Fortran Implementation of Problem 13

View source code here on GitHub!

integer Problem0013/p0013()
  1! Project Euler Problem 13
  2!
  3! Problem:
  4!
  5! Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
  6! 37107287533902102798797998220837590246510135740250
  7! 46376937677490009712648124896970078050417018260538
  8! 74324986199524741059474233309513058123726617309629
  9! 91942213363574161572522430563301811072406154908250
 10! 23067588207539346171171980310421047513778063246676
 11! 89261670696623633820136378418383684178734361726757
 12! 28112879812849979408065481931592621691275889832738
 13! 44274228917432520321923589422876796487670272189318
 14! 47451445736001306439091167216856844588711603153276
 15! 70386486105843025439939619828917593665686757934951
 16! 62176457141856560629502157223196586755079324193331
 17! 64906352462741904929101432445813822663347944758178
 18! 92575867718337217661963751590579239728245598838407
 19! 58203565325359399008402633568948830189458628227828
 20! 80181199384826282014278194139940567587151170094390
 21! 35398664372827112653829987240784473053190104293586
 22! 86515506006295864861532075273371959191420517255829
 23! 71693888707715466499115593487603532921714970056938
 24! 54370070576826684624621495650076471787294438377604
 25! 53282654108756828443191190634694037855217779295145
 26! 36123272525000296071075082563815656710885258350721
 27! 45876576172410976447339110607218265236877223636045
 28! 17423706905851860660448207621209813287860733969412
 29! 81142660418086830619328460811191061556940512689692
 30! 51934325451728388641918047049293215058642563049483
 31! 62467221648435076201727918039944693004732956340691
 32! 15732444386908125794514089057706229429197107928209
 33! 55037687525678773091862540744969844508330393682126
 34! 18336384825330154686196124348767681297534375946515
 35! 80386287592878490201521685554828717201219257766954
 36! 78182833757993103614740356856449095527097864797581
 37! 16726320100436897842553539920931837441497806860984
 38! 48403098129077791799088218795327364475675590848030
 39! 87086987551392711854517078544161852424320693150332
 40! 59959406895756536782107074926966537676326235447210
 41! 69793950679652694742597709739166693763042633987085
 42! 41052684708299085211399427365734116182760315001271
 43! 65378607361501080857009149939512557028198746004375
 44! 35829035317434717326932123578154982629742552737307
 45! 94953759765105305946966067683156574377167401875275
 46! 88902802571733229619176668713819931811048770190271
 47! 25267680276078003013678680992525463401061632866526
 48! 36270218540497705585629946580636237993140746255962
 49! 24074486908231174977792365466257246923322810917141
 50! 91430288197103288597806669760892938638285025333403
 51! 34413065578016127815921815005561868836468420090470
 52! 23053081172816430487623791969842487255036638784583
 53! 11487696932154902810424020138335124462181441773470
 54! 63783299490636259666498587618221225225512486764533
 55! 67720186971698544312419572409913959008952310058822
 56! 95548255300263520781532296796249481641953868218774
 57! 76085327132285723110424803456124867697064507995236
 58! 37774242535411291684276865538926205024910326572967
 59! 23701913275725675285653248258265463092207058596522
 60! 29798860272258331913126375147341994889534765745501
 61! 18495701454879288984856827726077713721403798879715
 62! 38298203783031473527721580348144513491373226651381
 63! 34829543829199918180278916522431027392251122869539
 64! 40957953066405232632538044100059654939159879593635
 65! 29746152185502371307642255121183693803580388584903
