Add more python solutions

Added python solutions for problems 11, 12, 13, 14, 15

Python/p003.py

@@ -10,7 +10,7 @@ def max_prime_factor(num):
         return num
 
     if num % 2 == 0:
-        return max_prime_factor(num / 2)
+        return max_prime_factor(num // 2)
 
     else:
         limit = math.floor(math.sqrt(num)) + 1
@@ -18,7 +18,7 @@ def max_prime_factor(num):
         for i in range(3, limit, 2):
             if num % i == 0:
                 if is_prime(i):
-                    return max_prime_factor(num / i)
+                    return max_prime_factor(num // i)
 
 def main():
     start = default_timer()
@@ -28,7 +28,7 @@ def main():
     end = default_timer()
 
     print('Project Euler, Problem 3')
-    print('Answer: {}'.format(int(res)))
+    print('Answer: {}'.format(res))
 
     print('Elapsed time: {:.9f} seconds'.format(end - start))
 

Python/p004.py

@@ -10,7 +10,7 @@ def is_palindrome(num, base):
     while tmp > 0:
         reverse = reverse * base
         reverse = reverse + tmp % base
-        tmp = int(tmp / base)
+        tmp = tmp // base
 
     if num == reverse:
         return 1

Python/p005.py

@@ -14,7 +14,7 @@ def main():
     end = default_timer()
 
     print('Project Euler, Problem 5')
-    print('Answer: {}'.format(int(res)))
+    print('Answer: {}'.format(res))
 
     print('Elapsed time: {:.9f} seconds'.format(end - start))
 

Python/p011.py

@@ -0,0 +1,129 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+    grid = [[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
+            [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
+            [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
+            [52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 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, 3, 45, 2, 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, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
+            [24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
+            [21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95],
+            [78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
+            [16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
+            [86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
+            [19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
+            [4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
+            [88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
+            [4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
+            [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
+            [20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
+            [1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]];
+
+    max_ = 0
+
+    for i in range(20):
+        for j in range(20):
+            prod = 1
+            k = j
+
+            while k < j + 4 and k < 20:
+                prod = prod * grid[i][k]
+                k = k + 1
+
+            if k == j + 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = j
+
+            while k > j - 4 and k >= 0:
+                prod = prod * grid[i][k]
+                k = k - 1
+
+            if k == j - 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = i
+
+            while k < i + 4 and k < 20:
+                prod = prod * grid[k][j]
+                k = k + 1
+
+            if k == i + 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = i
+
+            while k > i - 4 and k >= 0:
+                prod = prod * grid[k][j]
+                k = k - 1
+
+            if k == i - 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = i
+            w = j
+
+            while k < i + 4 and w < j + 4 and k < 20 and w < 20:
+                prod = prod * grid[k][w]
+                k = k + 1
+                w = w + 1
+
+            if k == i + 4 and w == j + 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = i
+            w = j
+
+            while k < i + 4 and w > j - 4 and k < 20 and w >= 0:
+                prod = prod * grid[k][w]
+                k = k + 1
+                w = w - 1
+
+            if k == i + 4 and w == j - 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = i
+            w = j
+
+            while k > i - 4 and w < j + 4 and k >= 0 and w < 20:
+                prod = prod * grid[k][w]
+                k = k - 1
+                w = w + 1
+
+            if k == i - 4 and w == j + 4 and prod > max_:
+                max_ = prod
+
+            prod = 1
+            k = i
+            w = j
+
+            while k > i - 4 and w > j - 4 and k >= 0 and w >= 0:
+                prod = prod * grid[k][w]
+                k = k - 1
+                w = w - 1
+
+            if k == i - 4 and w == j - 4 and prod > max_:
+                max_ = prod
+
+    end = default_timer()
+
+    print('Project Euler, Problem 11')
+    print('Answer: {}'.format(max_))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p012.py

@@ -0,0 +1,28 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+from projecteuler import count_divisors
+
+def main():
+    start = default_timer()
+
+    i = 0
+    triang = 0
+    finished = 0
+
+    while not finished:
+        i = i + 1
+        triang = triang + i
+
+        if count_divisors(triang) > 500:
+            finished = 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 12')
+    print('Answer: {}'.format(triang))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p013.py

@@ -0,0 +1,123 @@
+#!/usr/bin/python3
+
+import numpy as np
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+    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 = np.array(numbers)
+
+    sum_ = str(numbers.sum())
+
+    end = default_timer()
+
+    print('Project Euler, Problem 13')
+    print('Answer: {}'.format(sum_[:10]))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p014.py

@@ -0,0 +1,42 @@
+#!/usr/bin/python3 
+from numpy import zeros
+
+from timeit import default_timer
+
+collatz_found = zeros(1000000, dtype=int)
+
+def collatz_length(n):
+    if n == 1:
+        return 1
+
+    if n < 1000000 and collatz_found[n]:
+        return collatz_found[n]
+
+    if n % 2 == 0:
+        return 1 + collatz_length(n//2)
+    else:
+        return 1 + collatz_length(3*n+1)
+
+def main():
+    start = default_timer()
+
+    max_l = 0
+    max_ = 0
+
+    for i in range(1, 1000000):
+        count = collatz_length(i)
+        collatz_found[i] = count
+
+        if count > max_l:
+            max_l = count
+            max_ = i
+
+    end = default_timer()
+
+    print('Project Euler, Problem 14')
+    print('Answer: {}'.format(max_))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p015.py

@@ -0,0 +1,23 @@
+#!/usr/bin/python3
+
+from math import factorial
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+    count = factorial(40)
+    tmp = factorial(20)
+    tmp = tmp * tmp
+    count = count // tmp
+
+    end = default_timer()
+
+    print('Project Euler, Problem 15')
+    print('Answer: {}'.format(count))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/projecteuler.py

@@ -27,7 +27,7 @@ def gcd(a, b):
     return a
 
 def lcm(a, b):
-    return a * b / gcd(a, b)
+    return a * b // gcd(a, b)
 
 def lcmm(values, n):
     if n == 2:
@@ -58,3 +58,16 @@ def sieve(n):
                 primes[j] = 0
 
     return primes
+
+def count_divisors(n):
+    count = 0
+    limit = math.floor(math.sqrt(n))
+
+    for i in range(1, limit):
+        if n % i == 0:
+            count = count + 2
+
+        if n == limit * limit:
+            count = count - 1
+
+    return count