574 lines
20 KiB
C
574 lines
20 KiB
C
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// AI framework
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// - rlyeh, public domain.
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//
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// [src] original A-star code by @mmozeiko (PD) - https://gist.github.com/mmozeiko/68f0a8459ef2f98bcd879158011cc275
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// [src] original swarm/boids code by @Cultrarius (UNLICENSE) - https://github.com/Cultrarius/Swarmz
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// boids/swarm -----------------------------------------------------------------
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vec3 rnd3() { // random uniform
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float theta = randf() * C_PI * 2;
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float r = sqrt(randf());
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float z = sqrt(1.0f - r * r) * (randf() > 0.5f ? -1.0f : 1.0f);
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return vec3(r * cos(theta), r * sin(theta), z);
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}
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int less3(vec3 *lhs, vec3 *rhs) {
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if(lhs->x != rhs->x) return lhs->x - rhs->x;
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if(lhs->y != rhs->y) return lhs->y - rhs->y;
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if(lhs->z != rhs->z) return lhs->z - rhs->z;
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return 0;
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}
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uint64_t hash3(vec3 *v) {
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uint64_t h1 = hash_flt(v->x);
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uint64_t h2 = hash_flt(v->y);
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uint64_t h3 = hash_flt(v->z);
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return (h1 * 31 + h2) * 31 + h3;
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}
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vec3 clamplen3(vec3 v, float length) {
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return len3(v) <= length ? v : scale3(norm3(v), length);
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}
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float transform_distance(float distance, SWARM_DISTANCE type) {
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float quad;
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/**/ if (type == SWARM_DISTANCE_LINEAR) return distance;
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else if (type == SWARM_DISTANCE_QUADRATIC) return distance * distance;
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else if (type == SWARM_DISTANCE_INVERSE_LINEAR) return distance == 0 ? 0 : 1 / distance;
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else if (type == SWARM_DISTANCE_INVERSE_QUADRATIC) return (quad = distance * distance), (quad == 0 ? 0 : 1 / quad);
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return distance; // throw exception instead?
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}
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typedef struct nearby_boid_t {
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boid_t *boid;
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vec3 direction;
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float distance;
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} nearby_boid_t;
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static
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vec3 get_voxel_for_boid(float perception_radius, const boid_t *b) { // quantize position
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float r = absf(perception_radius);
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return vec3( (int)(b->position.x / r), (int)(b->position.y / r), (int)(b->position.z / r) );
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}
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static
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void check_voxel_for_boids(float perception_radius, float blindspot_angledeg_compare_value, array(boid_t*) voxel_cached, array(nearby_boid_t) *result, const vec3 voxelPos, const boid_t *b) {
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for each_array_ptr(voxel_cached, const boid_t*, test) {
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vec3 p1 = b->position;
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vec3 p2 = (*test)->position;
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vec3 vec = sub3(p2, p1);
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float distance = len3(vec);
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float compare_value = 0;
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float l1 = len3(vec);
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float l2 = len3(b->velocity);
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if (l1 != 0 && l2 != 0) {
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compare_value = dot3(neg3(b->velocity), vec) / (l1 * l2);
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}
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if ((&b) != test && distance <= perception_radius && (blindspot_angledeg_compare_value > compare_value || len3(b->velocity) == 0)) {
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nearby_boid_t nb;
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nb.boid = (boid_t*)*test;
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nb.distance = distance;
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nb.direction = vec;
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array_push(*result, nb);
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}
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}
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}
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static
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array(nearby_boid_t) get_nearby_boids(const swarm_t *self, const boid_t *b) {
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array(nearby_boid_t) result = 0;
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array_reserve(result, array_count(self->boids));
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vec3 voxelPos = get_voxel_for_boid(self->perception_radius, b);
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voxelPos.x -= 1;
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voxelPos.y -= 1;
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voxelPos.z -= 1;
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for (int x = 0; x < 3; x++) {
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for (int y = 0; y < 3; y++) {
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for (int z = 0; z < 3; z++) {
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array(boid_t*) *found = map_find(self->voxel_cache_, &voxelPos);
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if( found ) check_voxel_for_boids(self->perception_radius, self->blindspot_angledeg_compare_value_, *found, &result, voxelPos, b);
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voxelPos.z++;
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}
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voxelPos.z -= 3;
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voxelPos.y++;
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}
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voxelPos.y -= 3;
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voxelPos.x++;
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}
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return result;
