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hw-02: Final implementation

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This commit is contained in:
Tomáš Kléger 2025-10-22 08:44:14 +02:00
parent a3b40590a6
commit 3565364e12
1 changed files with 80 additions and 117 deletions
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203
homework-02-rail-building/main.c
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@ -1,3 +1,4 @@
#include <math.h>
#include <stdbool.h> #include <stdbool.h>
#include <stdio.h> #include <stdio.h>
#include <stdlib.h> #include <stdlib.h>
@ -6,117 +7,107 @@
#define debug(...) ((void)0) #define debug(...) ((void)0)
#else #else
#define debug(fmt, ...) \ #define debug(fmt, ...) \
fprintf(stdout, "[DEBUG %s:%d %s()] " fmt "\n", __FILE__, __LINE__, \ printf("[DEBUG %s:%d %s()] " fmt "\n", __FILE__, __LINE__, \
__func__, ##__VA_ARGS__) __func__, ##__VA_ARGS__)
#endif #endif
typedef long long int lli; typedef long long int lli;
typedef long double ld;
typedef struct rails_t { typedef struct rails_t {
lli rail_length_1; lli r1;
lli *larger_length; lli r2;
lli rail_length_2; lli d;
lli *shorter_length;
lli total_distance;
} rails_t; } rails_t;
// find the pivot using the smaller of the rail lengths typedef struct eea_gcd_t {
// once pivot is found, the smallest step that will be used is lli g;
// gcd(rail length 1, rail length 2) lli x;
// lli y;
} eea_gcd_t;
int invalid_input() { int invalid_input() {
printf("Nespravny vstup.\n"); printf("Nespravny vstup.\n");
return EXIT_FAILURE; return EXIT_FAILURE;
} }
// https://www.geeksforgeeks.org/dsa/steins-algorithm-for-finding-gcd/ eea_gcd_t extended_euclidian_gcd(lli a, lli b) {
int gcd(int a, int b) { if (a == 0) {
if (a == 0) eea_gcd_t res;
return b; res.g = b;
if (b == 0) res.x = 0;
return a; res.y = 1;
return res;
int k;
for (k = 0; ((a | b) & 1) == 0; ++k) {
a >>= 1;
b >>= 1;
} }
while ((a & 1) == 0) eea_gcd_t res = extended_euclidian_gcd(b % a, a);
a >>= 1;
do { lli x = res.y - (b / a) * res.x;
while ((b & 1) == 0) lli y = res.x;
b >>= 1;
if (a > b) { res.x = x;
a ^= b; res.y = y;
b ^= a;
a ^= b; return res;
} }
b = (b - a);
} while (b != 0);
return a << k;
}
lli find_pivot(rails_t rails) {
lli pivot = -1;
lli current_step;
lli ratio = (rails.total_distance / *rails.shorter_length);
for (lli i = 1; i < ratio; i++) {
current_step = rails.total_distance - i * (*rails.shorter_length);
if (current_step % (*rails.larger_length) == 0) {
debug("Found pivot %lld\n", i);
pivot = i;
break;
}
}
return pivot;
}
lli find_smallest_step(rails_t rails) {
return *rails.larger_length / gcd(rails.rail_length_1, rails.rail_length_2);
}
lli find_solutions(rails_t rails, bool verbose) { lli find_solutions(rails_t rails, bool verbose) {
lli variants = 0; lli variants = 0;
lli pivot = find_pivot(rails); if (rails.d == 0) {
lli smallest_step = find_smallest_step(rails); debug("Zero total distance");
debug("Smallest step = %lld", smallest_step); if (verbose) {
printf("= %lld * 0 + %lld * 0\n", rails.r1, rails.r2);
if (pivot != -1) {
lli i;
for (i = pivot;; i += smallest_step) {
if ((rails.total_distance - i * (*rails.shorter_length)) < 0) {
break;
} }
return 1;
}
if (rails.r1 == 0 && rails.d % rails.r2 == 0) {
if (verbose) {
