| /* Stable-sorting of an array using mergesort. | |
| Copyright (C) 2009-2026 Free Software Foundation, Inc. | |
| Written by Bruno Haible <bruno@clisp.org>, 2009. | |
| This file is free software: you can redistribute it and/or modify | |
| it under the terms of the GNU Lesser General Public License as | |
| published by the Free Software Foundation; either version 2.1 of the | |
| License, or (at your option) any later version. | |
| This file is distributed in the hope that it will be useful, | |
| but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| GNU Lesser General Public License for more details. | |
| You should have received a copy of the GNU Lesser General Public License | |
| along with this program. If not, see <https://www.gnu.org/licenses/>. */ | |
| /* This file implements stable sorting of an array, using the mergesort | |
| algorithm. | |
| Worst-case running time for an array of length N is O(N log N). | |
| Unlike the mpsort module, the algorithm here attempts to minimize not | |
| only the number of comparisons, but also the number of copying operations. | |
| Before including this file, you need to define | |
| ELEMENT The type of every array element. | |
| COMPARE A two-argument macro that takes two 'const ELEMENT *' | |
| pointers and returns a negative, zero, or positive 'int' | |
| value if the element pointed to by the first argument is, | |
| respectively, less, equal, or greater than the element | |
| pointed to by the second argument. | |
| STATIC The storage class of the functions being defined. | |
| STATIC_FROMTO (Optional.) Overrides STATIC for the 'merge_sort_fromto' | |
| function. | |
| Before including this file, you also need to include: | |
| #include <stddef.h> | |
| */ | |
| /* Merge the sorted arrays src1[0..n1-1] and src2[0..n2-1] into | |
| dst[0..n1+n2-1]. In case of ambiguity, put the elements of src1 | |
| before the elements of src2. | |
| n1 and n2 must be > 0. | |
| The arrays src1 and src2 must not overlap the dst array, except that | |
| src1 may be dst[n2..n1+n2-1], or src2 may be dst[n1..n1+n2-1]. */ | |
| static void | |
| merge (const ELEMENT *src1, size_t n1, | |
| const ELEMENT *src2, size_t n2, | |
| ELEMENT *dst) | |
| { | |
| for (;;) /* while (n1 > 0 && n2 > 0) */ | |
| { | |
| if (COMPARE (src1, src2) <= 0) | |
| { | |
| *dst++ = *src1++; | |
| n1--; | |
| if (n1 == 0) | |
| break; | |
| } | |
| else | |
| { | |
| *dst++ = *src2++; | |
| n2--; | |
| if (n2 == 0) | |
| break; | |
| } | |
| } | |
| /* Here n1 == 0 || n2 == 0 but also n1 > 0 || n2 > 0. */ | |
| if (n1 > 0) | |
| { | |
| if (dst != src1) | |
| do | |
| { | |
| *dst++ = *src1++; | |
| n1--; | |
| } | |
| while (n1 > 0); | |
| } | |
| else /* n2 > 0 */ | |
| { | |
| if (dst != src2) | |
| do | |
| { | |
| *dst++ = *src2++; | |
| n2--; | |
| } | |
| while (n2 > 0); | |
| } | |
| } | |
| /* Sort src[0..n-1] into dst[0..n-1], using tmp[0..n/2-1] as temporary | |
| (scratch) storage. | |
| The arrays src, dst, tmp must not overlap. */ | |
| #ifdef STATIC_FROMTO | |
| STATIC_FROMTO | |
| #else | |
| STATIC | |
| #endif | |
| void | |
| merge_sort_fromto (const ELEMENT *src, ELEMENT *dst, size_t n, ELEMENT *tmp) | |
| { | |
| switch (n) | |
| { | |
| case 0: | |
| return; | |
| case 1: | |
| /* Nothing to do. */ | |
| dst[0] = src[0]; | |
| return; | |
| case 2: | |
| /* Trivial case. */ | |
| if (COMPARE (&src[0], &src[1]) <= 0) | |
| { | |
| /* src[0] <= src[1] */ | |
| dst[0] = src[0]; | |
| dst[1] = src[1]; | |
| } | |
| else | |
| { | |
| dst[0] = src[1]; | |
| dst[1] = src[0]; | |
| } | |
| break; | |
| case 3: | |
| /* Simple case. */ | |
