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problems/013_problem/013_problem.py

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+# #  Problem 13:
+# 
+# [Euler Project #13](https://projecteuler.net/problem=13)
+# 
+# 
+# > Work out the first ten digits of the sum of the following one-hundred 50-digit 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
+# 
+# 
+# ---
+import os
+import pprint
+import time  # Typically imported for sleep function, to slow down execution in terminal.
+import typing
+import decorators  # Typically imported to compute execution duration of functions.
+import math
+import numpy
+
+# ### Import the data table above. Let's be lazy and use the nice multi-cursor feature of the code editor.
+
+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'
+]
+
+# Data Prep
+# - Firstly, this data input creates a list which have cells of the ```string``` data type.
+# - The strings should be parsed into type ```int``` at some point.
+# 
+# ### Solution Approach
+# Can we just employ old-school arithmetic by summing the integers by columns, right to left, <br>
+# carrying over anything greater than *9* to the next column?
+
+# loop over all 50 numbers in the input to convert the string 
+# into a list of characters, still as tpye: string
+for row in range(len(numbers)):  
+    numbers[row] = list(numbers[row])
+    
+    # loop across the newly formed list to convert the string
+    # character into an integer
+    for digit in range(len(numbers[row])):
+        numbers[row][digit] = int(numbers[row][digit])
+
+
+# time to employ the "old math" by running down the columns
+# and summing... Dont forget to carry-over!
+
+# Let's store the sums into a list...
+solution_digits=[]
+column_carryover = 0
+
+print(len(numbers))
+print(len(numbers[0]))
+
+for places in range(len(numbers[0])):
+    # initialize the column sum
+    places = len(numbers[0])-places-1
+    #print(places)
+    column_sum = 0
+    
+    for term in range(len(numbers)):
+        #print("row=",term,", column=",places)
+        column_sum+=numbers[term][places]
+    
+    column_sum+=column_carryover
+    print(column_sum)
+    column_carryover=0
+    column_sum_element = int(list(str(column_sum))[-1])
+    solution_digits.append(column_sum_element)
+
+
+    column_sum *= 0.1
+    column_carryover = column_sum.__trunc__()
+
+solution_digits.append(column_carryover)
+print(solution_digits)
+
+solution_digits.reverse()
+string=""
+for i in solution_digits[:10]:
+    string+=str(i)
+
+print("The solution is ",string)