代码

// 5D strict dominance n=3e5: prefix-bitset B=64 with dim0-canonical reindex (triangle)
// + 2-point AND over dims 1-4 truncated by the dim0 triangle + 5-pass responsibility BF.
// The prefix is stored over bit-index = pos_0[point] (dim0 position), so pref_0[b] is the
// contiguous triangle [0, b*B): we skip dim0 entirely and read only the first (b0*B)/64 u64s
// of dims 1-4. This halves AND traffic vs reading all 5 full rows.
#pragma GCC target("avx2,bmi")
#pragma GCC optimize("O3")
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <sys/mman.h>
#include <immintrin.h>

typedef unsigned u32;
typedef unsigned long long u64;

static int order[5][300010];
static int first_pos[5][300010];
static int cnt[300010];
static int ordrank[5][5][300010];
static int ordpos[5][5][300010];
static int pos[5][300010];
static u32 partial[300010];
static u32 corr[300010];
static int proc[300010];

static const unsigned char pc_lut_bytes[32] = {
        0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
        0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4};
static inline __m256i pc_bytes(__m256i v){
    const __m256i lut = _mm256_loadu_si256((const __m256i*)pc_lut_bytes);
    const __m256i m4 = _mm256_set1_epi8(0x0F);
    __m256i lo = _mm256_and_si256(v, m4);
    __m256i hi = _mm256_and_si256(_mm256_srli_epi16(v, 4), m4);
    lo = _mm256_shuffle_epi8(lut, lo); hi = _mm256_shuffle_epi8(lut, hi);
    return _mm256_add_epi8(lo, hi);
}
static inline u32 sum4(__m256i v){
    return (u32)(_mm256_extract_epi64(v,0) + _mm256_extract_epi64(v,1)
               + _mm256_extract_epi64(v,2) + _mm256_extract_epi64(v,3));
}

void count_5d(int n, const unsigned *x[5], unsigned *out) {
    int NW = (n + 63) >> 6;
    int NWp = (NW + 7) & ~7;
    const int B = 1024;
    int M = (n + B - 1) / B;

    for (int d = 0; d < 5; d++) {
        const unsigned *xd = x[d];
        memset(cnt, 0, sizeof(int) * (n + 1));
        for (int i = 0; i < n; i++) cnt[xd[i]]++;
        int s = 0;
        for (int v = 0; v <= (int)n; v++) { int c = cnt[v]; cnt[v] = s; s += c; }
        for (int i = 0; i < n; i++) first_pos[d][i] = cnt[xd[i]];
        memset(cnt, 0, sizeof(int) * (n + 1));
        for (int i = 0; i < n; i++) cnt[xd[i]]++;
        for (int v = 1; v <= (int)n; v++) cnt[v] += cnt[v-1];
        for (int i = n - 1; i >= 0; i--) order[d][--cnt[xd[i]]] = i;
        for (int t = 0; t < n; t++) pos[d][order[d][t]] = t;
    }
    for (int d = 0; d < 5; d++) {
        for (int a = 0; a < 5; a++)
            for (int t = 0; t < n; t++)
                ordrank[d][a][t] = first_pos[a][order[d][t]];
        for (int t = 0; t < n; t++) ordpos[d][0][t] = pos[0][order[d][t]];
        for (int a = 1; a < d; a++)
            for (int t = 0; t < n; t++)
                ordpos[d][a][t] = pos[a][order[d][t]];
    }

    // 2D blocking: within dim-0 superblocks, stable counting-sort by first_pos[1].
    const int S = 32768;
    {
        for (int s = 0; s < n; s += S) {
            int e = s + S; if (e > n) e = n;
            memset(cnt, 0, sizeof(int) * (n + 1));
            for (int t = s; t < e; t++) cnt[first_pos[1][order[0][t]]]++;
            for (int v = 1; v <= (int)n; v++) cnt[v] += cnt[v-1];
            for (int t = e - 1; t >= s; t--) {
                int j = order[0][t];
                proc[s + (--cnt[first_pos[1][j]])] = j;
            }
        }
    }

