problem with very big sums

[Jazpy]

I've been working through Project Euler's problems and I found a problem when trying to solve the 13th one, link in case any one is interested: http://projecteuler.net/problem=13

I figured first I'd get the sum of the 50, 100 digit numbers, but their sum is returning -100, at first I thought it was because I was using an int, but I tried switching the sum's type to "long" and "long long" with the same results, could anyone help me figure out why it's returning -100?

#include <iostream>
#include <string>
#include <fstream>
#include <vector>
#include <stdlib.h>

using std::string; using std::cout; using std::endl; using std::vector;

string read_string_from_file(string filename){
    std::ifstream file;
    file.open(filename.c_str());

    string temp_string = "";
    string return_string = "";

    while(std::getline(file, temp_string))
        return_string += temp_string;

    return return_string;
}

vector < string > split_string(string str, int elems){
    vector < string > substrings;

    for(int i = 0; i < str.length(); i += elems){
        string temp_string = str.substr(i, elems);

        substrings.push_back(temp_string);
    }

    return substrings;
}

int main(){
    string da_string = read_string_from_file("da_file.txt");
    vector < string> strings = split_string(da_string, 50);

    int sum = 0;

    for(int i = 0; i < strings.size(); i++)
        sum += atoi(strings [i].c_str());

    cout << sum << endl;

    return 0;
}

[Josue Molina]

atoi returns ints.

Edit: you need to use arbitrary-precision numbers. Look into these two:

http://gmplib.org/
http://www.tc.umn.edu/~ringx004/mapm-main.html

[Jazpy]

Thanks Josue, so if I did it the long way and converted the strings into longs it would work?

[vlad from moscow]

Neither integral type in C++ can accommodate numbers with 50 digits.

[Josue Molina]

The largest integral type you can declare is an unsigned long long, which goes from 0 to 18446744073709551615, and that's a 20 digit number.

You need to use a library like the ones I have given you, or write one yourself.

[Jazpy]

All right, thanks for the help.

[JLBorges]

You can solve this problem by using the humble int as the integer type for calculations.

#include <iostream>
#include <string>

int main()
{
    constexpr std::size_t DIGITS = 50 ;
    constexpr std::size_t N = 100 ;

    const std::string numbers[N] =
    {
        "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"
    };

    // sum up the 50 individual digits
    int sum_digits[DIGITS] = {0} ;
    for( const std::string& str : numbers )
    {
        static constexpr char LITERAL_ZERO = '0' ;
        for( std::size_t i = 0 ; i < DIGITS ; ++i )
            sum_digits[i] += str[i] - LITERAL_ZERO ;
    }

    // sum_digits[i] now contains the sum of the digit at position i in each number

    // sum_digits[0] == sum of the left-most (first) digit of each number
    // sum_digits[0] == sum of the second digit of each number
    // ...
    // sum_digits[99] == sum of the right-most (last) digit of each number

    // the maximum possible value of the sum for each digit is 9 * 100 == 900

    // see if you can take it up from here

    // hint: add digit by digit from right to left with carry
    // we need only first (most significant?) ten digits digits of the result
}

[Jazpy]

That's a great solution, Borges, thanks for the help, but could you tell me how this line works? I've never seen for loops being used like that:

for( const std::string& str : numbers )

[JLBorges]

That is the range-based for loop available in C++11.

#include <iostream>

int main()
{
    constexpr std::size_t N = 5 ;
    int a[N] { 0, 1, 2, 3, 4 } ;

    // add five to each element using a classical for loop (subscript)
    for( std::size_t i = 0 ; i < N ; ++i )
    {
        int& v = a[i] ;
        v += 5 ;
    }

    // add five to each element using a classical for loop (pointer)
    for( int* p = a ; p != a+N ; ++p )
    {
        int& v = *p ;
        v += 5 ;
    }

    // add five to each element using a range-based loop
    for( int& v : a )
    {
        v += 5 ;
    }
}

See: http://www.stroustrup.com/C++11FAQ.html#for
http://msdn.microsoft.com/en-us/library/vstudio/jj203382.aspx