.read()
f.close()
names = sorted(str_names.split(","))


# calc name score
def name_score(name):
    ret_score = 0
    for i in name:
        ret_score += alphabets_score[i]
    return ret_score

# sum scores
ans_score = 0
for i in range(len(names)):
    ans_score += (i + 1) * name_score(names[i])
ans_score
```




    871198282




```python
# problem 22
import numpy as np
# 問題文は 28123 だが、MathWorld によると 20161 より大きい数は表せるそう
# MAX=28124
MAX=20162



def divisors_sum(num):
    ret_list = []
    ret_list.append(1)
    for i in range(2, num//2 + 1):
        if num % i == 0:
            ret_list.append(i)
    return np.array(ret_list).sum()

# 過剰数のリストを作る
abundant_list = []
for i in range(2, MAX):
    if i < divisors_sum(i):
        abundant_list.append(i)

# 2 つの数の和を
isnot_sum_of_two_abundant = [True for i in range(MAX)]
for num1 in abundant_list:
    for num2 in abundant_list:
        if (num1 + num2) < MAX:
            isnot_sum_of_two_abundant[num1 + num2] = False
ans_sum = 0
for i in range(len(isnot_sum_of_two_abundant)):
    if isnot_sum_of_two_abundant[i]:
        ans_sum += i
ans_sum
```




    4179871




```python
# problem 24
from math import factorial

def lexi(chars, nth):
    if len(chars) == 0: return ""
    
    l = len(chars)
    f = factorial(l - 1)
    
    chars2 = chars[:]
    c = chars2.pop( nth // f)
    
    return str(c) + lexi(chars2, nth % f)

lexi([str(i) for i in range(10)], 1000000-1)
```




    '2783915460'




```python
# problem 25
digits = 1000
count = 1
num1 = 0
num2 = 1
while(True):
    num_tmp = num2
    num2 += num1
    num1 = num_tmp
    count += 1
    if len(str(num2)) == digits: break
count
```




    4782




```python
# problem 27
# http://qiita.com/hiroshi75/items/829707cac90eea2a7d6a

# n^2 + a*n * b が素数
# n は 0 から始めて1ずつ増やす
# n = 0 でも素数 -> b は素数
# n = 1 でも素数 -> a + b + 1 が素数 -> a + 1 は偶数 -> a は奇数

from math import sqrt

def is_prime(num):
    if num <= 0: return False
    tmp_max = int(math.sqrt(num)) + 1
    for i in range(2, tmp_max):
        if num % i == 0:
            return False
    return True

# a, b を与えて、いくつ素数を生成できるかを返す
def count_gen_prime(a, b):
    ret_count = 0
    i = 0
    while(True):
        if is_prime(i**2 + a*i + b):
            ret_count += 1
        else:
            break
        i += 1
    return ret_count
    

max_pair = (0, 0)
max_count = 0
search_range = range(-1000, 1001)
for a in search_range:
    for b in search_range:
        count_tmp = count_gen_prime(a, b)
        if count_tmp > max_count:
            max_count = count_tmp
            max_pair = (a, b)
print(max_pair)
print(max_pair[0] * max_pair[1])
```

    (-61, 971)
    -59231



```python
# problem 28
# 各大きさは 奇数 x 奇数
# ある大きさ a * a (a は奇数) の一番外にある四隅の合計を求める
# 外周における最小値は (a-2)^2 + 1 となる。この最小値を min_a とする
# すると右下は min_a + (a - 2) となり、そこから (a - 1) ずつ足すと四隅の値が求まる
# 四隅の値の合計は、4 * (min_a + (a-2)) + 3*(a-1) + 2*(a-1) + (a-1) = 4*min_a + 10*a -14 = 4*(a-2)^2 + 10*a -10 = 4*a^2 -6*a +6 (a=1 は除く)

def f(x):
    return 4 * x**2 - 6*x + 6

ans_sum = 1 # 外周が1のときの合計
for i in range(1, 501):
    a = 2 * i + 1 #  3 から 1001 までの奇数
    ans_sum += f(a)
ans_sum
```




    669171001




```python
# problem 29
# 本当は何か理論ある気がするけどゴリ押し

nums_list = []
search_range = range(2, 101)
for a in search_range:
    for b in search_range:
        if not a**b in nums_list:
            nums_list.append(a**b)
len(nums_list)
```




    9183




```python
# problem 30
# ゴリ押す

# sum of fifth powers of their digits
def sof(num):
    ret_sum = 0
    for i in str(num):
        ret_sum += int(i)**5
    return ret_sum

ans_sum = 0
for i in range(2, 1000000):
    if i == sof(i):
        print(i)
        ans_sum += i
ans_sum
```

    4150
    4151
    54748
    92727
    93084
    194979





    443839




```python
# problem 31
coin_list = [200, 100, 50, 20, 10, 5, 2, 1]

# num 内でとれる coin_list 内のコインの組み合わせ
# num = 0 の場合動かないので注意
def count_coin(num, coins):
    count = 0
    if len(coins) == 1:
        return 1
    for i in range((num // coins[0]) + 1):
        # coins 内で最も大きな coin を指定枚使い、残りをそれ未満の coin で表す
        count += count_coin(num - coins[0] * i, coins[1:])
    return count
count_coin(200, coin_list)
```




    3




```python
# problem 32

```