代码

// 4D strict dominance via prefix-bitset blocking + AVX2.
// v5: 2-point MLP in the AND+popcount loop + ordrank-table partial-block handling.
#pragma GCC target("avx2")
#include <cstring>
#include <cstdlib>
#include <immintrin.h>

typedef unsigned u32;
typedef unsigned long long u64;

static int order[4][100010];
static int first_pos[4][100010];
static int cnt[100010];
static int seen[100010];
static int ordrank[4][4][100010];
static int stamp = 0;
static u32 partial[100010];

static inline u32 pc256(__m256i v){
    const __m256i lut = _mm256_setr_epi8(
        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);
    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);
    __m256i s = _mm256_add_epi8(lo, hi);
    __m256i sad = _mm256_sad_epu8(s, _mm256_setzero_si256());
    return (u32)(_mm256_extract_epi64(sad,0) + _mm256_extract_epi64(sad,1)
               + _mm256_extract_epi64(sad,2) + _mm256_extract_epi64(sad,3));
}

void count_4d(int n, const unsigned *x[4], unsigned *out) {
    int NW = (n + 63) >> 6;
    const int B = 32;
    int M = (n + B - 1) / B;

    for (int d = 0; d < 4; 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 d = 0; d < 4; d++)
        for (int a = 0; a < 4; a++)
            for (int t = 0; t < n; t++)
                ordrank[d][a][t] = first_pos[a][order[d][t]];

    u64 *pref = (u64*)malloc((size_t)4 * (M + 1) * NW * sizeof(u64));
    for (int d = 0; d < 4; d++) {
        u64 *p = pref + (size_t)d * (M + 1) * NW;
        memset(p, 0, (size_t)NW * sizeof(u64));   // only block 0 = zeros
        for (int b = 0; b < M; b++) {
            u64 *cur = p + (size_t)(b + 1) * NW;
            u64 *prev = p + (size_t)b * NW;
            // vectorized copy of NW u64s (prev -> cur)
            int w = 0;
            for (; w + 16 <= NW; w += 16) {
                _mm256_storeu_si256((__m256i*)(cur + w),     _mm256_loadu_si256((const __m256i*)(prev + w)));
                _mm256_storeu_si256((__m256i*)(cur + w + 4), _mm256_loadu_si256((const __m256i*)(prev + w + 4)));
                _mm256_storeu_si256((__m256i*)(cur + w + 8), _mm256_loadu_si256((const __m256i*)(prev + w + 8)));
                _mm256_storeu_si256((__m256i*)(cur + w + 12), _mm256_loadu_si256((const __m256i*)(prev + w + 12)));
            }
            for (; w < NW; w++) cur[w] = prev[w];
            int e = (b + 1) * B; if (e > n) e = n;
            for (int t = b * B; t < e; t++) {
                int pt = order[d][t];
                cur[pt >> 6] |= 1ULL << (pt & 63);
            }
        }
    }

    u64 *p0 = pref;
    u64 *p1 = pref + (size_t)(M + 1) * NW;
    u64 *p2 = pref + (size_t)2 * (M + 1) * NW;
    u64 *p3 = pref + (size_t)3 * (M + 1) * NW;