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}
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static
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void update_boid(swarm_t *self, boid_t *b) {
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vec3 separation_sum = {0};
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vec3 heading_sum = {0};
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vec3 position_sum = {0};
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vec3 po = b->position;
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array(nearby_boid_t) nearby = get_nearby_boids(self, b); // @leak
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for each_array_ptr(nearby, nearby_boid_t, closeboid_t) {
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if (closeboid_t->distance == 0) {
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separation_sum = add3(separation_sum, scale3(rnd3(), 1000)); //addscale3
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}
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else {
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float separation_factor = transform_distance(closeboid_t->distance, self->separation_type);
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separation_sum = add3(separation_sum, scale3(neg3(closeboid_t->direction), separation_factor)); // addscale3
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}
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heading_sum = add3(heading_sum, closeboid_t->boid->velocity); // inc3
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position_sum = add3(position_sum, closeboid_t->boid->position); // inc3
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}
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vec3 steering_target = b->position;
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float target_distance = -1;
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for( int i = 0, end = array_count(self->steering_targets); i < end; ++i ) {
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vec3 *target = &self->steering_targets[i];
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float distance = transform_distance(len3(sub3(*target,b->position)), self->steering_target_type);
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if (target_distance < 0 || distance < target_distance) {
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steering_target = *target;
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target_distance = distance;
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}
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}
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int nearby_size = array_count(nearby);
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// Separation: steer to avoid crowding local flockmates
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vec3 separation = nearby_size > 0 ? scale3(separation_sum, 1.f / nearby_size) : separation_sum;
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// Alignment: steer towards the average heading of local flockmates
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vec3 alignment = nearby_size > 0 ? scale3(heading_sum, 1.f / nearby_size) : heading_sum;
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// Cohesion: steer to move toward the average position of local flockmates
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vec3 avgposition = nearby_size > 0 ? scale3(position_sum, 1.f / nearby_size) : b->position;
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vec3 cohesion = sub3(avgposition, b->position);
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// Steering: steer towards the nearest target location (like a moth to the light)
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vec3 steering = scale3(norm3(sub3(steering_target, b->position)), target_distance);
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// calculate boid acceleration
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vec3 acceleration;
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acceleration = scale3(separation, self->separation_weight);
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acceleration = add3(acceleration, scale3(alignment, self->alignment_weight));
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acceleration = add3(acceleration, scale3(cohesion, self->cohesion_weight));
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acceleration = add3(acceleration, scale3(steering, self->steering_weight));
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b->acceleration = clamplen3(acceleration, self->max_acceleration);
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}
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swarm_t swarm() {
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swarm_t self = {0};
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self.boids = NULL;
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self.perception_radius = 3; // 30
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self.separation_weight = 0.1; // 1
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self.separation_type = SWARM_DISTANCE_INVERSE_QUADRATIC;
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self.alignment_weight = 0.1; // 1
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self.cohesion_weight = 0.1; // 1
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self.steering_weight = 0.1; // 0.1
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// array_push(self.steering_targets, vec3(0,0,0));
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self.steering_target_type = SWARM_DISTANCE_LINEAR;
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self.blindspot_angledeg = 2; // 20
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self.max_acceleration = 1; // 10;
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self.max_velocity = 2; // 20;
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self.blindspot_angledeg_compare_value_ = 0; // = cos(M_PI * 2 * blindspot_angledeg / 360)
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map_init(self.voxel_cache_, less3, hash3);
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return self;
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}
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void swarm_update_acceleration_only(swarm_t *self) {
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self->perception_radius += !self->perception_radius; // 0->1
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// build voxel cache
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map_clear(self->voxel_cache_);
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for( int i = 0, end = array_count(self->boids); i < end; ++i ) {
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boid_t *b = &(self->boids)[i];
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vec3 *key = MALLOC(sizeof(vec3));
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*key = get_voxel_for_boid(self->perception_radius, b);
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array(boid_t*) *found = map_find_or_add_allocated_key( self->voxel_cache_, key, 0 );
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array_push(*found, b);
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}
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// update all boids
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for( int i = 0, end = array_count(self->boids); i < end; ++i ) {
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boid_t *b = &(self->boids)[i];
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update_boid(self, b);
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}
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}
