py/pairheap: Add generic implementation of pairing heap data structure.

3 files changed, 230 insertions, 0 deletions

diff --git a/py/pairheap.c b/py/pairheap.c
new file mode 100644
index 0000000000..caa51bf797
--- /dev/null
+++ b/py/pairheap.c
@@ -0,0 +1,139 @@
+/*
+ * This file is part of the MicroPython project, http://micropython.org/
+ *
+ * The MIT License (MIT)
+ *
+ * Copyright (c) 2020 Damien P. George
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+
+#include "py/pairheap.h"
+
+// The mp_pairheap_t.next pointer can take one of the following values:
+//   - NULL: the node is the top of the heap
+//   - LSB set: the node is the last of the children and points to its parent node
+//   - other: the node is a child and not the last child
+// The macros below help manage this pointer.
+#define NEXT_MAKE_RIGHTMOST_PARENT(parent) ((void*)((uintptr_t)(parent) | 1))
+#define NEXT_IS_RIGHTMOST_PARENT(next) ((uintptr_t)(next) & 1)
+#define NEXT_GET_RIGHTMOST_PARENT(next) ((void*)((uintptr_t)(next) & ~1))
+
+// O(1), stable
+mp_pairheap_t *mp_pairheap_meld(mp_pairheap_lt_t lt, mp_pairheap_t *heap1, mp_pairheap_t *heap2) {
+    if (heap1 == NULL) {
+        return heap2;
+    }
+    if (heap2 == NULL) {
+        return heap1;
+    }
+    if (lt(heap1, heap2)) {
+        if (heap1->child == NULL) {
+            heap1->child = heap2;
+        } else {
+            heap1->child_last->next = heap2;
+        }
+        heap1->child_last = heap2;
+        heap2->next = NEXT_MAKE_RIGHTMOST_PARENT(heap1);
+        return heap1;
+    } else {
+        heap1->next = heap2->child;
+        heap2->child = heap1;
+        if (heap1->next == NULL) {
+            heap2->child_last = heap1;
+            heap1->next = NEXT_MAKE_RIGHTMOST_PARENT(heap2);
+        }
+        return heap2;
+    }
+}
+
+// amortised O(log N), stable
+mp_pairheap_t *mp_pairheap_pairing(mp_pairheap_lt_t lt, mp_pairheap_t *child) {
+    if (child == NULL) {
+        return NULL;
+    }
+    mp_pairheap_t *heap = NULL;
+    while (!NEXT_IS_RIGHTMOST_PARENT(child)) {
+        mp_pairheap_t *n1 = child;
+        child = child->next;
+        if (!NEXT_IS_RIGHTMOST_PARENT(child)) {
+            mp_pairheap_t *n2 = child;
+            child = child->next;
+            n1 = mp_pairheap_meld(lt, n1, n2);
+        }
+        heap = mp_pairheap_meld(lt, heap, n1);
+    }
+    heap->next = NULL;
+    return heap;
+}
+
+// amortised O(log N), stable
+mp_pairheap_t *mp_pairheap_delete(mp_pairheap_lt_t lt, mp_pairheap_t *heap, mp_pairheap_t *node) {
+    // Simple case of the top being the node to delete
+    if (node == heap) {
+        return mp_pairheap_pairing(lt, heap->child);
+    }
+
+    // Case where node is not in the heap
+    if (node->next == NULL) {
+        return heap;
+    }
+
+    // Find parent of node
+    mp_pairheap_t *parent = node;
+    while (!NEXT_IS_RIGHTMOST_PARENT(parent->next)) {
+        parent = parent->next;
+    }
+    parent = NEXT_GET_RIGHTMOST_PARENT(parent->next);
+
+    // Replace node with pairing of its children
+    mp_pairheap_t *next;
+    if (node == parent->child && node->child == NULL) {
+        if (NEXT_IS_RIGHTMOST_PARENT(node->next)) {
+            parent->child = NULL;
+        } else {
+            parent->child = node->next;
+        }
+        node->next = NULL;
+        return heap;
+    } else if (node == parent->child) {