    // ---- pass 1: AND + popcount, 2 points at a time ----
    for (int pos = 0; pos < n; pos += 2) {
        int j0 = order[0][pos];
        int j1 = (pos + 1 < n) ? order[0][pos + 1] : -1;
        {
            int pf = pos + 16;
            if (pf < n) {
                int jf = order[0][pf];
                _mm_prefetch((const char*)(p0 + (size_t)(first_pos[0][jf] / B) * NW), _MM_HINT_T0);
                _mm_prefetch((const char*)(p1 + (size_t)(first_pos[1][jf] / B) * NW), _MM_HINT_T0);
                _mm_prefetch((const char*)(p2 + (size_t)(first_pos[2][jf] / B) * NW), _MM_HINT_T0);
                _mm_prefetch((const char*)(p3 + (size_t)(first_pos[3][jf] / B) * NW), _MM_HINT_T0);
            }
        }
        const u64 *q0a = p0 + (size_t)(first_pos[0][j0] / B) * NW;
        const u64 *q1a = p1 + (size_t)(first_pos[1][j0] / B) * NW;
        const u64 *q2a = p2 + (size_t)(first_pos[2][j0] / B) * NW;
        const u64 *q3a = p3 + (size_t)(first_pos[3][j0] / B) * NW;
        const u64 *q0b = q0a, *q1b = q1a, *q2b = q2a, *q3b = q3a;
        if (j1 >= 0) {
            q0b = p0 + (size_t)(first_pos[0][j1] / B) * NW;
            q1b = p1 + (size_t)(first_pos[1][j1] / B) * NW;
            q2b = p2 + (size_t)(first_pos[2][j1] / B) * NW;
            q3b = p3 + (size_t)(first_pos[3][j1] / B) * NW;
        }
        u32 c0 = 0, c1 = 0;
        int w = 0;
        for (; w + 4 <= NW; w += 4) {
            __m256i a0 = _mm256_loadu_si256((const __m256i*)(q0a + w));
            __m256i a1 = _mm256_loadu_si256((const __m256i*)(q1a + w));
            __m256i a2 = _mm256_loadu_si256((const __m256i*)(q2a + w));
            __m256i a3 = _mm256_loadu_si256((const __m256i*)(q3a + w));
            __m256i b0 = _mm256_loadu_si256((const __m256i*)(q0b + w));
            __m256i b1 = _mm256_loadu_si256((const __m256i*)(q1b + w));
            __m256i b2 = _mm256_loadu_si256((const __m256i*)(q2b + w));
            __m256i b3 = _mm256_loadu_si256((const __m256i*)(q3b + w));
            c0 += pc256(_mm256_and_si256(_mm256_and_si256(a0,a1), _mm256_and_si256(a2,a3)));
            c1 += pc256(_mm256_and_si256(_mm256_and_si256(b0,b1), _mm256_and_si256(b2,b3)));
        }
        for (; w < NW; w++) {
            c0 += (u32)__builtin_popcountll(q0a[w] & q1a[w] & q2a[w] & q3a[w]);
            if (j1 >= 0) c1 += (u32)__builtin_popcountll(q0b[w] & q1b[w] & q2b[w] & q3b[w]);
        }
        partial[j0] = c0;
        if (j1 >= 0) partial[j1] = c1;
    }

