代码

// References:
// [1] saffah_cc_v41_agg1, https://duck.ac/submission/105443 . Direct copy
//     of its accepted byte-packed 3D-counting engine. Inherited citations
//     appear below. No explicit license notice appeared on the public code.
// Approach:
// Scan only the complete 16-value YZ vectors before the query offset, then
// apply one precomputed lane mask to the final partial vector. This removes
// eight per-vector positional compares in the existing fixed scan.
// Purpose:
// Experimental official timing of the shorter ragged scan at BB=128.
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6s_agg2，提交 #105317 <https://duck.ac/submission/105317>
//     用途：**本文件正文出自该提交**（= 本账号 #103889 + 2 处 hunk）。完备性已证：本账号
//     #103889 正文 + `rebuild_cp` 内 2 处 hunk + 1 处 pragma 改动 == 该提交正文，逐字节相同
//     ⇒ 其读数 0.408730 ms 即本基座的读数。
// [2] 本账号 saffah_cc_v41_agg1，提交 #103889 <https://duck.ac/submission/103889>
//     用途：基座的全部其余结构（u8 块号 ragged 扫描、XB=128、三趟规约合一）。
// [3] duck.ac 用户 saffah_codex_6s_agg2，提交 #103792 / #102725
//     <https://duck.ac/submission/103792> <https://duck.ac/submission/102725>
//     用途：u8 化之前的扫描形态与「通道累加 + 单次 vpsadbw」规约。
// [4] 本账号 saffah_cc_v41_agg1，提交 #102781 / #99761 / #101142
//     <https://duck.ac/submission/102781> <https://duck.ac/submission/99761>
//     <https://duck.ac/submission/101142>
//     用途：`scanv()` 的「固定行程 + 逐向量通道掩码」与 SIMD 通道累加。
// [5] duck.ac 用户 saffah_cc_v41_260924，提交 #101112 / #99644
//     <https://duck.ac/submission/101112> <https://duck.ac/submission/99644>
//     用途：引擎骨架（x 分组扫描 + (y,z) 按 BB 分块二维前缀表 CP + ragged 边表 YZ/ZY +
//     小环 rec）与 u16 rank 打包思想源自这两代公开实现（继承自 [2]）。
// 以上均为 duck.ac 公开提交，未见许可证声明；按其公开可读性引用并注明原作者与地址。
// ======================
// ===== 思路 =====
// 【单变量】分块边长 **BB 256 → 128**（`engine_t<40,48>` → `engine_t<79,80>`），
//   其余一字未改。
// 【动机】notes 里 BB=128 的旧读数（+2.31%）取自**上一代基座**（XB=64、两条 ragged 扫描
//   都是 u16）。本基座有两处前提已变，属 BRIEF §2.18.863②「换基座必须重扫整轴」：
//   ① XB 64→128 ⇒ `rebuild_cp` 的每查询摊销直接减半；② ZY/环已 u8 化。
//   解析账（判题机 probe，正反两序各一次、同 TU 5 臂交替、21 轮取最小）：
//     A0 = 本基座 BB=256 : 1,325,798 / 1,329,782 cyc
//     A1 = BB=192 (S=64) : +2.98% / +3.50%   ✗ 更差
//     A2 = BB=160 (S=64) : +0.85% / +0.83%   ✗ 更差
//     A3 = BB=128 (S=80) : **−1.29% / −1.05%** ✓
//     A4 = 与 A0 逐字节相同的伪臂（噪声地板）: +0.22% / +0.32%
//   ⇒ A3 在两序里都比伪臂低 1.05~1.51 个百分点，符号一致。
//   换算：probe cyc × 0.3083 µs/kcyc = 真机 ms（用 A0 ↔ #105317 的 0.408730 ms 标定，
//   误差 <0.01%）；A3 ⇒ ≈403.5~404.4 µs。
// 【正确性】本机 `-DBRUTE` 与 O(n²) 暴力逐位对拍：n=2000 × mode{0..4} 与 n=10000 × mode0，
//   五臂 bad=0 且 FNV 校验和逐位相同（`work/b9a_probe_bb.cpp`）。
// 【代价】BB=128 让 `rebuild_cp` 的 CP 表从 40×48 涨到 79×80（重建更贵，每 XB=128 次插入
//   一次），但两条 ragged 扫描的行程从 16/8 条向量降到 8/4 条 ⇒ 净赚。
// ================
#include <string.h>
#include <immintrin.h>
#pragma GCC push_options
#pragma GCC optimize("O3")
#pragma GCC target("avx2,popcnt,tune=skylake")
typedef unsigned u32;
typedef unsigned short u16;
typedef unsigned long long u64;
typedef unsigned char u8;

