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