 66! 41698116222072977186158236678424689157993532961922
 67! 62467957194401269043877107275048102390895523597457
 68! 23189706772547915061505504953922979530901129967519
 69! 86188088225875314529584099251203829009407770775672
 70! 11306739708304724483816533873502340845647058077308
 71! 82959174767140363198008187129011875491310547126581
 72! 97623331044818386269515456334926366572897563400500
 73! 42846280183517070527831839425882145521227251250327
 74! 55121603546981200581762165212827652751691296897789
 75! 32238195734329339946437501907836945765883352399886
 76! 75506164965184775180738168837861091527357929701337
 77! 62177842752192623401942399639168044983993173312731
 78! 32924185707147349566916674687634660915035914677504
 79! 99518671430235219628894890102423325116913619626622
 80! 73267460800591547471830798392868535206946944540724
 81! 76841822524674417161514036427982273348055556214818
 82! 97142617910342598647204516893989422179826088076852
 83! 87783646182799346313767754307809363333018982642090
 84! 10848802521674670883215120185883543223812876952786
 85! 71329612474782464538636993009049310363619763878039
 86! 62184073572399794223406235393808339651327408011116
 87! 66627891981488087797941876876144230030984490851411
 88! 60661826293682836764744779239180335110989069790714
 89! 85786944089552990653640447425576083659976645795096
 90! 66024396409905389607120198219976047599490197230297
 91! 64913982680032973156037120041377903785566085089252
 92! 16730939319872750275468906903707539413042652315011
 93! 94809377245048795150954100921645863754710598436791
 94! 78639167021187492431995700641917969777599028300699
 95! 15368713711936614952811305876380278410754449733078
 96! 40789923115535562561142322423255033685442488917353
 97! 44889911501440648020369068063960672322193204149535
 98! 41503128880339536053299340368006977710650566631954
 99! 81234880673210146739058568557934581403627822703280
100! 82616570773948327592232845941706525094512325230608
101! 22918802058777319719839450180888072429661980811197
102! 77158542502016545090413245809786882778948721859617
103! 72107838435069186155435662884062257473692284509516
104! 20849603980134001723930671666823555245252804609722
105! 53503534226472524250874054075591789781264330331690
106
107module Problem0013
108    use constants
109    implicit none
110contains
111    integer(i18t) function p0013() result(answer)
112        integer(i18t), dimension(3, 100) :: numbers
113        integer(i18t), dimension(3) :: arr = (/ 0, 0, 0 /)
114        integer(i18t) :: ten18 = 1000000000000000000_i18t
115        integer(i18t) :: ten10 = 10000000000_i18t
116        integer :: i, j
117
118        ! Manually initialize the grid
119        data numbers / &
120            37107287533902_i18t, 102798797998220837_i18t, 590246510135740250_i18t, 46376937677490_i18t,   9712648124896970_i18t,  78050417018260538_i18t, 74324986199524_i18t, 741059474233309513_i18t,  58123726617309629_i18t, 91942213363574_i18t, 161572522430563301_i18t, 811072406154908250_i18t, &
121            23067588207539_i18t, 346171171980310421_i18t,  47513778063246676_i18t, 89261670696623_i18t, 633820136378418383_i18t, 684178734361726757_i18t, 28112879812849_i18t, 979408065481931592_i18t, 621691275889832738_i18t, 44274228917432_i18t, 520321923589422876_i18t, 796487670272189318_i18t, &
122            47451445736001_i18t, 306439091167216856_i18t, 844588711603153276_i18t, 70386486105843_i18t,  25439939619828917_i18t, 593665686757934951_i18t, 62176457141856_i18t, 560629502157223196_i18t, 586755079324193331_i18t, 64906352462741_i18t, 904929101432445813_i18t, 822663347944758178_i18t, &
