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quickselect.c
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156 lines (143 loc) · 7.21 KB
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#include "data.table.h"
// from good ol' Numerical Recipes in C
static inline void iswap(int *a, int *b) { int tmp = *a; *a = *b; *b = tmp; }
static inline void dswap(double *a, double *b) { double tmp = *a; *a = *b; *b = tmp; }
static inline void i64swap(int64_t *a, int64_t *b) { int64_t tmp = *a; *a = *b; *b = tmp; }
#undef BODY
#define BODY(SWAP) \
if (n == 0) return NA_REAL; \
int med = n / 2 - (n % 2 == 0); \
unsigned long ir = n - 1, l = 0; \
for(;;) { \
if (ir <= l + 1) { \
if (ir == l + 1 && x[ir] < x[l]) { \
SWAP(x + l, x + ir); \
} \
break; \
} else { \
unsigned long mid = (l + ir) >> 1; \
SWAP(x + mid, x + l + 1); \
if (x[l] > x[ir]) { \
SWAP(x + l, x + ir); \
} \
if (x[l + 1] > x[ir]) { \
SWAP(x + l + 1, x + ir); \
} \
if (x[l] > x[l + 1]) { \
SWAP(x + l, x + l + 1); \
} \
unsigned long i = l + 1, j = ir; \
a = x[l + 1]; \
for (;;) { \
do i++; while (x[i] < a); \
do j--; while (x[j] > a); \
if (j < i) break; \
SWAP(x + i, x + j); \
} \
x[l + 1] = x[j]; \
x[j] = a; \
if (j >= med) ir = j - 1; \
if (j <= med) l = i; \
} \
} \
a = x[med]; \
if (n % 2 == 1) { \
return (double)a; \
} else { \
b = x[med + 1]; \
for (int i = med + 2; i < n; i++) { \
if (x[i] < b) b = x[i]; \
} \
return ((double)a + (double)b) / 2.0; \
}
double dquickselect(double *x, int n)
{
double a, b;
BODY(dswap);
}
double iquickselect(int *x, int n)
{
int a, b;
BODY(iswap);
}
double i64quickselect(int64_t *x, int n)
{
int64_t a, b;
BODY(i64swap);
}
// Floyd-Rivest selection algorithm
// https://en.wikipedia.org/wiki/Floyd%E2%80%93Rivest_algorithm
#undef DEFINE_FLOYD_RIVEST_SELECT_FN
#define DEFINE_FLOYD_RIVEST_SELECT_FN(SELECT_FN, TYPE, SWAP) \
static void SELECT_FN(TYPE *x, unsigned long left, unsigned long right, unsigned long k) { \
while (right > left) { \
if (right - left > 600) { \
unsigned long n = right - left + 1; \
unsigned long i = k - left + 1; \
double z = log((double)n); \
double s = 0.5 * exp(2.0 * z / 3.0); \
double sd = 0.5 * sqrt(z * s * (n - s) / n); \
long delta = (long)i - (long)(n / 2); \
if (delta < 0) sd = -sd; \
else if (delta == 0) sd = 0.0; \
double new_left = (double)k - (double)i * s / n + sd; \
double new_right = (double)k + (double)(n - i) * s / n + sd; \
unsigned long newL = (unsigned long)MAX((long)left, (long)new_left); \
unsigned long newR = (unsigned long)MIN((long)right, (long)new_right); \
SELECT_FN(x, newL, newR, k); \
} \
TYPE pivot = x[k]; \
unsigned long i = left, j = right; \
SWAP(x + left, x + k); \
if (x[right] > pivot) { \
SWAP(x + right, x + left); \
} \
while (i < j) { \
SWAP(x + i, x + j); \
i++; j--; \
while (x[i] < pivot) i++; \
while (x[j] > pivot) j--; \
} \
if (x[left] == pivot) { \
SWAP(x + left, x + j); \
} else { \
j++; \
SWAP(x + j, x + right); \
} \
if (j <= k) left = j + 1; \
if (k <= j) right = j - 1; \
} \
}
DEFINE_FLOYD_RIVEST_SELECT_FN(dfloyd_rivest_select, double, dswap)
DEFINE_FLOYD_RIVEST_SELECT_FN(ifloyd_rivest_select, int, iswap)
DEFINE_FLOYD_RIVEST_SELECT_FN(i64floyd_rivest_select, int64_t, i64swap)
#undef FLOYD_RIVEST_BODY
#define FLOYD_RIVEST_BODY(TYPE, SELECTFN) \
if (n == 0) return NA_REAL; \
unsigned long med = n / 2 - (n % 2 == 0); \
SELECTFN(x, 0, n - 1, med); \
a = x[med]; \
if (n % 2 == 1) { \
return (double)a; \
} else { \
b = x[med + 1]; \
for (unsigned long i = med + 2; i < (unsigned long)n; i++) { \
if (x[i] < b) b = x[i]; \
} \
return ((double)a + (double)b) / 2.0; \
}
double dfloyd_rivest(double *x, int n)
{
double a, b;
FLOYD_RIVEST_BODY(double, dfloyd_rivest_select);
}
double ifloyd_rivest(int *x, int n)
{
int a, b;
FLOYD_RIVEST_BODY(int, ifloyd_rivest_select);
}
double i64floyd_rivest(int64_t *x, int n)
{
int64_t a, b;
FLOYD_RIVEST_BODY(int64_t, i64floyd_rivest_select);
}