    // Build only dims 1..4, indexed by bit = pos_0 (dim0 position). pref_0 is the free triangle.
    size_t prefsz = (size_t)4 * (M + 1) * NWp * sizeof(u64);
    void *rawp = malloc(prefsz + 64);
    u64 *pref = (u64*)(((size_t)rawp + 63) & ~(size_t)63);
    for (int d = 1; d < 5; d++) {
        u64 *p = pref + (size_t)(d - 1) * (M + 1) * NWp;
        memset(p, 0, (size_t)NWp * sizeof(u64));
        for (int b = 0; b < M; b++) {
            u64 *cur = p + (size_t)(b + 1) * NWp;
            u64 *prev = p + (size_t)b * NWp;
            memcpy(cur, prev, (size_t)NWp * sizeof(u64));
            int e = (b + 1) * B; if (e > n) e = n;
            for (int t = b * B; t < e; t++) {
                int r = ordpos[d][0][t];
                cur[r >> 6] |= 1ULL << (r & 63);
            }
        }
    }

    u64 *p1 = pref;
    u64 *p2 = pref + (size_t)(M + 1) * NWp;
    u64 *p3 = pref + (size_t)2 * (M + 1) * NWp;
    u64 *p4 = pref + (size_t)3 * (M + 1) * NWp;

    // ---- pass 1: coarse AND + popcount over dims 1-4, truncated by dim0 triangle ----
    for (int pos = 0; pos < n; pos += 2) {
        int pa = proc[pos];
        int pb = (pos + 1 < n) ? proc[pos + 1] : -1;
        int Wa = ((first_pos[0][pa] / B) * B) >> 6;
        int Wb = (pb >= 0) ? (((first_pos[0][pb] / B) * B) >> 6) : 0;
        const u64 *qa1 = p1 + (size_t)(first_pos[1][pa] / B) * NWp;
        const u64 *qa2 = p2 + (size_t)(first_pos[2][pa] / B) * NWp;
        const u64 *qa3 = p3 + (size_t)(first_pos[3][pa] / B) * NWp;
        const u64 *qa4 = p4 + (size_t)(first_pos[4][pa] / B) * NWp;
        const u64 *qb1 = qa1, *qb2 = qa2, *qb3 = qa3, *qb4 = qa4;
        if (pb >= 0) {
            qb1 = p1 + (size_t)(first_pos[1][pb] / B) * NWp;
            qb2 = p2 + (size_t)(first_pos[2][pb] / B) * NWp;
            qb3 = p3 + (size_t)(first_pos[3][pb] / B) * NWp;
            qb4 = p4 + (size_t)(first_pos[4][pb] / B) * NWp;
        }
        int Wm = Wa < Wb ? Wa : Wb;
        __m256i accA = _mm256_setzero_si256();
        __m256i accB = _mm256_setzero_si256();
        int w = 0;
        for (; w + 4 <= Wm; w += 4) {
            __m256i a1 = _mm256_load_si256((const __m256i*)(qa1 + w));
            __m256i a2 = _mm256_load_si256((const __m256i*)(qa2 + w));
            __m256i a3 = _mm256_load_si256((const __m256i*)(qa3 + w));
            __m256i a4 = _mm256_load_si256((const __m256i*)(qa4 + w));
            __m256i b1 = _mm256_load_si256((const __m256i*)(qb1 + w));
            __m256i b2 = _mm256_load_si256((const __m256i*)(qb2 + w));
            __m256i b3 = _mm256_load_si256((const __m256i*)(qb3 + w));
            __m256i b4 = _mm256_load_si256((const __m256i*)(qb4 + w));
            __m256i ra = _mm256_and_si256(_mm256_and_si256(a1,a2), _mm256_and_si256(a3,a4));
            __m256i rb = _mm256_and_si256(_mm256_and_si256(b1,b2), _mm256_and_si256(b3,b4));
            accA = _mm256_add_epi64(accA, _mm256_sad_epu8(pc_bytes(ra), _mm256_setzero_si256()));
            accB = _mm256_add_epi64(accB, _mm256_sad_epu8(pc_bytes(rb), _mm256_setzero_si256()));
        }
        u32 cA = sum4(accA), cB = sum4(accB);
        for (; w < Wm; w++) {
            cA += (u32)__builtin_popcountll(qa1[w] & qa2[w] & qa3[w] & qa4[w]);
            cB += (u32)__builtin_popcountll(qb1[w] & qb2[w] & qb3[w] & qb4[w]);
        }
        for (; w < Wa; w++) {
            cA += (u32)__builtin_popcountll(qa1[w] & qa2[w] & qa3[w] & qa4[w]);
        }
        int wb = Wm;
        for (; wb < Wb; wb++) {
            cB += (u32)__builtin_popcountll(qb1[wb] & qb2[wb] & qb3[wb] & qb4[wb]);
        }
        partial[pa] = cA;
        if (pb >= 0) partial[pb] = cB;
    }

