Question:
Task: ch21-quadtree-dp-build-single
            Target file: student_kernel.cu

            Implementation requirements:
- quadtree_build_parent should create a QuadWork covering all points and launch quadtree_node.
- quadtree_node must emit leaves when reaching depth or point thresholds, updating perm and leaf metadata with atomics.
- Otherwise perform two-pass quadrant partitioning (count, scan, scatter) into a device buffer in NW/NE/SW/SE order.
- Launch child nodes for non-empty quadrants, synchronize, and free temporary buffers before returning.

            Here is the current student_kernel.cu:

            ```cuda
            // ch21-quadtree-dp-build-single / student_kernel.cu
#include <cuda_runtime.h>
#include <stdint.h>

// ----------------------------- Data types -----------------------------
struct Bounds { float minx, miny, maxx, maxy; };
__device__ __host__ inline Bounds make_bounds(float a,float b,float c,float d){ return Bounds{a,b,c,d}; }

struct QuadWork {
  const float* x;
  const float* y;
  const int*   idx;         // indices of points for this segment
  int          begin;       // segment begin (relative to idx)
  int          count;       // segment length
  Bounds       b;
  int          depth;
  int          max_depth;
  int          min_points;
  // outputs/globals
  int*         perm;        // output permutation (length n)
  int*         leafOffset;  // length >= n
  int*         leafCount;   // length >= n
  int*         leafCounter; // single int in device memory
  int*         permCursor;  // single int in device memory
};

// Prototypes
__global__ void quadtree_build_parent(const float* x, const float* y, int n,
                                      Bounds root, int max_depth, int min_points,
                                      int* perm, int* leafOffset, int* leafCount,
                                      int* leafCounter, int* permCursor,
                                      const int* idx_root);

__global__ void quadtree_node(QuadWork w);

// ----------------------------- Helpers -----------------------------
__device__ __host__ inline bool in_NW(float px, float py, const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return (px < mx) && (py >= my);
}
__device__ __host__ inline bool in_NE(float px, float py, const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return (px >= mx) && (py >= my);
}
__device__ __host__ inline bool in_SW(float px, float py, const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return (px < mx) && (py < my);
}
__device__ __host__ inline bool in_SE(float px, float py, const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return (px >= mx) && (py < my);
}

__device__ __host__ inline Bounds child_bounds_NW(const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return make_bounds(b.minx, my, mx, b.maxy);
}
__device__ __host__ inline Bounds child_bounds_NE(const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return make_bounds(mx, my, b.maxx, b.maxy);
}
__device__ __host__ inline Bounds child_bounds_SW(const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return make_bounds(b.minx, b.miny, mx, my);
}
__device__ __host__ inline Bounds child_bounds_SE(const Bounds& b){
  float mx=0.5f*(b.minx+b.maxx), my=0.5f*(b.miny+b.maxy);
  return make_bounds(mx, b.miny, b.maxx, my);
}

// ----------------------------- Kernels -----------------------------
__global__ void quadtree_build_parent(const float* x, const float* y, int n,
                                      Bounds root, int max_depth, int min_points,
                                      int* perm, int* leafOffset, int* leafCount,
                                      int* leafCounter, int* permCursor,
                                      const int* idx_root)
{
  // TODO: Construct a QuadWork item for the root node and invoke child kernels
  // to recursively partition the point set.
  if (blockIdx.x == 0 && threadIdx.x == 0) {
    (void)x; (void)y; (void)n;
    (void)root; (void)max_depth; (void)min_points;
    (void)perm; (void)leafOffset; (void)leafCount;
    (void)leafCounter; (void)permCursor; (void)idx_root;
  }
}

__global__ void quadtree_node(QuadWork w)
{
  // TODO: Recursively process the current node, partitioning points into child
  // quadrants and recording leaf metadata.
  if (threadIdx.x == 0) {
    (void)w;
  }
}
            ```


Question:
Task: ch21-quadtree-dp-pack-coalesced
            Target file: student_kernel.cu

            Implementation requirements:
- Use shared memory arrays to track counts, offsets, and cursors for four quadrants.
- Count the number of indices per quadrant within the segment.
- Compute exclusive offsets in NW, NE, SW, SE order.
- Scatter indices back into idx_out[segBegin:segBegin+segCount) with stable ordering within each quadrant.

            Here is the current student_kernel.cu:

            ```cuda
            // ch21-quadtree-dp-pack-coalesced / student_kernel.cu
#include <cuda_runtime.h>
#include <stdint.h>

// TODO: Implement quadrant classification helpers
// Each function should determine if point (px, py) belongs to the specified quadrant
// of the bounding box [minx, miny, maxx, maxy].
//
// Hints:
// - Compute midpoint: mx = (minx + maxx) / 2, my = (miny + maxy) / 2
// - NW (Northwest): px < mx AND py >= my
// - NE (Northeast): px >= mx AND py >= my
// - SW (Southwest): px < mx AND py < my
// - SE (Southeast): px >= mx AND py < my

extern "C" __global__
void pack_quadrants_singleblock(const float* __restrict__ x,
                                const float* __restrict__ y,
                                const int*   __restrict__ idx_in,
                                int*         __restrict__ idx_out,
                                int segBegin, int segCount,
                                float minx, float miny, float maxx, float maxy)
{
  // TODO: Implement quadrant packing with shared memory count/scan/scatter:
  //
  // Step 1: Count phase
  // - Each thread classifies its assigned points into one of 4 quadrants
  // - Use your quadrant helper functions (in_NW, in_NE, in_SW, in_SE)
  // - Store per-thread counts for each quadrant in shared memory
  //
  // Step 2: Parallel scan (prefix sum)
  // - Compute exclusive scan of counts for each quadrant to get write offsets
  // - This ensures stable ordering (preserves input order within each quadrant)
  // - Use __syncthreads() between phases
  //
  // Step 3: Scatter phase
  // - Each thread writes its assigned points to idx_out at computed offsets
  // - NW quadrant: starts at offset 0
  // - NE quadrant: starts at offset count_NW
  // - SW quadrant: starts at offset count_NW + count_NE
  // - SE quadrant: starts at offset count_NW + count_NE + count_SW
  //
  // Hints:
  // - Single block kernel: use blockDim.x threads
  // - Shared memory arrays for counts and offsets
  // - Points are indexed via idx_in[segBegin + i]
  // - Point coordinates: x[idx], y[idx]
  (void)x; (void)y; (void)idx_in; (void)idx_out;
  (void)segBegin; (void)segCount;
  (void)minx; (void)miny; (void)maxx; (void)maxy;
}
            ```