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Added comments to code for problem 11 to 14

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++)
    {

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 <stdio.h>
 #include <stdlib.h>
 #include <time.h>
@@ -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)

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 <stdio.h>
 #include <stdlib.h>
 #include <time.h>
@@ -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);
 

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 <stdio.h>
 #include <stdlib.h>
 #include <time.h>
 
+#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)