1 #ifndef ASSORTED_SORTS_GROUP
2 #define ASSORTED_SORTS_GROUP
6 // Author : Chris Koeritz
8 // Copyright (c) 1991-$now By Author. This program is free software; you can
9 // redistribute it and/or modify it under the terms of the GNU General Public
10 // License as published by the Free Software Foundation:
11 // http://www.gnu.org/licenses/gpl.html
12 // or under the terms of the GNU Library license:
13 // http://www.gnu.org/licenses/lgpl.html
14 // at your preference. Those licenses describe your legal rights to this
15 // software, and no other rights or warranties apply.
16 // Please send updates for this code to: fred@gruntose.com -- Thanks, fred.
19 #include <mathematics/chaos.h>
21 #include <system_helper.h>
23 namespace algorithms {
26 * general considerations:
28 * + Generic objects to be sorted must support comparison operators.
30 * + If the "reverse" flag is true, the arrays will be sorted in reverse order.
31 * Reverse order here means "descending", such that array element i is always greater than or equal to array element i+1.
32 * Normal order is "ascending", such that element i is always less than or equal to array element i+1.
36 //! dumps the contents of the list out, assuming that the type can be turned into an int.
38 basis::astring dump_list(type v[], int size)
41 for (int i = 0; i < size; i++) {
42 ret += basis::a_sprintf("%d ", (int)v[i]);
47 //! shell sort algorithm.
49 * Sorts a C array of the "type" with "n" elements.
50 * Operates on the original array.
51 * Performs within O(n^2) time (depending on the gap size used).
52 * Algorithm is based on Kernighan and Ritchie's "The C Programming Language".
55 void shell_sort(type v[], int n, bool reverse = false)
59 /* the gap sizes decrease quadratically(?). they partition the array of
60 * items that need to be sorted into first two groups, then four, then
61 * eight, etc. the inner loop iterates across each gap's worth of the array.
63 for (gap = n / 2; gap > 0; gap /= 2) {
64 // the i indexed loop is the base for where the comparisons are made in
65 // the j indexed loop. it makes sure that each item past the edge of
66 // the gap sized partition gets considered.
67 for (i = gap; i < n; i++) {
68 // the j indexed loop looks at the values in our current gap and ensures
69 // that they are in sorted order.
72 for (j = i - gap; j >= 0 && v[j] > v[j + gap]; j = j - gap) {
73 // swap the elements that are disordered.
80 for (j = i - gap; j >= 0 && v[j] < v[j + gap]; j = j - gap) {
81 // swap the elements that are disordered.
96 * merges two sorted arrays into a single sorted array.
99 basis::array<type> merge(basis::array<type> &first, basis::array<type> &second, bool reverse)
101 basis::array<type> to_return;
102 // operate until we've consumed both of the arrays.
103 while ((first.length() > 0) || (second.length() > 0)) {
104 if (first.length() <= 0) {
105 // nothing left in first, so use the second.
106 to_return += second[0];
108 } else if (second.length() <= 0) {
109 to_return += first[0];
111 } else if ((!reverse && (first[0] <= second[0])) || (reverse && (first[0] >= second[0]))) {
112 // the first list has a better value to add next.
113 to_return += first[0];
116 // the second list has a better value to add next.
117 to_return += second[0];
127 * operates in O(n log(n)) time.
128 * returns a new array with sorted data.
131 basis::array<type> merge_sort(const basis::array<type> &v, bool reverse = false)
133 if (v.length() <= 1) {
134 return basis::array<type>(v);
136 int midway = v.length() / 2;
137 basis::array<type> firstPart = merge_sort(v.subarray(0, midway - 1), reverse);
138 basis::array<type> secondPart = merge_sort(v.subarray(midway, v.length() - 1), reverse);
139 return merge(firstPart, secondPart, reverse);
145 * a heap is a structure that can quickly return the highest (or lowest) value,
146 * depending on how the priority of the item is defined.
147 * a "normal" heap keeps the highest element available first; a reverse sorted heap
148 * keeps the lowest element available first.
149 * restructuring the heap is fast, and is O(n log(n)).
150 * the implicit structure is a binary tree
151 * represented in a flat array, where the children of a node at position n are
152 * in positions n * 2 + 1 and n * 2 + 2 (zero based).
154 //hmmm: move this class out to basis?.
159 heap(type to_sort[], int n, bool reverse)
163 _heapspace = to_sort;
167 //! swaps the values in the heap stored at positions a and b.
168 void swap_values(int a, int b)
170 type temp = _heapspace[a];
171 _heapspace[a] = _heapspace[b];
172 _heapspace[b] = temp;
175 //! get the index of the parent of the node at i.
