From c4b8566bb4f8fc6b9f79d7047a263e5b94822385 Mon Sep 17 00:00:00 2001 From: Daniele Fucini Date: Sun, 22 Sep 2019 21:35:10 +0200 Subject: [PATCH] Add comments Added comments to code for problem 11 to 14 --- C/p011.c | 4 +-- C/p012.c | 21 +++++++++++ C/p013.c | 105 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ C/p014.c | 31 ++++++++++++++-- 4 files changed, 156 insertions(+), 5 deletions(-) diff --git a/C/p011.c b/C/p011.c index 99dbfa1..308f33e 100644 --- a/C/p011.c +++ b/C/p011.c @@ -70,7 +70,7 @@ int main(int argc, char **argv) { prod *= grid[i][k]; } - + if(prod > max) { max = prod; @@ -102,7 +102,7 @@ int main(int argc, char **argv) } } } - + /* The last diagonal is handled separately.*/ for(i = 0; i < 17; i++) { diff --git a/C/p012.c b/C/p012.c index e420431..099952f 100644 --- a/C/p012.c +++ b/C/p012.c @@ -1,3 +1,22 @@ +/* The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. + * The first ten terms would be: + * + * 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... + * + * Let us list the factors of the first seven triangle numbers: + * + * 1: 1 + * 3: 1,3 + * 6: 1,2,3,6 + * 10: 1,2,5,10 + * 15: 1,3,5,15 + * 21: 1,3,7,21 + * 28: 1,2,4,7,14,28 + * + * We can see that 28 is the first triangle number to have over five divisors. + * + * What is the value of the first triangle number to have over five hundred divisors?*/ + #include #include #include @@ -11,10 +30,12 @@ int main(int argc, char **argv) clock_gettime(CLOCK_MONOTONIC, &start); + /* Generate all triangle numbers until the first one with more than 500 divisors is found.*/ while(!finished) { i++; triang += i; + /* Use the function implemented in projecteuler.c to count divisors of a number.*/ count = count_divisors(triang); if(count > 500) diff --git a/C/p013.c b/C/p013.c index 0c1bf22..fa1cae1 100644 --- a/C/p013.c +++ b/C/p013.c @@ -1,3 +1,106 @@ +/* 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*/ + #include #include #include @@ -63,6 +166,8 @@ int main(int argc, char **argv) clock_gettime(CLOCK_MONOTONIC, &start); + /* Using the GNU Multiple Precision Arithmetic Library (GMP) + * to sum the numbers and get the first 10 digits of the sum.*/ mpz_inits(a, b, NULL); mpz_set_str(a, n[0], 10); diff --git a/C/p014.c b/C/p014.c index f21948d..bfa28b3 100644 --- a/C/p014.c +++ b/C/p014.c @@ -1,10 +1,28 @@ +/* The following iterative sequence is defined for the set of positive integers: + * + * n → n/2 (n is even) + * n → 3n + 1 (n is odd) + * + * Using the rule above and starting with 13, we generate the following sequence: + * + * 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 + * + * It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), + * it is thought that all starting numbers finish at 1. + * + * Which starting number, under one million, produces the longest chain? + * + * NOTE: Once the chain starts the terms are allowed to go above one million.*/ + #include #include #include +#define N 1000000 + int collatz_length(long int n); -int collatz_found[1000000] = {0}; +int collatz_found[N] = {0}; int main(int argc, char **argv) { @@ -14,8 +32,10 @@ int main(int argc, char **argv) clock_gettime(CLOCK_MONOTONIC, &start); - for(i = 1; i < 1000000; i++) + for(i = 1; i < N; i++) { + /* For each number from 1 to 1000000, find the length of the sequence + * and save its value, so that it can be used for the next numbers.*/ count = collatz_length(i); collatz_found[i] = count; @@ -38,12 +58,17 @@ int main(int argc, char **argv) return 0; } +/* Recursive function to calculate the Collatz sequence for n. + * If n is even, Collatz(n)=1+Collatz(n/2), if n is odd + * Collatz(n)=1+Collatz(3*n+1).*/ int collatz_length(long int n) { if(n == 1) return 1; - if(n < 1000000 && collatz_found[n]) + /* If Collatz(n) has been previously calculated, + * just return the value.*/ + if(n < N && collatz_found[n]) return collatz_found[n]; if(n % 2 == 0)