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void swarm_update_acceleration_and_velocity_only(swarm_t *self, float delta) {
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self->blindspot_angledeg_compare_value_ = cosf(C_PI * 2 * self->blindspot_angledeg / 360.0f);
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swarm_update_acceleration_only(self);
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for( int i = 0, end = array_count(self->boids); i < end; ++i ) {
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boid_t *b = &(self->boids)[i];
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b->velocity = clamplen3(add3(b->velocity, scale3(b->acceleration, delta)), self->max_velocity);
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}
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}
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void swarm_update(swarm_t *self, float delta) {
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swarm_update_acceleration_and_velocity_only(self, delta);
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for( int i = 0, end = array_count(self->boids); i < end; ++i ) {
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boid_t *b = &(self->boids)[i];
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b->prev_position = b->position;
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b->position = add3(b->position, scale3(b->velocity, delta));
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}
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}
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int ui_swarm(swarm_t *self) {
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const char *distances[] = {
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"Linear",
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"Inverse Linear",
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"Quadratic",
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"Inverse Quadratic"
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};
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int rc = 0;
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rc |= ui_float( "Perception Radius", &self->perception_radius);
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ui_separator();
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rc |= ui_float( "Separation Weight", &self->separation_weight);
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rc |= ui_radio( "Separation Type", distances, countof(distances), (int*)&self->separation_type);
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ui_separator();
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rc |= ui_float( "Alignment Weight", &self->alignment_weight);
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rc |= ui_float( "Cohesion Weight", &self->cohesion_weight);
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ui_separator();
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rc |= ui_float( "Steering Weight", &self->steering_weight);
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//array(vec3) steering_targets;
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rc |= ui_radio( "Steering Target Type", distances, countof(distances), (int*)&self->steering_target_type);
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ui_separator();
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rc |= ui_float( "Blindspot Angle", &self->blindspot_angledeg);
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rc |= ui_float( "Max Acceleration", &self->max_acceleration);
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rc |= ui_float( "Max Velocity", &self->max_velocity);
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return rc;
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}
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// pathfinding -----------------------------------------------------------------
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int pathfind_astar(int width, int height, const unsigned* map, vec2i src, vec2i dst, vec2i* path, size_t maxpath) {
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#define ALLOW_DIAGONAL_MOVEMENT 1
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#if ALLOW_DIAGONAL_MOVEMENT
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#define ASTAR_DIR_COUNT 8
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#else
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#define ASTAR_DIR_COUNT 4
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#endif
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static const vec2i dir[ASTAR_DIR_COUNT] =
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{
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{ 1, 0 },
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{ 0, 1 },
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{ -1, 0 },
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{ 0, -1 },
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#if ALLOW_DIAGONAL_MOVEMENT
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{ 1, 1 },
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{ 1, -1 },
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{ -1, 1 },
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{ -1, -1 },
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#endif
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};
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#define ASTAR_POS_TYPE vec2i
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#define ASTAR_POS_START src
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#define ASTAR_POS_FINISH dst
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#define ASTAR_POS_INDEX(p) ((p).y * width + (p).x)
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#define ASTAR_MAX_INDEX (width * height)
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#define ASTAR_INDEX_POS(p, i) \
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do { \
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(p).x = (i) % width; \
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(p).y = (i) / width; \
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} while (0)
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#define ASTAR_POS_EQUAL(a, b) ((a).x == (b).x && (a).y == (b).y)
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#define ASTAR_MAP_IS_FREE(p) ((p).y >= 0 && (p).y < height && (p).x >= 0 && (p).x < width && (char)map[(p).y * width + (p).x] == 0)
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#define ASTAR_NEXT_POS(p, i) \
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do { \
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(p).x += dir[i].x; \
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(p).y += dir[i].y; \
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} while (0)
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#define ASTAR_PREV_POS(p, i) \
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do { \
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(p).x -= dir[i].x; \
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(p).y -= dir[i].y; \
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} while (0)
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#define ASTAR_GET_COST(a, b) (abs((a).x - (b).x) + abs((a).y - (b).y))
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#if ALLOW_DIAGONAL_MOVEMENT
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#define ASTAR_EXTRA_COST(i) (i < 4 ? 5 : 7) // 7/5 is approx sqrt(2)
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#define ASTAR_COST_MUL 5
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#endif
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size_t path_count = 0;
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#define ASTAR_PATH(p) if (path_count < maxpath) path[path_count++] = p
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// tempwork memory, not thread-safe.