123            92575867718337_i18t, 217661963751590579_i18t, 239728245598838407_i18t, 58203565325359_i18t, 399008402633568948_i18t, 830189458628227828_i18t, 80181199384826_i18t, 282014278194139940_i18t, 567587151170094390_i18t, 35398664372827_i18t, 112653829987240784_i18t, 473053190104293586_i18t, &
124            86515506006295_i18t, 864861532075273371_i18t, 959191420517255829_i18t, 71693888707715_i18t, 466499115593487603_i18t, 532921714970056938_i18t, 54370070576826_i18t, 684624621495650076_i18t, 471787294438377604_i18t, 53282654108756_i18t, 828443191190634694_i18t,  37855217779295145_i18t, &
125            36123272525000_i18t, 296071075082563815_i18t, 656710885258350721_i18t, 45876576172410_i18t, 976447339110607218_i18t, 265236877223636045_i18t, 17423706905851_i18t, 860660448207621209_i18t, 813287860733969412_i18t, 81142660418086_i18t, 830619328460811191_i18t,  61556940512689692_i18t, &
126            51934325451728_i18t, 388641918047049293_i18t, 215058642563049483_i18t, 62467221648435_i18t,  76201727918039944_i18t, 693004732956340691_i18t, 15732444386908_i18t, 125794514089057706_i18t, 229429197107928209_i18t, 55037687525678_i18t, 773091862540744969_i18t, 844508330393682126_i18t, &
127            18336384825330_i18t, 154686196124348767_i18t, 681297534375946515_i18t, 80386287592878_i18t, 490201521685554828_i18t, 717201219257766954_i18t, 78182833757993_i18t, 103614740356856449_i18t,  95527097864797581_i18t, 16726320100436_i18t, 897842553539920931_i18t, 837441497806860984_i18t, &
128            48403098129077_i18t, 791799088218795327_i18t, 364475675590848030_i18t, 87086987551392_i18t, 711854517078544161_i18t, 852424320693150332_i18t, 59959406895756_i18t, 536782107074926966_i18t, 537676326235447210_i18t, 69793950679652_i18t, 694742597709739166_i18t, 693763042633987085_i18t, &
129            41052684708299_i18t,  85211399427365734_i18t, 116182760315001271_i18t, 65378607361501_i18t,  80857009149939512_i18t, 557028198746004375_i18t, 35829035317434_i18t, 717326932123578154_i18t, 982629742552737307_i18t, 94953759765105_i18t, 305946966067683156_i18t, 574377167401875275_i18t, &
130            88902802571733_i18t, 229619176668713819_i18t, 931811048770190271_i18t, 25267680276078_i18t,   3013678680992525_i18t, 463401061632866526_i18t, 36270218540497_i18t, 705585629946580636_i18t, 237993140746255962_i18t, 24074486908231_i18t, 174977792365466257_i18t, 246923322810917141_i18t, &
131            91430288197103_i18t, 288597806669760892_i18t, 938638285025333403_i18t, 34413065578016_i18t, 127815921815005561_i18t, 868836468420090470_i18t, 23053081172816_i18t, 430487623791969842_i18t, 487255036638784583_i18t, 11487696932154_i18t, 902810424020138335_i18t, 124462181441773470_i18t, &
132            63783299490636_i18t, 259666498587618221_i18t, 225225512486764533_i18t, 67720186971698_i18t, 544312419572409913_i18t, 959008952310058822_i18t, 95548255300263_i18t, 520781532296796249_i18t, 481641953868218774_i18t, 76085327132285_i18t, 723110424803456124_i18t, 867697064507995236_i18t, &
133            37774242535411_i18t, 291684276865538926_i18t, 205024910326572967_i18t, 23701913275725_i18t, 675285653248258265_i18t, 463092207058596522_i18t, 29798860272258_i18t, 331913126375147341_i18t, 994889534765745501_i18t, 18495701454879_i18t, 288984856827726077_i18t, 713721403798879715_i18t, &
134            38298203783031_i18t, 473527721580348144_i18t, 513491373226651381_i18t, 34829543829199_i18t, 918180278916522431_i18t,  27392251122869539_i18t, 40957953066405_i18t, 232632538044100059_i18t, 654939159879593635_i18t, 29746152185502_i18t, 371307642255121183_i18t, 693803580388584903_i18t, &