    // ---- pass 2: 5-pass responsibility brute force (exact, zero dedup) ----
    memset(corr, 0, sizeof(u32) * n);

    {
        int* A0 = ordrank[0][1];
        int* A1 = ordrank[0][2];
        int* A2 = ordrank[0][3];
        int* A3 = ordrank[0][4];
        int* Dsel = ordrank[0][0];
        int* Ord = order[0];
        for (int t = 0; t < n; t++) {
            int j = Ord[t];
            int f = Dsel[t];
            int bs = (f / B) * B;
            int t0 = ordrank[0][1][t];
            int t1 = ordrank[0][2][t];
            int t2 = ordrank[0][3][t];
            int t3 = ordrank[0][4][t];
            __m256i v0 = _mm256_set1_epi32(t0);
            __m256i v1 = _mm256_set1_epi32(t1);
            __m256i v2 = _mm256_set1_epi32(t2);
            __m256i v3 = _mm256_set1_epi32(t3);
            int p = bs;
            int cntm = 0;
            for (; p + 16 <= f; p += 16) {
                __m256i a0 = _mm256_loadu_si256((const __m256i*)(A0 + p));
                __m256i a0b = _mm256_loadu_si256((const __m256i*)(A0 + p + 8));
                __m256i a1 = _mm256_loadu_si256((const __m256i*)(A1 + p));
                __m256i a1b = _mm256_loadu_si256((const __m256i*)(A1 + p + 8));
                __m256i a2 = _mm256_loadu_si256((const __m256i*)(A2 + p));
                __m256i a2b = _mm256_loadu_si256((const __m256i*)(A2 + p + 8));
                __m256i a3 = _mm256_loadu_si256((const __m256i*)(A3 + p));
                __m256i a3b = _mm256_loadu_si256((const __m256i*)(A3 + p + 8));
                __m256i ma = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0), _mm256_cmpgt_epi32(v1,a1)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2), _mm256_cmpgt_epi32(v3,a3)));
                __m256i mb = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0b), _mm256_cmpgt_epi32(v1,a1b)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2b), _mm256_cmpgt_epi32(v3,a3b)));
                int mask = _mm256_movemask_ps(_mm256_castsi256_ps(ma)) | (_mm256_movemask_ps(_mm256_castsi256_ps(mb)) << 8);
                cntm += __builtin_popcount(mask);
            }
            for (; p < f; p++) {
                if (A0[p] < t0 && A1[p] < t1 && A2[p] < t2 && A3[p] < t3) cntm++;
            }
            corr[j] += cntm;
        }
    }

    {
        int* A0 = ordpos[1][0];
        int* A1 = ordrank[1][2];
        int* A2 = ordrank[1][3];
        int* A3 = ordrank[1][4];
        int* Dsel = ordrank[1][1];
        int* Ord = order[1];
        for (int t = 0; t < n; t++) {
            int j = Ord[t];
            int f = Dsel[t];
            int bs = (f / B) * B;
            int t0 = (ordrank[1][0][t] / B) * B;
            int t1 = ordrank[1][2][t];
            int t2 = ordrank[1][3][t];
            int t3 = ordrank[1][4][t];
            __m256i v0 = _mm256_set1_epi32(t0);
            __m256i v1 = _mm256_set1_epi32(t1);
            __m256i v2 = _mm256_set1_epi32(t2);
            __m256i v3 = _mm256_set1_epi32(t3);
            int p = bs;
            int cntm = 0;
            for (; p + 16 <= f; p += 16) {
                __m256i a0 = _mm256_loadu_si256((const __m256i*)(A0 + p));
                __m256i a0b = _mm256_loadu_si256((const __m256i*)(A0 + p + 8));
                __m256i a1 = _mm256_loadu_si256((const __m256i*)(A1 + p));
                __m256i a1b = _mm256_loadu_si256((const __m256i*)(A1 + p + 8));
                __m256i a2 = _mm256_loadu_si256((const __m256i*)(A2 + p));
                __m256i a2b = _mm256_loadu_si256((const __m256i*)(A2 + p + 8));
                __m256i a3 = _mm256_loadu_si256((const __m256i*)(A3 + p));
                __m256i a3b = _mm256_loadu_si256((const __m256i*)(A3 + p + 8));
                __m256i ma = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0), _mm256_cmpgt_epi32(v1,a1)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2), _mm256_cmpgt_epi32(v3,a3)));
                __m256i mb = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0b), _mm256_cmpgt_epi32(v1,a1b)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2b), _mm256_cmpgt_epi32(v3,a3b)));
                int mask = _mm256_movemask_ps(_mm256_castsi256_ps(ma)) | (_mm256_movemask_ps(_mm256_castsi256_ps(mb)) << 8);
                cntm += __builtin_popcount(mask);
            }
            for (; p < f; p++) {
                if (A0[p] < t0 && A1[p] < t1 && A2[p] < t2 && A3[p] < t3) cntm++;
            }
            corr[j] += cntm;
        }
    }