printf("= %lld * %lld + %lld * 0\n", rails.r1, rails.d / rails.r2,
rails.r2);
}
return 1;
}
if (rails.r2 == 0 && rails.d % rails.r1 == 0) {
if (verbose) {
printf("= %lld * 0 + %lld * %lld\n", rails.r1, rails.r2,
rails.d / rails.r1);
}
return 1;
}
eea_gcd_t eea = extended_euclidian_gcd(rails.r1, rails.r2);
lli g = eea.g;
if (rails.d % g != 0) {
return 0;
}
ld d_g = (ld)rails.d / (ld)g;
ld x0 = (ld)eea.x * d_g;
ld y0 = (ld)eea.y * d_g;
lli a_g = rails.r1 / g;
lli b_g = rails.r2 / g;
lli n_min = (lli)ceil(-x0 / (ld)b_g);
lli n_max = (lli)floor(y0 / (ld)a_g);
if (n_max < n_min) {
return 0;
}
variants += n_max - n_min + 1;
if (verbose) { if (verbose) {
for (lli n = n_min; n <= n_max; n++) {
if (*rails.shorter_length == rails.rail_length_1) { lli x = x0 + n * b_g;
printf("= %lld * %lld + %lld * %lld\n", rails.rail_length_1, i, lli y = y0 - n * a_g;
rails.rail_length_2, printf("= %lld * %lld + %lld * %lld\n", rails.r1, x, rails.r2, y);
(rails.total_distance - i * rails.rail_length_1) /
rails.rail_length_2);
} else {
printf("= %lld * %lld + %lld * %lld\n", rails.rail_length_1,
(rails.total_distance - i * rails.rail_length_2) /
rails.rail_length_1,
rails.rail_length_2, i);
}
}
variants++;
} }
} }
@ -128,7 +119,7 @@ int main() {
lli rail_length_1 = -1, rail_length_2 = -1; lli rail_length_1 = -1, rail_length_2 = -1;
if (scanf(" %lld %lld", &rail_length_1, &rail_length_2) != 2 || if (scanf(" %lld %lld", &rail_length_1, &rail_length_2) != 2 ||
(rail_length_1 <= 0 && rail_length_2 <= 0) || (rail_length_1 <= 0 || rail_length_2 <= 0) ||
(rail_length_1 == rail_length_2)) { (rail_length_1 == rail_length_2)) {
return invalid_input(); return invalid_input();
} }
@ -143,47 +134,19 @@ int main() {
return invalid_input(); return invalid_input();
} }
lli variants = 0;
bool verbose = operand == '+';
if (total_distance < 0) { if (total_distance < 0) {
return invalid_input(); return invalid_input();
} }
if (total_distance == 0) {
if (verbose) {
printf("= %lld * 0 + %lld * 0\n", rail_length_1, rail_length_2);
}
variants++;
} else if (rail_length_1 == 0 && total_distance % rail_length_2 == 0) {
if (verbose) {
printf("= %lld * %lld + %lld * 0\n", rail_length_1,
total_distance / rail_length_2, rail_length_2);
}
} else if (rail_length_2 == 0 && total_distance % rail_length_1 == 0) {
if (verbose) {
printf("= %lld * 0 + %lld * %lld\n", rail_length_1, rail_length_2,
total_distance / rail_length_1);
}
} else if (rail_length_1 > 0 && rail_length_2 > 0) {
lli *smaller = lli variants = 0;
rail_length_1 > rail_length_2 ? &rail_length_2 : &rail_length_1; bool verbose = operand == '+';
lli *larger =
rail_length_1 > rail_length_2 ? &rail_length_1 : &rail_length_2; if (rail_length_1 > 0 && rail_length_2 > 0) {
rails_t rails; rails_t rails;
rails.rail_length_1 = rail_length_1; rails.r1 = rail_length_1;
rails.rail_length_2 = rail_length_2; rails.r2 = rail_length_2;
rails.total_distance = total_distance; rails.d = total_distance;
rails.shorter_length = smaller;
rails.larger_length = larger;
if (total_distance % rail_length_1 == 0) {
if (verbose) {
printf("= %lld * %lld + %lld * 0\n", rail_length_1,
total_distance / rail_length_1, rail_length_2);
}
variants++;
}
variants += find_solutions(rails, verbose); variants += find_solutions(rails, verbose);
} }