135            41698116222072_i18t, 977186158236678424_i18t, 689157993532961922_i18t, 62467957194401_i18t, 269043877107275048_i18t, 102390895523597457_i18t, 23189706772547_i18t, 915061505504953922_i18t, 979530901129967519_i18t, 86188088225875_i18t, 314529584099251203_i18t, 829009407770775672_i18t, &
136            11306739708304_i18t, 724483816533873502_i18t, 340845647058077308_i18t, 82959174767140_i18t, 363198008187129011_i18t, 875491310547126581_i18t, 97623331044818_i18t, 386269515456334926_i18t, 366572897563400500_i18t, 42846280183517_i18t,  70527831839425882_i18t, 145521227251250327_i18t, &
137            55121603546981_i18t, 200581762165212827_i18t, 652751691296897789_i18t, 32238195734329_i18t, 339946437501907836_i18t, 945765883352399886_i18t, 75506164965184_i18t, 775180738168837861_i18t,  91527357929701337_i18t, 62177842752192_i18t, 623401942399639168_i18t,  44983993173312731_i18t, &
138            32924185707147_i18t, 349566916674687634_i18t, 660915035914677504_i18t, 99518671430235_i18t, 219628894890102423_i18t, 325116913619626622_i18t, 73267460800591_i18t, 547471830798392868_i18t, 535206946944540724_i18t, 76841822524674_i18t, 417161514036427982_i18t, 273348055556214818_i18t, &
139            97142617910342_i18t, 598647204516893989_i18t, 422179826088076852_i18t, 87783646182799_i18t, 346313767754307809_i18t, 363333018982642090_i18t, 10848802521674_i18t, 670883215120185883_i18t, 543223812876952786_i18t, 71329612474782_i18t, 464538636993009049_i18t, 310363619763878039_i18t, &
140            62184073572399_i18t, 794223406235393808_i18t, 339651327408011116_i18t, 66627891981488_i18t,  87797941876876144_i18t, 230030984490851411_i18t, 60661826293682_i18t, 836764744779239180_i18t, 335110989069790714_i18t, 85786944089552_i18t, 990653640447425576_i18t,  83659976645795096_i18t, &
141            66024396409905_i18t, 389607120198219976_i18t,  47599490197230297_i18t, 64913982680032_i18t, 973156037120041377_i18t, 903785566085089252_i18t, 16730939319872_i18t, 750275468906903707_i18t, 539413042652315011_i18t, 94809377245048_i18t, 795150954100921645_i18t, 863754710598436791_i18t, &
142            78639167021187_i18t, 492431995700641917_i18t, 969777599028300699_i18t, 15368713711936_i18t, 614952811305876380_i18t, 278410754449733078_i18t, 40789923115535_i18t, 562561142322423255_i18t,  33685442488917353_i18t, 44889911501440_i18t, 648020369068063960_i18t, 672322193204149535_i18t, &
143            41503128880339_i18t, 536053299340368006_i18t, 977710650566631954_i18t, 81234880673210_i18t, 146739058568557934_i18t, 581403627822703280_i18t, 82616570773948_i18t, 327592232845941706_i18t, 525094512325230608_i18t, 22918802058777_i18t, 319719839450180888_i18t,  72429661980811197_i18t, &
144            77158542502016_i18t, 545090413245809786_i18t, 882778948721859617_i18t, 72107838435069_i18t, 186155435662884062_i18t, 257473692284509516_i18t, 20849603980134_i18t,   1723930671666823_i18t, 555245252804609722_i18t, 53503534226472_i18t, 524250874054075591_i18t, 789781264330331690_i18t /
145
146        do i = 1, 100
147            do j = 1, 3
148                arr(j) = arr(j) + numbers(j, i)
149            end do
150            do j = 3, 2, -1
151                if (arr(j) > ten18) then
152                    arr(j - 1) = arr(j - 1) + arr(j) / ten18
153                    arr(j) = mod(arr(j), ten18)
154                end if
155            end do
156        end do
157        do while (arr(1) > ten10)
158            arr(1) = arr(1) / 10
159        end do
160        answer = arr(1)
161    end function p0013
162end module Problem0013

Tags: large-numbers