// serial version created by James Villemarette for CISC 372, Fall 2021
// version 2
#include
#include
#include
#include
#define default_solve 51
#define default_report_after 50
/**
* I found it took me ~60 seconds for one of my four cores to solve 51.
*/
int solve = default_solve;
int report_after = default_report_after;
/**
* https://en.wikipedia.org/wiki/Sums_of_three_cubes#Computational_results
*
* This code solves the sum of three cubes problem.
* x^3 + y^3 + z^3 = k
* or as we’ll be using it
* a^3 + b^3 + c^3 = solve
* (because it’s easier to visually differentiate a & c vs x & y)
*
* k is trivial to solve in some cases.
* Say k = 8,
* x^3 + y^3 + z^3 => 1^3 + (-1)^3 + 2^3 = 8
*
* But for k = 42 and k = 33, they were only solved in 2019 by supercomputers.
*
* Parallelize this code.
*/
/**
* Check all possible combinations for the solve.
*
* All possible combinations
* (-a) + b + c
* a + (-b) + c
* a + b + (-c)
* (-a) + (-b) + c
* a + (-b) + (-c)
* (-a) + (-b) + (-c)
*
* Exits the program when a solution is found.
*/
void check(int a, int b, int c) {
double da = pow((double)a, 3.0);
double db = pow((double)b, 3.0);
double dc = pow((double)c, 3.0);
if(
da + db + dc == solve ||
(-da) + db + dc == solve ||
da + (-db) + dc == solve ||
da + db + (-dc) == solve ||
(-da) + (-db) + dc == solve ||
da + (-db) + (-dc) == solve ||
(-da) + (-db) + (-dc) == solve
) {
printf(“Solution found for %d\n”, solve);
if( da + db + dc == solve )
printf(“a=%d, b=%d, c=%d\n”, a, b, c);
if( (-da) + db + dc == solve )
printf(“a=-%d, b=%d, c=%d\n”, a, b, c);
if( da + (-db) + dc == solve )
printf(“a=%d, b=-%d, c=%d\n”, a, b, c);
if( da + db + (-dc) == solve )
printf(“a=%d, b=%d, c=-%d\n”, a, b, c);
if( (-da) + (-db) + dc == solve )
printf(“a=-%d, b=-%d, c=%d\n”, a, b, c);
if( da + (-db) + (-dc) == solve )
printf(“a=%d, b=-%d, c=-%d\n”, a, b, c);
if( (-da) + (-db) + (-dc) == solve )
printf(“a=-%d, b=-%d, c=-%d\n”, a, b, c);
exit(0);
}
}
int main(int argc, char *argv[]) {
// setup
int a = 0;
int b = 0;
int c = 0;
int report = 1;
int itr = 0;
if(argc <= 1) {
printf("No arguments were passed. Assuming default solve of 51.\n");
} else {
if(argc == 2) {
solve = atoi(argv[1]);
} else if(argc == 3) {
solve = atoi(argv[2]);
report_after = atoi(argv[3]);
}
}
printf("Solving sum of cubes for %d\n", solve);
while(1) {
clock_t tic = clock();
a += 1;
for(int t_b = b; t_b > 0; t_b–)
for(int t_c = c; t_c > 0; t_c–)
check(a, t_b, t_c);
b += 1;
for(int t_a = a; t_a > 0; t_a–)
for(int t_c = c; t_c > 0; t_c–)
check(t_a, b, t_c);
c += 1;
for(int t_a = a; t_a > 0; t_a–)
for(int t_b = b; t_b > 0; t_b–)
check(t_a, t_b, c);
clock_t toc = clock();
itr += 1;
if( itr > report_after ) {
printf(
“Report #%d: a=%d, b=%d, c=%d, time=%.2f seconds\n”,
report, a, b, c, (double)(toc – tic) * 100.0 / CLOCKS_PER_SEC
);
report += 1;
itr = 0;
}
}
return 0;
}