solutions.problem13.solve()   A
last analyzed

Complexity

Conditions 4

Size

Total Lines 121
Code Lines 11

Duplication

Lines 0
Ratio 0 %

Importance

Changes 0
Metric Value
cc 4
eloc 11
nop 0
dl 0
loc 121
rs 9.85
c 0
b 0
f 0

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1
"""
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Project Euler Problem 13: Large Sum
3
===================================
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.. module:: solutions.problem13
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   :synopsis: My solution to problem #13.
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The source code for this problem can be
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`found here <https://bitbucket.org/nekedome/project-euler/src/master/solutions/problem13.py>`_.
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Problem Statement
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#################
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Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
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.. math::
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18
    37107287533902102798797998220837590246510135740250 \\\\
19
    46376937677490009712648124896970078050417018260538 \\\\
20
    74324986199524741059474233309513058123726617309629 \\\\
21
    91942213363574161572522430563301811072406154908250 \\\\
22
    23067588207539346171171980310421047513778063246676 \\\\
23
    89261670696623633820136378418383684178734361726757 \\\\
24
    28112879812849979408065481931592621691275889832738 \\\\
25
    44274228917432520321923589422876796487670272189318 \\\\
26
    47451445736001306439091167216856844588711603153276 \\\\
27
    70386486105843025439939619828917593665686757934951 \\\\
28
    62176457141856560629502157223196586755079324193331 \\\\
29
    64906352462741904929101432445813822663347944758178 \\\\
30
    92575867718337217661963751590579239728245598838407 \\\\
31
    58203565325359399008402633568948830189458628227828 \\\\
32
    80181199384826282014278194139940567587151170094390 \\\\
33
    35398664372827112653829987240784473053190104293586 \\\\
34
    86515506006295864861532075273371959191420517255829 \\\\
35
    71693888707715466499115593487603532921714970056938 \\\\
36
    54370070576826684624621495650076471787294438377604 \\\\
37
    53282654108756828443191190634694037855217779295145 \\\\
38
    36123272525000296071075082563815656710885258350721 \\\\
39
    45876576172410976447339110607218265236877223636045 \\\\
40
    17423706905851860660448207621209813287860733969412 \\\\
41
    81142660418086830619328460811191061556940512689692 \\\\
42
    51934325451728388641918047049293215058642563049483 \\\\
43
    62467221648435076201727918039944693004732956340691 \\\\
44
    15732444386908125794514089057706229429197107928209 \\\\
45
    55037687525678773091862540744969844508330393682126 \\\\
46
    18336384825330154686196124348767681297534375946515 \\\\
47
    80386287592878490201521685554828717201219257766954 \\\\
48
    78182833757993103614740356856449095527097864797581 \\\\
49
    16726320100436897842553539920931837441497806860984 \\\\
50
    48403098129077791799088218795327364475675590848030 \\\\
51
    87086987551392711854517078544161852424320693150332 \\\\
52
    59959406895756536782107074926966537676326235447210 \\\\
53
    69793950679652694742597709739166693763042633987085 \\\\
54
    41052684708299085211399427365734116182760315001271 \\\\
55
    65378607361501080857009149939512557028198746004375 \\\\
56
    35829035317434717326932123578154982629742552737307 \\\\
57
    94953759765105305946966067683156574377167401875275 \\\\
58
    88902802571733229619176668713819931811048770190271 \\\\
59
    25267680276078003013678680992525463401061632866526 \\\\
60
    36270218540497705585629946580636237993140746255962 \\\\
61
    24074486908231174977792365466257246923322810917141 \\\\
62
    91430288197103288597806669760892938638285025333403 \\\\
63
    34413065578016127815921815005561868836468420090470 \\\\
64
    23053081172816430487623791969842487255036638784583 \\\\
65
    11487696932154902810424020138335124462181441773470 \\\\
66
    63783299490636259666498587618221225225512486764533 \\\\
67
    67720186971698544312419572409913959008952310058822 \\\\
68
    95548255300263520781532296796249481641953868218774 \\\\
69
    76085327132285723110424803456124867697064507995236 \\\\
70
    37774242535411291684276865538926205024910326572967 \\\\
71
    23701913275725675285653248258265463092207058596522 \\\\
72
    29798860272258331913126375147341994889534765745501 \\\\
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    18495701454879288984856827726077713721403798879715 \\\\
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    38298203783031473527721580348144513491373226651381 \\\\
75
    34829543829199918180278916522431027392251122869539 \\\\
76
    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 \\\\
89
    62177842752192623401942399639168044983993173312731 \\\\
