// Please send updates for this code to: fred@gruntose.com -- Thanks, fred.
//////////////
+#include <stdio.h>
+//temp!
+
namespace algorithms {
-/*
- * general considerations:
- *
- * + Generic objects to be sorted must support comparison operators.
- *
- * + If the "reverse" flag is true, the arrays will be sorted in reverse order.
- * Reverse order here means "descending", such that array element i is always greater than or equal to array element i+1.
- * Normal order is "ascending", such that element i is always less than or equal to array element i+1.
- *
- */
-
-//! shell sort algorithm.
-/*!
- * Sorts a C array of the "type" with "n" elements.
- * Operates on the original array.
- * Performs in O(n log(n)) time.
- * Algorithm is based on Kernighan and Ritchie's "The C Programming Language".
-*/
-template <class type>
-void shell_sort(type v[], int n, bool reverse = false)
-{
- type temp;
- int gap, i, j;
- /* the gap sizes decrease quadratically(?). they partition the array of
- * items that need to be sorted into first two groups, then four, then
- * eight, etc. the inner loop iterates across each gap's worth of the array.
+ /*
+ * general considerations:
+ *
+ * + Generic objects to be sorted must support comparison operators.
+ *
+ * + If the "reverse" flag is true, the arrays will be sorted in reverse order.
+ * Reverse order here means "descending", such that array element i is always greater than or equal to array element i+1.
+ * Normal order is "ascending", such that element i is always less than or equal to array element i+1.
+ *
*/
- for (gap = n / 2; gap > 0; gap /= 2) {
- // the i indexed loop is the base for where the comparisons are made in
- // the j indexed loop. it makes sure that each item past the edge of
- // the gap sized partition gets considered.
- for (i = gap; i < n; i++) {
- // the j indexed loop looks at the values in our current gap and ensures
- // that they are in sorted order.
- if (!reverse) {
- // normal ordering.
- for (j = i - gap; j >= 0 && v[j] > v[j + gap]; j = j - gap) {
- // swap the elements that are disordered.
- temp = v[j]; v[j] = v[j + gap]; v[j + gap] = temp;
- }
- } else {
- // reversed ordering.
- for (j = i - gap; j >= 0 && v[j] < v[j + gap]; j = j - gap) {
- // swap the elements that are disordered.
- temp = v[j]; v[j] = v[j + gap]; v[j + gap] = temp;
- }
- }
- }
- }
-}
-
-//////////////
-/*!
- * sorted array merge
- *
- * merges two sorted arrays into a single sorted array.
- */
-template <class type>
-basis::array<type> merge(const basis::array<type> &first, basis::array<type> &second, bool reverse)
-{
- int first_iter = 0;
- int second_iter = 0;
- //hmmm: careful below; remember differences in heap allocated objects versus new-ed ones.
- //this might be really inefficient to return on stack..?
- basis::array<type> to_return;
- // operate until we've consumed both of the arrays.
- while ((first_iter < first.length()) && (second_iter < second.length())) {
- if ( (!reverse && (first[first_iter] <= second[second_iter]))
- || (reverse && (first[first_iter] >= second[second_iter])) ) {
- // next item from first array goes into the merged array next.
- to_return += first[first_iter++];
- } else {
- // next item from second array goes into the merged array next.
- to_return += second[second_iter++];
+ //! dumps the contents of the list out, assuming that the type can be turned into an int.
+ template<class type>
+ basis::astring dump_list(type v[], int size)
+ {
+ basis::astring ret;
+ for (int i = 0; i < size; i++) {
+ ret += basis::a_sprintf("%d ", (int)v[i]);
}
+ return ret;
}
- return to_return;
-}
-
-/*!
- * merge sort
- *
- * operates in O(n log(n)) time.
- * returns a new array with sorted data.
- */
-template <class type>
-basis::array<type> merge_sort(const basis::array<type> &v, bool reverse = false)
-{
- if (v.length() <= 1) {
- return new basis::array<type>(v);
+
+ //! shell sort algorithm.
+ /*!
+ * Sorts a C array of the "type" with "n" elements.
+ * Operates on the original array.
+ * Performs in O(n log(n)) time.
+ * Algorithm is based on Kernighan and Ritchie's "The C Programming Language".
+ */
+ template<class type>
+ void shell_sort(type v[], int n, bool reverse = false)
+ {
+ type temp;
+ int gap, i, j;
+ /* the gap sizes decrease quadratically(?). they partition the array of
+ * items that need to be sorted into first two groups, then four, then
+ * eight, etc. the inner loop iterates across each gap's worth of the array.
+ */
+ for (gap = n / 2; gap > 0; gap /= 2) {
+ // the i indexed loop is the base for where the comparisons are made in
+ // the j indexed loop. it makes sure that each item past the edge of
+ // the gap sized partition gets considered.
+ for (i = gap; i < n; i++) {
+ // the j indexed loop looks at the values in our current gap and ensures
+ // that they are in sorted order.
+ if (!reverse) {
+ // normal ordering.
+ for (j = i - gap; j >= 0 && v[j] > v[j + gap]; j = j - gap) {
+ // swap the elements that are disordered.