    {
        int* A0 = ordpos[2][0];
        int* A1 = ordpos[2][1];
        int* A2 = ordrank[2][3];
        int* A3 = ordrank[2][4];
        int* Dsel = ordrank[2][2];
        int* Ord = order[2];
        for (int t = 0; t < n; t++) {
            int j = Ord[t];
            int f = Dsel[t];
            int bs = (f / B) * B;
            int t0 = (ordrank[2][0][t] / B) * B;
            int t1 = (ordrank[2][1][t] / B) * B;
            int t2 = ordrank[2][3][t];
            int t3 = ordrank[2][4][t];
            __m256i v0 = _mm256_set1_epi32(t0);
            __m256i v1 = _mm256_set1_epi32(t1);
            __m256i v2 = _mm256_set1_epi32(t2);
            __m256i v3 = _mm256_set1_epi32(t3);
            int p = bs;
            int cntm = 0;
            for (; p + 16 <= f; p += 16) {
                __m256i a0 = _mm256_loadu_si256((const __m256i*)(A0 + p));
                __m256i a0b = _mm256_loadu_si256((const __m256i*)(A0 + p + 8));
                __m256i a1 = _mm256_loadu_si256((const __m256i*)(A1 + p));
                __m256i a1b = _mm256_loadu_si256((const __m256i*)(A1 + p + 8));
                __m256i a2 = _mm256_loadu_si256((const __m256i*)(A2 + p));
                __m256i a2b = _mm256_loadu_si256((const __m256i*)(A2 + p + 8));
                __m256i a3 = _mm256_loadu_si256((const __m256i*)(A3 + p));
                __m256i a3b = _mm256_loadu_si256((const __m256i*)(A3 + p + 8));
                __m256i ma = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0), _mm256_cmpgt_epi32(v1,a1)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2), _mm256_cmpgt_epi32(v3,a3)));
                __m256i mb = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0b), _mm256_cmpgt_epi32(v1,a1b)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2b), _mm256_cmpgt_epi32(v3,a3b)));
                int mask = _mm256_movemask_ps(_mm256_castsi256_ps(ma)) | (_mm256_movemask_ps(_mm256_castsi256_ps(mb)) << 8);
                cntm += __builtin_popcount(mask);
            }
            for (; p < f; p++) {
                if (A0[p] < t0 && A1[p] < t1 && A2[p] < t2 && A3[p] < t3) cntm++;
            }
            corr[j] += cntm;
        }
    }

