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#include <algds/sort.h>
#include <errno.h>
#include <ctype.h>
#include <algds/vec.h>
#include <algds/str.h>
#include <stdio.h>
typedef struct {
int x;
int y;
int z;
} Vec3;
long distance(Vec3 a, Vec3 b) {
long dx = a.x - b.x;
long dy = a.y - b.y;
long dz = a.z - b.z;
return dx * dx + dy * dy + dz * dz;
}
#define PANIC do { \
fprintf(stderr, "panic at %s:%d\n", __FILE__, __LINE__); \
abort(); \
} while (0)
void expect_char(char e) {
int c = fpeek(stdin);
if (c != e) {
PANIC;
}
fgetc(stdin);
}
bool string2long(const char *s, long *num) {
char *end;
errno = 0;
*num = strtol(s, &end, 10);
if (end == s) {
return false;
}
if (errno != 0) {
return false;
}
return true;
}
int64_t parse_integer() {
long ret;
StrBuilder sb;
StrBuilder_init(&sb);
while (1) {
int c = fpeek(stdin);
if (isdigit(c)) {
fgetc(stdin);
StrBuilder_append_char(&sb, c);
} else {
break;
}
}
if (strlen(sb.buf) == 0) {
PANIC;
}
StrBuilder_append_char(&sb, '\0');
if (!string2long(sb.buf, &ret)) {
PANIC;
}
free(sb.buf);
return ret;
}
Vec3 parse_vec3() {
int x = parse_integer();
expect_char(',');
int y = parse_integer();
expect_char(',');
int z = parse_integer();
return (Vec3){.x = x, .y = y, .z = z};
}
void Vec3_show(Vec3 self, FILE *fp) {
fprintf(fp, "(%d,%d,%d)", self.x, self.y, self.z);
}
VECTOR_DEF(Vec3)
VECTOR_IMPL(Vec3)
typedef struct {
int ia;
int ib;
long distance;
} DistanceEntry;
void DistanceEntry_show(DistanceEntry self, FILE *fp) {
fprintf(fp, "(%d->%d: %ld)", self.ia, self.ib, self.distance);
}
VECTOR_DEF(DistanceEntry)
VECTOR_IMPL(DistanceEntry)
int DistanceEntry_cmp(DistanceEntry a, DistanceEntry b) {
if (a.distance < b.distance) return -1;
if (a.distance > b.distance) return 1;
return 0;
}
QSORT_DEF(DistanceEntry)
QSORT_IMPL(DistanceEntry)
VECTOR_DEF(IntVector);
VECTOR_IMPL(IntVector);
void mark_circuit(IntVector *circuit, IntVectorVector *neighbors, int nid, int cid) {
circuit->buffer[nid] = cid;
for (int i = 0; i < neighbors->buffer[nid].size; i++) {
int next = neighbors->buffer[nid].buffer[i];
if (circuit->buffer[next] != cid) {
mark_circuit(circuit, neighbors, next, cid);
}
}
}
int main() {
Vec3Vector junctions;
Vec3Vector_init(&junctions);
while (1) {
int c = fpeek(stdin);
if (!isdigit(c)) {
break;
}
Vec3 v = parse_vec3();
c = fpeek(stdin);
if (c == '\n') {
fgetc(stdin);
}
Vec3Vector_push_back(&junctions, v);
}
DistanceEntryVector distances;
DistanceEntryVector_init(&distances);
for (int i = 0; i < Vec3Vector_len(&junctions); i++) {
for (int j = i + 1; j < Vec3Vector_len(&junctions); j++) {
long d = distance(junctions.buffer[i], junctions.buffer[j]);
DistanceEntryVector_push_back(&distances, (DistanceEntry){.ia = i, .ib = j, .distance = d});
}
}
DistanceEntry_qsort(distances.buffer, distances.size);
IntVectorVector neighbors;
IntVectorVector_init(&neighbors);
for (int i = 0; i < junctions.size; i++) {
IntVector v;
IntVector_init(&v);
IntVectorVector_push_back(&neighbors, v);
}
for (int i = 0; i < 1000; i++) {
int ida = distances.buffer[i].ia;
int idb = distances.buffer[i].ib;
IntVector_push_back(&neighbors.buffer[ida], idb);
IntVector_push_back(&neighbors.buffer[idb], ida);
}
IntVector circuit;
IntVector_init(&circuit);
for (int i = 0; i < junctions.size; i++) {
IntVector_push_back(&circuit, i);
}
for (int i = 0; i < junctions.size; i++) {
if (circuit.buffer[i] == i) {
mark_circuit(&circuit, &neighbors, i, i);
}
}
IntVector circuit_size;
IntVector_init(&circuit_size);
for (int i = 0; i < junctions.size; i++) {
IntVector_push_back(&circuit_size, 0);
}
for (int i = 0; i < circuit.size; i++) {
int cid = circuit.buffer[i];
circuit_size.buffer[cid]++;
}
Int_qsort(circuit_size.buffer, circuit_size.size);
int len = circuit_size.size;
long ret = circuit_size.buffer[len - 1] * circuit_size.buffer[len - 2] * circuit_size.buffer[len - 3];
printf("%ld\n", ret);
IntVector_free(&circuit_size);
IntVector_free(&circuit);
for (int i = 0; i < neighbors.size; i++) {
IntVector_free(&neighbors.buffer[i]);
}
IntVectorVector_free(&neighbors);
DistanceEntryVector_free(&distances);
Vec3Vector_free(&junctions);
return 0;
}
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