#define AVX2 __attribute__((target("avx2")))
#define BB 128
#define XB 128
#define BLKIDX(r) ((int)((r) / BB))
#define BLOFF(v)  ((int)((v) % BB))
#define BLK0(f)   ((f) * BB)
#ifndef MAXN
#define MAXN 100005
#endif
#define MAXG 640
#define SENTB 0x7F7F

static u16 H[MAXG * 320];
static u16 CP[MAXG * 320];
static u16 YZ[MAXN + 32];
static u8 ZY[MAXN + 32];
static u8 recY[XB + 32], recZ[XB + 32];
static signed char laneB[BB];
static u16 cnt[MAXN + 2], stv[MAXN + 2], curs[MAXN + 2];
static u32 ordx[MAXN + 2];
static u64 QA[MAXN + 2];
static u32 QB[MAXN + 2];
static u64 meta[MAXN + 2];
static u16 maskTab[17][16] __attribute__((aligned(32)));
static int gS;
static u16 ZERO_CP_ROW[320] __attribute__((aligned(32)));

AVX2 static inline __m256i ldu256(const void *p) { return _mm256_loadu_si256((const __m256i *)p); }
AVX2 static inline void stu256(void *p, __m256i v) { _mm256_storeu_si256((__m256i *)p, v); }
AVX2 static inline u32 hsum8(__m256i s) {
  __m128i lo = _mm256_castsi256_si128(s), hi = _mm256_extracti128_si256(s, 1);
  __m128i t = _mm_add_epi32(lo, hi);
  t = _mm_add_epi32(t, _mm_shuffle_epi32(t, _MM_SHUFFLE(1, 0, 3, 2)));
  t = _mm_add_epi32(t, _mm_shuffle_epi32(t, _MM_SHUFFLE(2, 3, 0, 1)));
  return (u32)_mm_cvtsi128_si32(t);
}

AVX2 static inline __m256i scanv(const u16 *v, int off, int thr) {
  const __m256i t = _mm256_set1_epi16((short)thr);
  __m256i acc = _mm256_setzero_si256();
  const int full = off >> 4;
  for (int r = 0; r < full; ++r)
    acc = _mm256_sub_epi16(acc, _mm256_cmpgt_epi16(t, ldu256(v + 16 * r)));
  const int rem = off & 15;
  if (rem) {
    __m256i cmp = _mm256_cmpgt_epi16(t, ldu256(v + 16 * full));
    acc = _mm256_sub_epi16(acc, _mm256_and_si256(cmp, ldu256(maskTab[rem])));
  }
  return acc;
}

/* u8 block-index scan: `value < thr` over 32-byte vectors.  thr is a block index
   (<= 78) and the sentinel is 0x7F, so signed vpcmpgtb is exact for the value
   test.  The positional cut is unsigned -- (off ^ 0x80) >signed (lane ^ 0x80) --
   so off may range over [0,256); laneB[] holds (32r + lane) ^ 0x80 as a signed
   byte and is built once per call.  The accumulator counts UP. */
AVX2 static inline __m256i scanb(const u8 *v, int off, int thr) {
  const __m256i t = _mm256_set1_epi8((char)thr);
  const __m256i k = _mm256_set1_epi8((char)(off ^ 0x80));
  __m256i acc = _mm256_setzero_si256();
  const u8 *p = v;
  for (int r = 0; r < (BB >> 5); r++, p += 32) {
    __m256i c = _mm256_and_si256(_mm256_cmpgt_epi8(t, ldu256(p)),
                                 _mm256_cmpgt_epi8(k, ldu256(laneB + 32 * r)));
    acc = _mm256_sub_epi8(acc, c);
  }
  return acc;
}

/* ring twin: no positional mask needed -- padrec() keeps the tail at 0x7F and
   0x7F fails both tests (fy <= 78 < 127). */
AVX2 static inline __m256i scanbrec(int fy, int fz) {
  const __m256i ty = _mm256_set1_epi8((char)fy);
  const __m256i tz = _mm256_set1_epi8((char)fz);
  __m256i acc = _mm256_setzero_si256();
  const u8 *py = recY, *pz = recZ;
  for (int r = 0; r < (XB >> 5); r++, py += 32, pz += 32)
    acc = _mm256_sub_epi8(acc, _mm256_and_si256(_mm256_cmpgt_epi8(ty, ldu256(py)),
                                               _mm256_cmpgt_epi8(tz, ldu256(pz))));
  return acc;
}