+ temp = v[j];
+ v[j] = v[j + gap];
+ v[j + gap] = temp;
+ }
+ } else {
+ // reversed ordering.
+ for (j = i - gap; j >= 0 && v[j] < v[j + gap]; j = j - gap) {
+ // swap the elements that are disordered.
+ temp = v[j];
+ v[j] = v[j + gap];
+ v[j + gap] = temp;
+ }
+ }
+ }
+ }
}
- int midway = v.length() / 2;
- basis::array<type> firstPart = merge_sort(v.subarray(0, midway - 1));
- basis::array<type> secondPart = merge_sort(v.subarray(midway, v.length() - 1));
- return merge(firstPart, secondPart, reverse);
-}
//////////////
-/*
- * a heap is a structure that can quickly return the highest (or lowest) value,
- * depending on how the priority of the item is defined. restructuring is
- * also fast, when new data are added. the implicit structure is a binary tree
- * represented in a flat array, where the children of a node at position n are
- * in positions n * 2 + 1 and n * 2 + 2 (zero based).
- */
-//hmmm: move this class out to basis?.
-template <class type>
-class heap
-{
-public:
- heap(int max_elements, bool reverse) {
- _max_elements = max_elements;
- _reverse = reverse;
- _heapspace = new basis::array<type> (_max_elements);
+ /*!
+ * sorted array merge
+ *
+ * merges two sorted arrays into a single sorted array.
+ */
+ template<class type>
+ basis::array<type> merge(basis::array<type> &first, basis::array<type> &second,
+ bool reverse)
+ {
+ basis::array<type> to_return;
+ // operate until we've consumed both of the arrays.
+ while ((first.length() > 0) || (second.length() > 0)) {
+ if (first.length() <= 0) {
+ // nothing left in first, so use the second.
+ to_return += second[0];
+ second.zap(0, 0);
+ } else if (second.length() <= 0) {
+ to_return += first[0];
+ first.zap(0, 0);
+ } else if ( (!reverse && (first[0] <= second[0]))
+ || (reverse && (first[0] >= second[0]))) {
+ // the first list has a better value to add next.
+ to_return += first[0];
+ first.zap(0, 0);
+ } else {
+ // the second list has a better value to add next.
+ to_return += second[0];
+ second.zap(0, 0);
+ }
+ }
+ return to_return;
}
- virtual ~heap() {
- WHACK(_heapspace);
+ /*!
+ * merge sort
+ *
+ * operates in O(n log(n)) time.
+ * returns a new array with sorted data.
+ */
+ template<class type>
+ basis::array<type> merge_sort(const basis::array<type> &v, bool reverse = false)
+ {
+ if (v.length() <= 1) {
+ return basis::array<type>(v);
+ }
+ int midway = v.length() / 2;
+ basis::array<type> firstPart = merge_sort(v.subarray(0, midway - 1), reverse);
+ basis::array<type> secondPart = merge_sort(v.subarray(midway, v.length() - 1), reverse);
+ return merge(firstPart, secondPart, reverse);
}
- //! swaps the values in the heap stored at positions a and b.
- void swap(int a, int b)
+//////////////
+
+ /*!
+ * a heap is a structure that can quickly return the highest (or lowest) value,
+ * depending on how the priority of the item is defined.
+ * a "normal" heap keeps the highest element available first; a reverse sorted heap
+ * keeps the lowest element available first.
+ * restructuring the heap is fast, and is O(n log(n)).
+ * the implicit structure is a binary tree
+ * represented in a flat array, where the children of a node at position n are
+ * in positions n * 2 + 1 and n * 2 + 2 (zero based).
+ */
+//hmmm: move this class out to basis?.
+ template<class type>
+ class heap
{
- type temp = _heapspace[a];
- _heapspace[a] = _heapspace[b];
- _heapspace[b] = temp;
- }
+ public:
+ heap(type to_sort[], int n, bool reverse)
+ {
+ _total = n;
+ _reverse = reverse;
+ _heapspace = to_sort;
+ heapify();
+ }
+
+ //! swaps the values in the heap stored at positions a and b.
+ void swap_values(int a, int b)
+ {
+ type temp = _heapspace[a];
+ _heapspace[a] = _heapspace[b];
+ _heapspace[b] = temp;
+ }
+
+ //! get the index of the parent of the node at i.
+ /*! this will not return the parent index of the root, since there is no parent. */
+ int parent_index(int i)
+ {
+ return i / 2; // rely on integer division to shave off remainder.
+ }
+
+ //! returns the left child of node at position i.
+ int left_child(int i)
+ {
+ return 2 * i + 1;
+ }
- //! re-sorts the heapspace to maintain the heap ordering.
- void heapify()
+ //! returns the right child of node at position i.
+ int right_child(int i)
+ {
+ return 2 * i + 2;
+ }
+
+ //! re-sorts the heapspace to maintain the heap ordering.
+ void heapify()
+ {
+ int start = parent_index(_total - 1);
+ // iterate from the back of the array towards the front, so depth-first.
+ while (start >= 0) {
+ // sift down the node at the index 'start' such that all nodes below it are heapified.