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#define ASTAR_TEMP_SIZE (ASTAR_MAX_INDEX * (sizeof(unsigned)*2) + sizeof(unsigned)*4) // (16<<20)
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#define ASTAR_TEMP temp
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static array(char) ASTAR_TEMP; do_once array_resize(ASTAR_TEMP, ASTAR_TEMP_SIZE);
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// #if 1 "astar.h"
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{
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// generic A* pathfinding
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//
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// INTERFACE
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//
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// mandatory macros
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#ifndef ASTAR_POS_TYPE
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#error ASTAR_POS_TYPE should specify position type
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_POS_START
|
||
|
|
#error ASTAR_POS_START should specify start position
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_POS_FINISH
|
||
|
|
#error ASTAR_POS_FINISH should specify finish position
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_POS_INDEX
|
||
|
|
#error ASTAR_POS_INDEX(p) should specify macro to map position to index
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_MAX_INDEX
|
||
|
|
#error ASTAR_MAX_INDEX should specify max count of indices the position can map to
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_INDEX_POS
|
||
|
|
#error ASTAR_INDEX_POS(i) should specify macro to map index to position
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_POS_EQUAL
|
||
|
|
#error ASTAR_POS_EQUAL(a, b) should specify macro to compare if two positions are the same
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_MAP_IS_FREE
|
||
|
|
#error ASTAR_MAP_IS_FREE(p) should specify macro to check if map at position p is free
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_NEXT_POS
|
||
|
|
#error ASTAR_NEXT_POS(p, i) should specify macro to get next position in specific direction
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_PREV_POS
|
||
|
|
#error ASTAR_PREV_POS(p, i) should specify macro to get previous position from specific direction
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_DIR_COUNT
|
||
|
|
#error ASTAR_DIR_COUNT should specify possible direction count
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_GET_COST
|
||
|
|
#error ASTAR_GET_COST(a, b) should specify macro to get get cost between two positions
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef ASTAR_PATH
|
||
|
|
#error ASTAR_PATH(p) should specify macro that will be invoked on each position for path (in reverse order), including start/finish positions