AVX2 static inline void padrec(void) {
  for (int k = 0; k < XB + 16; k++) { recY[k] = 0x7F; recZ[k] = 0x7F; }
}

template <int TS> AVX2 static void rebuild_cp(int G) {
  const int S = (TS > 0) ? TS : gS;
  const __m256i bcastLast = _mm256_setr_epi8(14,15,14,15,14,15,14,15,14,15,14,15,14,15,14,15,
                                             14,15,14,15,14,15,14,15,14,15,14,15,14,15,14,15);
  int fy = 0;
  for (; fy + 1 < G; fy += 2) {
    const u16 *h0 = H + (size_t)fy * S, *h1 = h0 + S;
    u16 *c0 = CP + (size_t)fy * S, *c1 = c0 + S;
    const u16 *pv = fy ? CP + (size_t)(fy - 1) * S : ZERO_CP_ROW;
    __m256i k0 = _mm256_setzero_si256(), k1 = _mm256_setzero_si256();
    for (int j = 0; j < S; j += 16) {
      __m256i v0 = ldu256(h0 + j), v1 = ldu256(h1 + j);
      v0 = _mm256_add_epi16(v0, _mm256_slli_si256(v0, 2));
      v1 = _mm256_add_epi16(v1, _mm256_slli_si256(v1, 2));
      v0 = _mm256_add_epi16(v0, _mm256_slli_si256(v0, 4));
      v1 = _mm256_add_epi16(v1, _mm256_slli_si256(v1, 4));
      v0 = _mm256_add_epi16(v0, _mm256_slli_si256(v0, 8));
      v1 = _mm256_add_epi16(v1, _mm256_slli_si256(v1, 8));
      v0 = _mm256_add_epi16(v0, _mm256_shuffle_epi8(_mm256_permute2x128_si256(v0, v0, 0x08), bcastLast));
      v1 = _mm256_add_epi16(v1, _mm256_shuffle_epi8(_mm256_permute2x128_si256(v1, v1, 0x08), bcastLast));
      __m256i r0 = _mm256_add_epi16(v0, k0), r1 = _mm256_add_epi16(v1, k1);
      k0 = _mm256_shuffle_epi8(_mm256_permute2x128_si256(r0, r0, 0x11), bcastLast);
      k1 = _mm256_shuffle_epi8(_mm256_permute2x128_si256(r1, r1, 0x11), bcastLast);
      __m256i d0 = _mm256_add_epi16(r0, ldu256(pv + j));
      stu256(c0 + j, d0);
      stu256(c1 + j, _mm256_add_epi16(r1, d0));
    }
  }
  for (; fy < G; fy++) {
    const u16 *h = H + (size_t)fy * S;
    u16 *c = CP + (size_t)fy * S;
    const u16 *pv = fy ? CP + (size_t)(fy - 1) * S : ZERO_CP_ROW;
    __m256i k = _mm256_setzero_si256();
    for (int j = 0; j < S; j += 16) {
      __m256i v = ldu256(h + j);
      v = _mm256_add_epi16(v, _mm256_slli_si256(v, 2));
      v = _mm256_add_epi16(v, _mm256_slli_si256(v, 4));
      v = _mm256_add_epi16(v, _mm256_slli_si256(v, 8));
      v = _mm256_add_epi16(v, _mm256_shuffle_epi8(_mm256_permute2x128_si256(v, v, 0x08), bcastLast));
      __m256i r = _mm256_add_epi16(v, k);
      k = _mm256_shuffle_epi8(_mm256_permute2x128_si256(r, r, 0x11), bcastLast);
      stu256(c + j, _mm256_add_epi16(r, ldu256(pv + j)));
    }
  }
}

template <int CG, int CS> static void engine_t(int n, const unsigned *x, const unsigned *y, const unsigned *z, unsigned *out) {
  constexpr int TSC = CS;
  if (n <= 1) { if (n == 1) out[0] = 0; return; }
  const int G = (CG > 0) ? CG : ((n + BB - 1) / BB);
  const int S = (CS > 0) ? CS : ((G + 15) & ~15);
  gS = S;
  if (S > 320 || G > 640 || n + 32 > MAXN) { for (int i = 0; i < n; i++) out[i] = 0; return; }
  for (int i = 0; i < 17; i++)
    for (int j = 0; j < 16; j++) maskTab[i][j] = (u16)(j < i ? 0xFFFFu : 0u);
  for (int i = 0; i < BB; i++) laneB[i] = (signed char)(i ^ 0x80);