+ sift_down(start, _total - 1);
+ start--; // move the start upwards towards the root.
+ }
+ }
+
+ void sift_down(int start, int end)
+ {
+ int root = start;
+
+ // while the current root still has a kid...
+ while (left_child(root) <= end) {
+ int child = left_child(root);
+ // figure out which child to swap with.
+ int swap = root;
+ // check if the root should be swapped with this kid.
+ if ((!_reverse && (_heapspace[swap] > _heapspace[child]))
+ || (_reverse && (_heapspace[swap] < _heapspace[child])))
+ {
+ swap = child;
+ }
+ // check if the other child should be swapped with the root or left kid.
+ if ((child + 1 <= end)
+ && ((!_reverse && (_heapspace[swap] > _heapspace[child + 1]))
+ || (_reverse && (_heapspace[swap] < _heapspace[child + 1]))))
+ {
+ swap = child + 1;
+ }
+ if (swap == root) {
+ // the root has the largest (or smallest) element, so we're done.
+ return;
+ } else {
+ swap_values(root, swap);
+ root = swap;
+ // repeat to continue sifting down the child now.
+ }
+ }
+ }
+
+ //! re-sorts the heapspace to maintain the heap ordering. this uses sift_up.
+ void alt_heapify()
+ {
+ int end = 1; // start at first child.
+
+ while (end < _total) {
+ // sift down the node at the index 'start' such that all nodes below it are heapified.
+ sift_up(0, end++);
+ }
+ }
+
+ //! start is how far up in the heap to sort. end is the node to sift.
+ void sift_up(int start, int end)
+ {
+ int child = end;
+ // loop until we hit the starting node, where we're done.
+ while (child > start) {
+ int parent = parent_index(child);
+ if ((!_reverse && (_heapspace[parent] < _heapspace[child]))
+ || (_reverse && (_heapspace[parent] > _heapspace[child])))
+ {
+ swap_values(parent, child);
+ child = parent;
+ // continue sifting at the parent now.
+ } else {
+ // done sorting.
+ return;
+ }
+ }
+ }
+
+ private:
+ bool _reverse = false; // is the sorting in reverse?
+ int _total = 0;
+ int *_heapspace = NULL_POINTER;
+ };
+
+ /*!
+ * heap sort
+ *
+ * operates in O(n log(n)).
+ * sorts the original array.
+ */
+ template<class type>
+ void heap_sort(type v[], int n, bool reverse = false)
{
+ // reverse the sense of "reverse", since our algorithm expects a normal heap (with largest on top).
+ heap<type> hap(v, n, !reverse);
- }
+ //temp
+// printf("hey after heaping: %s\n", dump_list(v, n).s());
+
+ int end = n - 1;
+ while (end > 0) {
- void add(type to_add) {
- //
- }
-
-
-private:
- int _max_elements;
- bool _reverse;
- basis::array<type> *_heapspace = NULL_POINTER;
-};
-
-/*!
- * heap sort
- *
- * operates in O(n log(n)).
- * sorts the original array.
- */
-template <class type>
-void heap_sort(type v[], int n, bool reverse = false)
-{
- // use heap. do sorty.
-}
+//printf("moving value %d\n", (int)v[0]);
+ // 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.
+ hap.swap_values(end, 0);
+ // reduce the heap size by 1.
+ end--;
+ // that swap ruined the heap property, so re-heapify.
+ hap.sift_down(0, end);
+ }
+ }
//////////////
-template <class type>
-void partition(type v[], int start, int end)
-{
+ template<class type>
+ void partition(type v[], int start, int end)
+ {
-}
+ }
//! the recursive version of quick sort that does the work for our convenience method.
-template <class type>
-void inner_quick_sort(type v[], int n, int start, int end, bool reverse = false)
-{
- if (start >= end) {
- // nothing to see here.
- } else {
- // figure out where to pivot, and sort both halves around the pivot index.
- int pivot = partition(v, start, end);
- quicksort(v, start, pivot - 1);
- quicksort(v, pivot + 1, end);
+ template<class type>
+ void inner_quick_sort(type v[], int n, int start, int end, bool reverse = false)
+ {
+ if (start >= end) {
+ // nothing to see here.
+ } else {
+ // figure out where to pivot, and sort both halves around the pivot index.
+ int pivot = partition(v, start, end);
+ quicksort(v, start, pivot - 1);
+ quicksort(v, pivot + 1, end);
+ }
}
-}
-
-/*!
- * quick sort
- *
- * operates in O(n log(n)) time on average, worst case O(n^2).
- * sorts the original array.
- */
-template <class type>
-void quick_sort(type v[], int n, bool reverse = false)
-{
- inner_quick_sort(v, n, 0, n-1, reverse);
-}
-
-} // namespace.
+
+ /*!
+ * quick sort
+ *
+ * operates in O(n log(n)) time on average, worst case O(n^2).
+ * sorts the original array.
+ */
+ template<class type>
+ void quick_sort(type v[], int n, bool reverse = false)
+ {
+ inner_quick_sort(v, n, 0, n - 1, reverse);
+ }
+
+} // namespace.
#endif // outer guard.
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