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#if !defined(ASTAR_TEMP) || !defined(ASTAR_TEMP_SIZE)
|
||
|
|
#error ASTAR_TEMP and ASTAR_TEMP_SIZE should specify variable & size for temporary memory (should be at least ASTAR_MAX_INDEX * 4 + extra)
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// optional macros
|
||
|
|
|
||
|
|
// adds extra cost for specific direction (useful for increasing cost for diagonal movements)
|
||
|
|
#ifndef ASTAR_EXTRA_COST
|
||
|
|
#define ASTAR_EXTRA_COST(i) 1
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// multiplier for adding cost values (current_cost + mul * new_cost) - useful when using extra cost for diagonal movements
|
||
|
|
#ifndef ASTAR_COST_MUL
|
||
|
|
#define ASTAR_COST_MUL 1
|
||
|
|
#endif
|
||
|
|
|
||
|
|
//
|
||
|
|
// IMPLEMENTATION
|
||
|
|
//
|
||
|
|
|
||
|
|
#if ASTAR_DIR_COUNT <= 4
|
||
|
|
#define ASTAR_DIR_BITS 2
|
||
|
|
#elif ASTAR_DIR_COUNT <= 8
|
||
|
|
#define ASTAR_DIR_BITS 3
|
||
|
|
#elif ASTAR_DIR_COUNT <= 16
|
||
|
|
#define ASTAR_DIR_BITS 4
|
||
|
|
#elif ASTAR_DIR_COUNT <= 32
|
||
|
|
#define ASTAR_DIR_BITS 5
|
||
|
|
#elif ASTAR_DIR_COUNT <= 64
|
||
|
|
#define ASTAR_DIR_BITS 6
|
||
|
|
#else
|
||
|
|
#error Too many elements for ASTAR_DIR_COUNT, 64 is max
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#define ASTAR_COST_BITS (32 - 1 - ASTAR_DIR_BITS)
|
||
|
|
|
||
|
|
#define ASTAR_HEAP_SWAP(a, b) \
|
||
|
|
do { \
|
||
|
|
heapnode t = heap[a]; \
|
||
|
|
heap[a] = heap[b]; \
|
||
|
|
heap[b] = t; \
|
||
|
|
} while (0) \
|
||
|
|
|
||
|
|
#define ASTAR_HEAP_PUSH(idx, c) \
|
||
|
|
do { \
|
||
|
|
heap[heap_count].index = idx; \
|
||
|
|
heap[heap_count].cost = c; \
|
||
|
|
int i = heap_count++; \
|
||
|
|
int p = (i - 1) / 2; \
|
||
|
|
while (i != 0 && heap[p].cost > heap[i].cost) \
|
||
|
|
{ \
|
||
|
|
ASTAR_HEAP_SWAP(i, p); \
|
||
|
|
i = p; \
|
||
|
|
p = (i - 1) / 2; \
|
||
|
|
} \
|
||
|
|
} while (0)
|
||
|
|
|
||
|
|
#define ASTAR_HEAP_POP() \
|
||
|
|
do { \
|
||
|
|
heap[0] = heap[--heap_count]; \
|
||
|
|
int i = 0; \
|
||
|
|
for (;;) \
|
||
|
|
{ \
|
||
|
|
int l = 2 * i + 1; \
|
||
|
|
int r = 2 * i + 2; \
|
||
|
|
int s = i; \
|
||
|
|
if (l < heap_count && heap[l].cost < heap[i].cost) s = l; \
|
||
|
|
if (r < heap_count && heap[r].cost < heap[s].cost) s = r; \
|
||
|
|
if (s == i) break; \
|
||
|
|
ASTAR_HEAP_SWAP(i, s); \
|
||
|
|
i = s; \
|
||
|
|
} \
|
||
|
|
} while (0)
|
||
|
|
|
||
|
|
typedef union {
|
||
|
|
struct {
|
||
|
|
unsigned int cost : ASTAR_COST_BITS;
|
||
|
|
unsigned int dir : ASTAR_DIR_BITS;
|
||
|
|
unsigned int visited : 1;
|
||
|
|
};
|
||
|
|
unsigned int all;
|
||
|
|
} node;
|
||
|
|
|
||
|
|
typedef struct {
|
||
|
|
unsigned int index;
|
||
|
|
unsigned int cost;
|
||
|
|
} heapnode;
|
||
|
|
|
||
|
|
if (ASTAR_TEMP_SIZE >= sizeof(node) * ASTAR_MAX_INDEX + sizeof(heapnode))
|
||
|
|
{
|
||
|
|
node* nodes = (node*)ASTAR_TEMP;
|
||
|