    {
        int* A0 = ordpos[3][0];
        int* A1 = ordpos[3][1];
        int* A2 = ordpos[3][2];
        int* A3 = ordrank[3][4];
        int* Dsel = ordrank[3][3];
        int* Ord = order[3];
        for (int t = 0; t < n; t++) {
            int j = Ord[t];
            int f = Dsel[t];
            int bs = (f / B) * B;
            int t0 = (ordrank[3][0][t] / B) * B;
            int t1 = (ordrank[3][1][t] / B) * B;
            int t2 = (ordrank[3][2][t] / B) * B;
            int t3 = ordrank[3][4][t];
            __m256i v0 = _mm256_set1_epi32(t0);
            __m256i v1 = _mm256_set1_epi32(t1);
            __m256i v2 = _mm256_set1_epi32(t2);
            __m256i v3 = _mm256_set1_epi32(t3);
            int p = bs;
            int cntm = 0;
            for (; p + 16 <= f; p += 16) {
                __m256i a0 = _mm256_loadu_si256((const __m256i*)(A0 + p));
                __m256i a0b = _mm256_loadu_si256((const __m256i*)(A0 + p + 8));
                __m256i a1 = _mm256_loadu_si256((const __m256i*)(A1 + p));
                __m256i a1b = _mm256_loadu_si256((const __m256i*)(A1 + p + 8));
                __m256i a2 = _mm256_loadu_si256((const __m256i*)(A2 + p));
                __m256i a2b = _mm256_loadu_si256((const __m256i*)(A2 + p + 8));
                __m256i a3 = _mm256_loadu_si256((const __m256i*)(A3 + p));
                __m256i a3b = _mm256_loadu_si256((const __m256i*)(A3 + p + 8));
                __m256i ma = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0), _mm256_cmpgt_epi32(v1,a1)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2), _mm256_cmpgt_epi32(v3,a3)));
                __m256i mb = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0b), _mm256_cmpgt_epi32(v1,a1b)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2b), _mm256_cmpgt_epi32(v3,a3b)));
                int mask = _mm256_movemask_ps(_mm256_castsi256_ps(ma)) | (_mm256_movemask_ps(_mm256_castsi256_ps(mb)) << 8);
                cntm += __builtin_popcount(mask);
            }
            for (; p < f; p++) {
                if (A0[p] < t0 && A1[p] < t1 && A2[p] < t2 && A3[p] < t3) cntm++;
            }
            corr[j] += cntm;
        }
    }

    {
        int* A0 = ordpos[4][0];
        int* A1 = ordpos[4][1];
        int* A2 = ordpos[4][2];
        int* A3 = ordpos[4][3];
        int* Dsel = ordrank[4][4];
        int* Ord = order[4];
        for (int t = 0; t < n; t++) {
            int j = Ord[t];
            int f = Dsel[t];
            int bs = (f / B) * B;
            int t0 = (ordrank[4][0][t] / B) * B;
            int t1 = (ordrank[4][1][t] / B) * B;
            int t2 = (ordrank[4][2][t] / B) * B;
            int t3 = (ordrank[4][3][t] / B) * B;
            __m256i v0 = _mm256_set1_epi32(t0);
            __m256i v1 = _mm256_set1_epi32(t1);
            __m256i v2 = _mm256_set1_epi32(t2);
            __m256i v3 = _mm256_set1_epi32(t3);
            int p = bs;
            int cntm = 0;
            for (; p + 16 <= f; p += 16) {
                __m256i a0 = _mm256_loadu_si256((const __m256i*)(A0 + p));
                __m256i a0b = _mm256_loadu_si256((const __m256i*)(A0 + p + 8));
                __m256i a1 = _mm256_loadu_si256((const __m256i*)(A1 + p));
                __m256i a1b = _mm256_loadu_si256((const __m256i*)(A1 + p + 8));
                __m256i a2 = _mm256_loadu_si256((const __m256i*)(A2 + p));
                __m256i a2b = _mm256_loadu_si256((const __m256i*)(A2 + p + 8));
                __m256i a3 = _mm256_loadu_si256((const __m256i*)(A3 + p));
                __m256i a3b = _mm256_loadu_si256((const __m256i*)(A3 + p + 8));
                __m256i ma = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0), _mm256_cmpgt_epi32(v1,a1)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2), _mm256_cmpgt_epi32(v3,a3)));
                __m256i mb = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(v0,a0b), _mm256_cmpgt_epi32(v1,a1b)), _mm256_and_si256(_mm256_cmpgt_epi32(v2,a2b), _mm256_cmpgt_epi32(v3,a3b)));
                int mask = _mm256_movemask_ps(_mm256_castsi256_ps(ma)) | (_mm256_movemask_ps(_mm256_castsi256_ps(mb)) << 8);
                cntm += __builtin_popcount(mask);
            }
            for (; p < f; p++) {
                if (A0[p] < t0 && A1[p] < t1 && A2[p] < t2 && A3[p] < t3) cntm++;
            }
            corr[j] += cntm;
        }
    }

    for (int i = 0; i < n; i++) out[i] = partial[i] + corr[i];
    free(rawp);
}

评测结果