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- /************************************************
- Programmer : Muhammad Azri bin Jasni @ Abdul Rani
- Program : project euler problem 13.cpp
- Link : http://projecteuler.net/problem=13
- Description: Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
- Note : I want to know how to install new library into Dev-C++ 4.9.9.2
- *************************************************
- At first, I thought of a manual addition for each digits. As we can see, 50 digits
- go outside the boundary of normal int or even long long[16/32 bits]. So, that's what I thought.
- I create string array strNumbers[] first because it is such a hassle to write it for each digits.
- Made a little loop that
- -check each char using substr()
- -change it to c-string using .c_str() and
- -convert to int using atoi()
- -store into the array number[][]
- Remember how we do manual addition? We just add up the first digits. If its more than 9, the
- excess digits at front will be brought to the next digit summation. I actually don't remember
- correct mathematical term for that. Just look into the example. You can skip this part if you know already.
- ///////Example: Skip if you want
- 19
- +11
- ---
- 30
- ---
- So yeah, 9+1 = 10. But only 0 being used, while the 1 being brought forward.
- In programming, we can do this by using modulus division with 10.
- See... 10 divide 10 equals 1 with 0 remainder. If 19 divide 10 results in 1 with remainder of 9.
- So, put the remainder first, while the real result being brought forward. That's our manual sum algorithm.
- Of course, need to remember we do it from right-to-left like reading manga.
- ///////End example
- The storage was into a int array result[] from right to left. This result array should be larger than 50.
- But, according to little experiment with paper and pen, even if every numbers here are digits 9 (largest possible combination),
- the answers should be around 2 or 3 bits more(52/53), that's it. I might be wrong, because at first I used 50 rows of numbers. D:
- Change to 100 rows, and there my effort doesn't go to waste. YAY. What really interesting is the answer exactly 50 digits.
- Oh, we only need the first 10 digits. Because I initalize the array to zeros, I can ignore first zeros,
- then check for actual 10 first digits. Gotta display 'em all! ["pika!"]
- Phew. Now, I need internet connection to actually post this online. Btw, we can also made summation of chunks of 10 bit digits,
- but I won't do it. It reduce the total processes, thus reduce time, but I don't really check for performance and am lazy.
- EDIT: It's wrong. =_=;
- */
- /*
- http://suchideas.com/journal/2007/07/installing-gmp-on-windows/
- */
- /*BigInt: http://www.cplusplus.com/forum/lounge/32041/*/
- #include <iostream>
- #include <string>
- using namespace std;
- int main()
- {
- /*Local declaration*/
- const int row = 100, column = 50;
- string strNumber[] = //the lazy first storage
- {
- "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"
- };
- int number[row][column];//the real storage array
- for (int i=0;i<row;i++)
- {
- for (int j=0;j<column;j++)
- {
- number[i][j]=atoi( strNumber[i].substr(j,1).c_str() );
- }
- }
- const int resultSize = 54;//result array size
- int result[resultSize]={}, counter = resultSize-1;//the result storage and counter for moving about, this count may actually not required
- long sumCounter = 0;
- /*END Local declaration*/
- for (int j=column-1;j>=0;j--,counter--)
- {
- for (int i=0;i<row-1;i++)
- {
- sumCounter = sumCounter + number[i][j] + number[i+1][j];
- result[counter]= sumCounter%10;
- sumCounter = sumCounter/10;
- }
- }
- /*
- //If you want to display the whole result including zeros
- for (int i =0; i<resultSize;i++)
- {
- cout << result[i];
- } cout << endl;
- //
- */
- int count = 0;//check only first 10 digit
- bool firstCounter = true; //counter to make sure it is the leading zeros.
- for (int j=0;j<resultSize,count<10;j++)
- {
- if (result[j]==0 && firstCounter)//skip zeros
- continue;
- else
- {
- if (firstCounter)
- firstCounter = false;//This is required to debug error of removing results zeros
- //althought the answer still correct without this, right algorithm still important
- cout << result[j];
- count++;
- }
- }
- cout << endl;
- /*These lines below are the cross-platform alternative to getch()*/
- //cin.ignore(1110,'\n'); //needed only when have input to remove our "ENTER" = '\n'
- cin.get();
- return 0;
- }
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