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    32924185707147349566916674687634660915035914677504 \\\\
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    99518671430235219628894890102423325116913619626622 \\\\
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    73267460800591547471830798392868535206946944540724 \\\\
93
    76841822524674417161514036427982273348055556214818 \\\\
94
    97142617910342598647204516893989422179826088076852 \\\\
95
    87783646182799346313767754307809363333018982642090 \\\\
96
    10848802521674670883215120185883543223812876952786 \\\\
97
    71329612474782464538636993009049310363619763878039 \\\\
98
    62184073572399794223406235393808339651327408011116 \\\\
99
    66627891981488087797941876876144230030984490851411 \\\\
100
    60661826293682836764744779239180335110989069790714 \\\\
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    85786944089552990653640447425576083659976645795096 \\\\
102
    66024396409905389607120198219976047599490197230297 \\\\
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    64913982680032973156037120041377903785566085089252 \\\\
104
    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 \\\\
115
    72107838435069186155435662884062257473692284509516 \\\\
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    20849603980134001723930671666823555245252804609722 \\\\
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    53503534226472524250874054075591789781264330331690
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Solution Discussion
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###################
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Simply use Python's arbitrary precision arithmetic to compute this large sum, then divide by the appropriate power of
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:math:`10` to leave the :math:`10` most significant digits.
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Solution Implementation
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#######################
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.. literalinclude:: ../../solutions/problem13.py
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   :language: python
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   :lines: 133-
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"""
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from lib.digital import num_digits
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def solve():
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    """ Compute the answer to Project Euler's problem #13 """
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    # Build a list of integers
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    numbers = """
141
        37107287533902102798797998220837590246510135740250
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        46376937677490009712648124896970078050417018260538
143
        74324986199524741059474233309513058123726617309629
144
        91942213363574161572522430563301811072406154908250
145
        23067588207539346171171980310421047513778063246676
146
        89261670696623633820136378418383684178734361726757
147
        28112879812849979408065481931592621691275889832738
148
        44274228917432520321923589422876796487670272189318
149
        47451445736001306439091167216856844588711603153276
150
        70386486105843025439939619828917593665686757934951
151
        62176457141856560629502157223196586755079324193331
152
        64906352462741904929101432445813822663347944758178
153
        92575867718337217661963751590579239728245598838407
154
        58203565325359399008402633568948830189458628227828
155
        80181199384826282014278194139940567587151170094390
156
        35398664372827112653829987240784473053190104293586
157
        86515506006295864861532075273371959191420517255829
158
        71693888707715466499115593487603532921714970056938
159
        54370070576826684624621495650076471787294438377604
160
        53282654108756828443191190634694037855217779295145
161
        36123272525000296071075082563815656710885258350721
162
        45876576172410976447339110607218265236877223636045
163
        17423706905851860660448207621209813287860733969412
164
        81142660418086830619328460811191061556940512689692
165
        51934325451728388641918047049293215058642563049483
166
        62467221648435076201727918039944693004732956340691
167
        15732444386908125794514089057706229429197107928209
168
        55037687525678773091862540744969844508330393682126
169
        18336384825330154686196124348767681297534375946515
170
        80386287592878490201521685554828717201219257766954
171
        78182833757993103614740356856449095527097864797581
172
        16726320100436897842553539920931837441497806860984
173
        48403098129077791799088218795327364475675590848030
174
        87086987551392711854517078544161852424320693150332
175
        59959406895756536782107074926966537676326235447210
176
        69793950679652694742597709739166693763042633987085