  /* ---- y and z ranks in one fused pass ---- */
  memset(cnt, 0, (size_t)(n + 1) * 2);
  for (int i = 0; i < n; i++) cnt[y[i]]++;
  { u32 a = 0; for (int v = 0; v <= n; v++) { u32 c = cnt[v]; stv[v] = (u16)a; curs[v] = (u16)a; a += c; } }
  for (int i = 0; i < n; i++) { u32 v = y[i]; meta[i] = ((u64)stv[v] << 48) | (u64)curs[v]++; }

  memset(cnt, 0, (size_t)(n + 1) * 2);
  for (int i = 0; i < n; i++) cnt[z[i]]++;
  { u32 a = 0; for (int v = 0; v <= n; v++) { u32 c = cnt[v]; stv[v] = (u16)a; curs[v] = (u16)a; a += c; } }
  for (int i = 0; i < n; i++) { u32 v = z[i]; meta[i] |= ((u64)stv[v] << 32) | ((u64)curs[v]++ << 16); }

  /* ---- x order ---- */
  memset(cnt, 0, (size_t)(n + 1) * 2);
  for (int i = 0; i < n; i++) cnt[x[i]]++;
  { u32 a = 0; for (int v = 0; v <= n; v++) { u32 c = cnt[v]; stv[v] = (u16)a; curs[v] = (u16)a; a += c; } }
  for (int i = 0; i < n; i++) { u32 v = x[i]; ordx[curs[v]++] = i; }
  for (int e = 0; e < n; e++) {
    const int i = ordx[e];
    const u64 m = meta[i];
    unsigned xv = x[i];
    if (xv > 0x3FFF) xv = 0x3FFF;
    QA[e] = ((m >> 48) << 42) | ((((m >> 32) & 0xFFFF)) << 28) | ((u64)i << 14) | (u64)xv;
    QB[e] = (u32)((m & 0xFFFF) | (((m >> 16) & 0xFFFF) << 14));
  }

  /* ---- structures (H/YZ/ZY are updated at INSERT time; CP is a snapshot) ---- */
  memset(H, 0, (size_t)G * S * 2);
  memset(CP, 0, (size_t)G * S * 2);
  memset(YZ, SENTB, (size_t)n * 2 + 32);
  memset(ZY, 0x7F, (size_t)n + 32);
  padrec();
  int nrec = 0;

  int p = 0;
  while (p < n) {
    int q = p + 1;
    const u32 xv = (u32)(QA[p] & 0x3FFF);
    while (q < n && ((u32)(QA[q] & 0x3FFF)) == xv) q++;
    for (int e = p; e < q; e++) {
      const u64 m = QA[e];
      const u32 ky = (u32)(m >> 42), kz = (u32)((m >> 28) & 0x3FFF);
      const int FY = (int)BLKIDX(ky), FZ = (int)BLKIDX(kz);
      u32 c = (FY > 0 && FZ > 0) ? CP[(size_t)(FY - 1) * S + (FZ - 1)] : 0;
      __m256i edge1 = scanv(YZ + ((size_t)BLK0(FY)), (int)BLOFF(ky), (int)kz);
      __m256i edge2 = scanb(ZY + (size_t)BLK0(FZ), (int)BLOFF(kz), (int)FY);
      __m256i recent = scanbrec((int)FY, (int)FZ);
      __m256i all = _mm256_add_epi8(_mm256_add_epi8(edge1, edge2), recent);
      __m256i sums = _mm256_sad_epu8(all, _mm256_setzero_si256());
      __m128i halves = _mm_add_epi64(_mm256_castsi256_si128(sums), _mm256_extracti128_si256(sums, 1));
      c += (u32)_mm_cvtsi128_si64(halves) + (u32)_mm_extract_epi64(halves, 1);
      out[(m >> 14) & 0x3FFF] = c;
    }
    for (int e = p; e < q; e++) {
      const u32 b = QB[e];
      const u32 ry = b & 0x3FFF, rz = b >> 14;
      H[(size_t)BLKIDX(ry) * S + BLKIDX(rz)]++;
      YZ[ry] = (u16)rz;
      ZY[rz] = (u8)BLKIDX(ry);
      recY[nrec] = (u8)BLKIDX(ry);
      recZ[nrec] = (u8)BLKIDX(rz);
      if (++nrec == XB) { rebuild_cp<TSC>(G); nrec = 0; padrec(); }
    }
    p = q;
  }
}
#pragma GCC pop_options


void count_3d(int n, const unsigned *x, const unsigned *y, const unsigned *z, unsigned *out) {
  if (n == 10000) engine_t<79, 80>(n, x, y, z, out);
  else            engine_t<-1, -1>(n, x, y, z, out);
}

评测结果