    // ---- pass 2: partial-block correction (SIMD compares) ----
    for (int pos = 0; pos < n; pos++) {
        int j = order[0][pos];
        u32 c = partial[j];
        stamp++;
        int f0 = first_pos[0][j], f1 = first_pos[1][j], f2 = first_pos[2][j], f3 = first_pos[3][j];
        int t, mask, k;
        // dim 0 partial: check dims 1,2,3
        {
            int* r1 = ordrank[0][1]; int* r2 = ordrank[0][2]; int* r3 = ordrank[0][3];
            __m256i vf1 = _mm256_set1_epi32(f1), vf2 = _mm256_set1_epi32(f2), vf3 = _mm256_set1_epi32(f3);
            for (t = (f0 / B) * B; t + 8 <= f0; t += 8) {
                __m256i rr1 = _mm256_loadu_si256((const __m256i*)(r1+t));
                __m256i rr2 = _mm256_loadu_si256((const __m256i*)(r2+t));
                __m256i rr3 = _mm256_loadu_si256((const __m256i*)(r3+t));
                __m256i m = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(vf1,rr1), _mm256_cmpgt_epi32(vf2,rr2)), _mm256_cmpgt_epi32(vf3,rr3));
                mask = _mm256_movemask_ps(_mm256_castsi256_ps(m));
                while (mask) { k = __builtin_ctz(mask); int q = order[0][t+k]; if (seen[q] != stamp) { seen[q] = stamp; c++; } mask &= mask - 1; }
            }
            for (; t < f0; t++) if (r1[t] < f1 && r2[t] < f2 && r3[t] < f3) { int q = order[0][t]; if (seen[q] != stamp) { seen[q] = stamp; c++; } }
        }
        // dim 1 partial: check dims 0,2,3
        {
            int* r1 = ordrank[1][0]; int* r2 = ordrank[1][2]; int* r3 = ordrank[1][3];
            __m256i vf1 = _mm256_set1_epi32(f0), vf2 = _mm256_set1_epi32(f2), vf3 = _mm256_set1_epi32(f3);
            for (t = (f1 / B) * B; t + 8 <= f1; t += 8) {
                __m256i rr1 = _mm256_loadu_si256((const __m256i*)(r1+t));
                __m256i rr2 = _mm256_loadu_si256((const __m256i*)(r2+t));
                __m256i rr3 = _mm256_loadu_si256((const __m256i*)(r3+t));
                __m256i m = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(vf1,rr1), _mm256_cmpgt_epi32(vf2,rr2)), _mm256_cmpgt_epi32(vf3,rr3));
                mask = _mm256_movemask_ps(_mm256_castsi256_ps(m));
                while (mask) { k = __builtin_ctz(mask); int q = order[1][t+k]; if (seen[q] != stamp) { seen[q] = stamp; c++; } mask &= mask - 1; }
            }
            for (; t < f1; t++) if (r1[t] < f0 && r2[t] < f2 && r3[t] < f3) { int q = order[1][t]; if (seen[q] != stamp) { seen[q] = stamp; c++; } }
        }
        // dim 2 partial: check dims 0,1,3
        {
            int* r1 = ordrank[2][0]; int* r2 = ordrank[2][1]; int* r3 = ordrank[2][3];
            __m256i vf1 = _mm256_set1_epi32(f0), vf2 = _mm256_set1_epi32(f1), vf3 = _mm256_set1_epi32(f3);
            for (t = (f2 / B) * B; t + 8 <= f2; t += 8) {
                __m256i rr1 = _mm256_loadu_si256((const __m256i*)(r1+t));
                __m256i rr2 = _mm256_loadu_si256((const __m256i*)(r2+t));
                __m256i rr3 = _mm256_loadu_si256((const __m256i*)(r3+t));
                __m256i m = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(vf1,rr1), _mm256_cmpgt_epi32(vf2,rr2)), _mm256_cmpgt_epi32(vf3,rr3));
                mask = _mm256_movemask_ps(_mm256_castsi256_ps(m));
                while (mask) { k = __builtin_ctz(mask); int q = order[2][t+k]; if (seen[q] != stamp) { seen[q] = stamp; c++; } mask &= mask - 1; }
            }
            for (; t < f2; t++) if (r1[t] < f0 && r2[t] < f1 && r3[t] < f3) { int q = order[2][t]; if (seen[q] != stamp) { seen[q] = stamp; c++; } }
        }
        // dim 3 partial: check dims 0,1,2
        {
            int* r1 = ordrank[3][0]; int* r2 = ordrank[3][1]; int* r3 = ordrank[3][2];
            __m256i vf1 = _mm256_set1_epi32(f0), vf2 = _mm256_set1_epi32(f1), vf3 = _mm256_set1_epi32(f2);
            for (t = (f3 / B) * B; t + 8 <= f3; t += 8) {
                __m256i rr1 = _mm256_loadu_si256((const __m256i*)(r1+t));
                __m256i rr2 = _mm256_loadu_si256((const __m256i*)(r2+t));
                __m256i rr3 = _mm256_loadu_si256((const __m256i*)(r3+t));
                __m256i m = _mm256_and_si256(_mm256_and_si256(_mm256_cmpgt_epi32(vf1,rr1), _mm256_cmpgt_epi32(vf2,rr2)), _mm256_cmpgt_epi32(vf3,rr3));
                mask = _mm256_movemask_ps(_mm256_castsi256_ps(m));
                while (mask) { k = __builtin_ctz(mask); int q = order[3][t+k]; if (seen[q] != stamp) { seen[q] = stamp; c++; } mask &= mask - 1; }
            }
            for (; t < f3; t++) if (r1[t] < f0 && r2[t] < f1 && r3[t] < f2) { int q = order[3][t]; if (seen[q] != stamp) { seen[q] = stamp; c++; } }
        }
        out[j] = c;
    }
    free(pref);
}

评测结果