177
        41052684708299085211399427365734116182760315001271
178
        65378607361501080857009149939512557028198746004375
179
        35829035317434717326932123578154982629742552737307
180
        94953759765105305946966067683156574377167401875275
181
        88902802571733229619176668713819931811048770190271
182
        25267680276078003013678680992525463401061632866526
183
        36270218540497705585629946580636237993140746255962
184
        24074486908231174977792365466257246923322810917141
185
        91430288197103288597806669760892938638285025333403
186
        34413065578016127815921815005561868836468420090470
187
        23053081172816430487623791969842487255036638784583
188
        11487696932154902810424020138335124462181441773470
189
        63783299490636259666498587618221225225512486764533
190
        67720186971698544312419572409913959008952310058822
191
        95548255300263520781532296796249481641953868218774
192
        76085327132285723110424803456124867697064507995236
193
        37774242535411291684276865538926205024910326572967
194
        23701913275725675285653248258265463092207058596522
195
        29798860272258331913126375147341994889534765745501
196
        18495701454879288984856827726077713721403798879715
197
        38298203783031473527721580348144513491373226651381
198
        34829543829199918180278916522431027392251122869539
199
        40957953066405232632538044100059654939159879593635
200
        29746152185502371307642255121183693803580388584903
201
        41698116222072977186158236678424689157993532961922
202
        62467957194401269043877107275048102390895523597457
203
        23189706772547915061505504953922979530901129967519
204
        86188088225875314529584099251203829009407770775672
205
        11306739708304724483816533873502340845647058077308
206
        82959174767140363198008187129011875491310547126581
207
        97623331044818386269515456334926366572897563400500
208
        42846280183517070527831839425882145521227251250327
209
        55121603546981200581762165212827652751691296897789
210
        32238195734329339946437501907836945765883352399886
211
        75506164965184775180738168837861091527357929701337
212
        62177842752192623401942399639168044983993173312731
213
        32924185707147349566916674687634660915035914677504
214
        99518671430235219628894890102423325116913619626622
215
        73267460800591547471830798392868535206946944540724
216
        76841822524674417161514036427982273348055556214818
217
        97142617910342598647204516893989422179826088076852
218
        87783646182799346313767754307809363333018982642090
219
        10848802521674670883215120185883543223812876952786
220
        71329612474782464538636993009049310363619763878039
221
        62184073572399794223406235393808339651327408011116
222
        66627891981488087797941876876144230030984490851411
223
        60661826293682836764744779239180335110989069790714
224
        85786944089552990653640447425576083659976645795096
225
        66024396409905389607120198219976047599490197230297
226
        64913982680032973156037120041377903785566085089252
227
        16730939319872750275468906903707539413042652315011
228
        94809377245048795150954100921645863754710598436791
229
        78639167021187492431995700641917969777599028300699
230
        15368713711936614952811305876380278410754449733078
231
        40789923115535562561142322423255033685442488917353
232
        44889911501440648020369068063960672322193204149535
233
        41503128880339536053299340368006977710650566631954
234
        81234880673210146739058568557934581403627822703280
235
        82616570773948327592232845941706525094512325230608
236
        22918802058777319719839450180888072429661980811197
237
        77158542502016545090413245809786882778948721859617
238
        72107838435069186155435662884062257473692284509516
239
        20849603980134001723930671666823555245252804609722
240
        53503534226472524250874054075591789781264330331690
241
    """
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    numbers = numbers.split("\n")
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    numbers = [number.strip() for number in numbers]
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    numbers = [int(number) for number in numbers if number != ""]
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    # Sum the list of integers
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    total = sum(numbers)
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    # Compute the number of digits in the sum, and how many to truncate to give the top 10 digits
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    target = 10
251
    n_digits = num_digits(total)
252
    truncate_digits = n_digits - target
253
254
    # Compute the final answer (first 10 digits)
255
    answer = total // (10 ** truncate_digits)
256
    return answer
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expected_answer = 5537376230
0 ignored issues
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