176 /*! this will not return the parent index of the root, since there is no parent. */
177 int parent_index(int i)
179 return i / 2; // rely on integer division to shave off remainder.
182 //! returns the left child of node at position i.
183 int left_child(int i)
188 //! returns the right child of node at position i.
189 int right_child(int i)
194 //! re-sorts the heapspace to maintain the heap ordering.
197 int start = parent_index(_total - 1);
198 // iterate from the back of the array towards the front, so depth-first.
200 // sift down the node at the index 'start' such that all nodes below it are heapified.
201 sift_down(start, _total - 1);
202 start--; // move the start upwards towards the root.
206 void sift_down(int start, int end)
210 // while the current root still has a kid...
211 while (left_child(root) <= end) {
212 int child = left_child(root);
213 // figure out which child to swap with.
215 // check if the root should be swapped with this kid.
216 if ((!_reverse && (_heapspace[swap] > _heapspace[child]))
217 || (_reverse && (_heapspace[swap] < _heapspace[child])))
221 // check if the other child should be swapped with the root or left kid.
222 if ((child + 1 <= end)
223 && ((!_reverse && (_heapspace[swap] > _heapspace[child + 1]))
224 || (_reverse && (_heapspace[swap] < _heapspace[child + 1]))))
229 // the root has the largest (or smallest) element, so we're done.
232 swap_values(root, swap);
234 // repeat to continue sifting down the child now.
239 //! re-sorts the heapspace to maintain the heap ordering. this uses sift_up.
242 int end = 1; // start at first child.
244 while (end < _total) {
245 // sift down the node at the index 'start' such that all nodes below it are heapified.
250 //! start is how far up in the heap to sort. end is the node to sift.
251 void sift_up(int start, int end)
254 // loop until we hit the starting node, where we're done.
255 while (child > start) {
256 int parent = parent_index(child);
257 if ((!_reverse && (_heapspace[parent] < _heapspace[child]))
258 || (_reverse && (_heapspace[parent] > _heapspace[child])))
260 swap_values(parent, child);
262 // continue sifting at the parent now.
271 bool _reverse; // is the sorting in reverse?
272 int _total; // how many total elements are there?
273 int *_heapspace; // track a pointer to the array.
279 * operates in O(n log(n)).
280 * sorts the original array.
283 void heap_sort(type v[], int n, bool reverse = false)
285 // reverse the sense of "reverse", since our algorithm expects a normal heap (with largest on top).
286 heap<type> hap(v, n, !reverse);
290 // a[0] is the root and largest value for a normal heap. The swap moves it to the real end of the list and takes it out of consideration.
291 hap.swap_values(end, 0);
292 // reduce the heap size by 1.
294 // that swap ruined the heap property, so re-heapify.
295 hap.sift_down(0, end);
301 //! swaps the values in the array stored at positions a and b.
303 void swap_values(type array[], int a, int b)
305 type temp = array[a];
310 // hoare's partition implementation.
312 int partition(type a[], int start, int end, bool reverse)
314 // printf("before partition: %s\n", dump_list(a + start, end - start + 1).s());
315 int pivot = a[start];
321 } while ((!reverse && (a[i] < pivot)) || (reverse && (a[i] > pivot)));
324 } while ((!reverse && (a[j] > pivot)) || (reverse && (a[j] < pivot)));
327 // printf("after partition: %s\n", dump_list(a + start, end - start + 1).s());
330 swap_values(a, i, j);
334 //! the recursive version of quick sort that does the work for our convenience method.
336 void inner_quick_sort(type v[], int start, int end, bool reverse)
339 // figure out where to pivot, and sort both halves around the pivot index.
340 int pivot = partition(v, start, end, reverse);
341 inner_quick_sort(v, start, pivot, reverse);
342 inner_quick_sort(v, pivot + 1, end, reverse);
349 * operates in O(n log(n)) time on average, worst case O(n^2).
350 * sorts the original array.
352 template <class type>
353 void quick_sort(type v[], int n, bool reverse = false)
355 inner_quick_sort(v, 0, n - 1, reverse);
360 //! handy method for randomizing the order of a list. not strictly a sorting function...
361 template <class type>
362 void randomize_list(type v[], int n)
364 mathematics::chaos randomizer;
365 for (int i = 0; i < n; i++) {
366 // we will swap with any element that is not prior to the current index; thus we allow
367 // swapping the element with itself and later, but not with anything earlier.
368 int swap_index = randomizer.inclusive(i, n - 1);
369 swap_values(v, i, swap_index);
375 #endif // outer guard.