| if (COMPARE (&src[0], &src[1]) <= 0) | |
| { | |
| if (COMPARE (&src[1], &src[2]) <= 0) | |
| { | |
| /* src[0] <= src[1] <= src[2] */ | |
| dst[0] = src[0]; | |
| dst[1] = src[1]; | |
| dst[2] = src[2]; | |
| } | |
| else if (COMPARE (&src[0], &src[2]) <= 0) | |
| { | |
| /* src[0] <= src[2] < src[1] */ | |
| dst[0] = src[0]; | |
| dst[1] = src[2]; | |
| dst[2] = src[1]; | |
| } | |
| else | |
| { | |
| /* src[2] < src[0] <= src[1] */ | |
| dst[0] = src[2]; | |
| dst[1] = src[0]; | |
| dst[2] = src[1]; | |
| } | |
| } | |
| else | |
| { | |
| if (COMPARE (&src[0], &src[2]) <= 0) | |
| { | |
| /* src[1] < src[0] <= src[2] */ | |
| dst[0] = src[1]; | |
| dst[1] = src[0]; | |
| dst[2] = src[2]; | |
| } | |
| else if (COMPARE (&src[1], &src[2]) <= 0) | |
| { | |
| /* src[1] <= src[2] < src[0] */ | |
| dst[0] = src[1]; | |
| dst[1] = src[2]; | |
| dst[2] = src[0]; | |
| } | |
| else | |
| { | |
| /* src[2] < src[1] < src[0] */ | |
| dst[0] = src[2]; | |
| dst[1] = src[1]; | |
| dst[2] = src[0]; | |
| } | |
| } | |
| break; | |
| default: | |
| { | |
| size_t n1 = n / 2; | |
| size_t n2 = (n + 1) / 2; | |
| /* Note: n1 + n2 = n, n1 <= n2. */ | |
| /* Sort src[n1..n-1] into dst[n1..n-1], scratching tmp[0..n2/2-1]. */ | |
| merge_sort_fromto (src + n1, dst + n1, n2, tmp); | |
| /* Sort src[0..n1-1] into tmp[0..n1-1], scratching dst[0..n1-1]. */ | |
| merge_sort_fromto (src, tmp, n1, dst); | |
| /* Merge the two half results. */ | |
| merge (tmp, n1, dst + n1, n2, dst); | |
| } | |
| break; | |
| } | |
| } | |
| /* Sort src[0..n-1], using tmp[0..n-1] as temporary (scratch) storage. | |
| The arrays src, tmp must not overlap. */ | |
| STATIC void | |
| merge_sort_inplace (ELEMENT *src, size_t n, ELEMENT *tmp) | |
| { | |
| switch (n) | |
| { | |
| case 0: | |
| case 1: | |
| /* Nothing to do. */ | |
| return; | |
| case 2: | |
| /* Trivial case. */ | |
| if (COMPARE (&src[0], &src[1]) <= 0) | |
| { | |
| /* src[0] <= src[1] */ | |
| } | |
| else | |
| { | |
| ELEMENT t = src[0]; | |
| src[0] = src[1]; | |
| src[1] = t; | |
| } | |
| break; | |
| case 3: | |
| /* Simple case. */ | |
| if (COMPARE (&src[0], &src[1]) <= 0) | |
| { | |
| if (COMPARE (&src[1], &src[2]) <= 0) | |
| { | |
| /* src[0] <= src[1] <= src[2] */ | |
| } | |
| else if (COMPARE (&src[0], &src[2]) <= 0) | |
| { | |
| /* src[0] <= src[2] < src[1] */ | |
| ELEMENT t = src[1]; | |
| src[1] = src[2]; | |
| src[2] = t; | |
| } | |
| else | |
| { | |
| /* src[2] < src[0] <= src[1] */ | |
| ELEMENT t = src[0]; | |
| src[0] = src[2]; | |
| src[2] = src[1]; | |
| src[1] = t; | |
| } | |
| } | |
| else | |
| { | |
| if (COMPARE (&src[0], &src[2]) <= 0) | |
| { | |
| /* src[1] < src[0] <= src[2] */ | |
| ELEMENT t = src[0]; | |
| src[0] = src[1]; | |
| src[1] = t; | |
| } | |
| else if (COMPARE (&src[1], &src[2]) <= 0) | |
| { | |
| /* src[1] <= src[2] < src[0] */ | |
| ELEMENT t = src[0]; | |
| src[0] = src[1]; | |
| src[1] = src[2]; | |
| src[2] = t; | |
| } | |
| else | |
| { | |
| /* src[2] < src[1] < src[0] */ | |
| ELEMENT t = src[0]; | |
| src[0] = src[2]; | |
| src[2] = t; | |
| } | |
| } | |
| break; | |
| default: | |
| { | |
| size_t n1 = n / 2; | |
| size_t n2 = (n + 1) / 2; | |
| /* Note: n1 + n2 = n, n1 <= n2. */ | |
| /* Sort src[n1..n-1], scratching tmp[0..n2-1]. */ | |
| merge_sort_inplace (src + n1, n2, tmp); | |
| /* Sort src[0..n1-1] into tmp[0..n1-1], scratching tmp[n1..2*n1-1]. */ | |
| merge_sort_fromto (src, tmp, n1, tmp + n1); | |
| /* Merge the two half results. */ | |
| merge (tmp, n1, src + n1, n2, src); | |
| } | |
| break; | |
| } | |
| } | |
| #undef ELEMENT | |
| #undef COMPARE | |
| #undef STATIC |