|
for (unsigned int i = 0; i < ASTAR_MAX_INDEX; i++)
|
||
|
|
{
|
||
|
|
nodes[i].all = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
heapnode* heap = (heapnode*)((char*)ASTAR_TEMP + sizeof(node) * ASTAR_MAX_INDEX);
|
||
|
|
unsigned int heap_max = (ASTAR_TEMP_SIZE - sizeof(node) * ASTAR_MAX_INDEX) / sizeof(heapnode);
|
||
|
|
int heap_count = 0;
|
||
|
|
|
||
|
|
ASTAR_POS_TYPE p = ASTAR_POS_START;
|
||
|
|
unsigned int nindex = ASTAR_POS_INDEX(p);
|
||
|
|
node* n = nodes + nindex;
|
||
|
|
n->cost = 0;
|
||
|
|
n->visited = 1;
|
||
|
|
ASTAR_HEAP_PUSH(nindex, ASTAR_GET_COST(p, ASTAR_POS_FINISH));
|
||
|
|
|
||
|
|
int found = 0;
|
||
|
|
while (heap_count != 0)
|
||
|
|
{
|
||
|
|
nindex = heap[0].index;
|
||
|
|
n = nodes + nindex;
|
||
|
|
ASTAR_HEAP_POP();
|
||
|
|
|
||
|
|
ASTAR_INDEX_POS(p, nindex);
|
||
|
|
if (ASTAR_POS_EQUAL(p, ASTAR_POS_FINISH))
|
||
|
|
{
|
||
|
|
found = 1;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
n->visited = 1;
|
||
|
|
|
||
|
|
for (unsigned int i = 0; i < ASTAR_DIR_COUNT; i++)
|
||
|
|
{
|
||
|
|
ASTAR_POS_TYPE next = p;
|
||
|
|
ASTAR_NEXT_POS(next, i);
|
||
|
|
if (ASTAR_MAP_IS_FREE(next))
|
||
|
|
{
|
||
|
|
unsigned int nnext_index = ASTAR_POS_INDEX(next);
|
||
|
|
node* nnext = nodes + nnext_index;
|
||
|
|
unsigned int cost = n->cost + ASTAR_EXTRA_COST(i);
|
||
|
|
if (nnext->visited == 0 || cost < nnext->cost)
|
||
|
|
{
|
||
|
|
nnext->cost = cost;
|
||
|
|
nnext->dir = i;
|
||
|
|
nnext->visited = 1;
|
||
|
|
if (heap_count == heap_max)
|
||
|
|
{
|
||
|
|
// out of memory
|
||
|
|
goto bail;
|
||
|
|
}
|
||
|
|
unsigned int new_cost = cost + ASTAR_COST_MUL * ASTAR_GET_COST(next, ASTAR_POS_FINISH);
|
||
|
|
ASTAR_HEAP_PUSH(nnext_index, new_cost);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
bail:
|
||
|
|
|
||
|
|
if (found)
|
||
|
|
{
|
||
|
|
ASTAR_PATH(p);
|
||
|
|
while (!ASTAR_POS_EQUAL(p, ASTAR_POS_START))
|
||
|
|
{
|
||
|
|
ASTAR_PREV_POS(p, n->dir);
|
||
|
|
n = nodes + ASTAR_POS_INDEX(p);
|
||
|
|
ASTAR_PATH(p);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// not enough temp memory
|
||
|
|
}
|
||
|
|
|
||
|
|
#undef ASTAR_POS_TYPE
|
||
|
|
#undef ASTAR_POS_START
|
||
|
|
#undef ASTAR_POS_FINISH
|
||
|
|
#undef ASTAR_POS_INDEX
|
||
|
|
#undef ASTAR_MAX_INDEX
|
||
|
|
#undef ASTAR_INDEX_POS
|
||
|
|
#undef ASTAR_POS_EQUAL
|
||
|
|
#undef ASTAR_MAP_IS_FREE
|
||
|
|
#undef ASTAR_NEXT_POS
|
||
|
|
#undef ASTAR_PREV_POS
|
||
|
|
#undef ASTAR_DIR_COUNT
|
||
|
|
#undef ASTAR_GET_COST
|
||
|
|
#undef ASTAR_EXTRA_COST
|
||
|
|
#undef ASTAR_COST_MUL
|
||
|
|
#undef ASTAR_PATH
|
||
|
|
#undef ASTAR_TEMP
|
||
|
|
#undef ASTAR_TEMP_SIZE
|
||
|
|
#undef ASTAR_COST_BITS
|
||
|
|
#undef ASTAR_DIR_BITS
|
||
|
|
#undef ASTAR_HEAP_SWAP
|
||
|
|
#undef ASTAR_HEAP_PUSH
|
||
|
|
#undef ASTAR_HEAP_POP
|
||
|
|
}
|
||
|
|
// #endif "astar.h"
|
||
|
|
|
||
|
|
return path_count;
|
||
|
|
}
|