+        next = node->next;
+        node->next = NULL;
+        node = mp_pairheap_pairing(lt, node->child);
+        parent->child = node;
+    } else {
+        mp_pairheap_t *n = parent->child;
+        while (node != n->next) {
+            n = n->next;
+        }
+        next = node->next;
+        node->next = NULL;
+        node = mp_pairheap_pairing(lt, node->child);
+        if (node == NULL) {
+            node = n;
+        } else {
+            n->next = node;
+        }
+    }
+    node->next = next;
+    if (NEXT_IS_RIGHTMOST_PARENT(next)) {
+        parent->child_last = node;
+    }
+    return heap;
+}
diff --git a/py/pairheap.h b/py/pairheap.h
new file mode 100644
index 0000000000..f9517f281e
--- /dev/null
+++ b/py/pairheap.h
@@ -0,0 +1,90 @@
+/*
+ * This file is part of the MicroPython project, http://micropython.org/
+ *
+ * The MIT License (MIT)
+ *
+ * Copyright (c) 2020 Damien P. George
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+#ifndef MICROPY_INCLUDED_PY_PAIRHEAP_H
+#define MICROPY_INCLUDED_PY_PAIRHEAP_H
+
+// This is an implementation of a pairing heap.  It is stable and has deletion
+// support.  Only the less-than operation needs to be defined on elements.
+//
+// See original paper for details:
+// Michael L. Fredman, Robert Sedjewick, Daniel D. Sleator, and Robert E. Tarjan.
+// The Pairing Heap: A New Form of Self-Adjusting Heap.
+// Algorithmica 1:111-129, 1986.
+// https://www.cs.cmu.edu/~sleator/papers/pairing-heaps.pdf
+
+#include "py/obj.h"
+
+// This struct forms the nodes of the heap and is intended to be extended, by
+// placing it first in another struct, to include additional information for the
+// element stored in the heap.  It includes "base" so it can be a MicroPython
+// object allocated on the heap and the GC can automatically trace all nodes by
+// following the tree structure.
+typedef struct _mp_pairheap_t {
+    mp_obj_base_t base;
+    struct _mp_pairheap_t *child;
+    struct _mp_pairheap_t *child_last;
+    struct _mp_pairheap_t *next;
+} mp_pairheap_t;
+
+// This is the function for the less-than operation on nodes/elements.
+typedef int (*mp_pairheap_lt_t)(mp_pairheap_t*, mp_pairheap_t*);
+
+// Core functions.
+mp_pairheap_t *mp_pairheap_meld(mp_pairheap_lt_t lt, mp_pairheap_t *heap1, mp_pairheap_t *heap2);
+mp_pairheap_t *mp_pairheap_pairing(mp_pairheap_lt_t lt, mp_pairheap_t *child);
+mp_pairheap_t *mp_pairheap_delete(mp_pairheap_lt_t lt, mp_pairheap_t *heap, mp_pairheap_t *node);
+
+// Create a new heap.
+static inline mp_pairheap_t *mp_pairheap_new(mp_pairheap_lt_t lt) {
+    (void)lt;
+    return NULL;
+}
+
+// Test if the heap is empty.
+static inline bool mp_pairheap_is_empty(mp_pairheap_lt_t lt, mp_pairheap_t *heap) {
+    (void)lt;
+    return heap == NULL;
+}
+
+// Peek at the top of the heap.  Will return NULL if empty.
+static inline mp_pairheap_t *mp_pairheap_peek(mp_pairheap_lt_t lt, mp_pairheap_t *heap) {
+    (void)lt;
+    return heap;
+}
+
+// Push new node onto existing heap.  Returns the new heap.
+static inline mp_pairheap_t *mp_pairheap_push(mp_pairheap_lt_t lt, mp_pairheap_t *heap, mp_pairheap_t *node) {
+    node->child = NULL;
+    node->next = NULL;
+    return mp_pairheap_meld(lt, node, heap); // node is first to be stable
+}
+
+// Pop the top off the heap, which must not be empty.  Returns the new heap.
+static inline mp_pairheap_t *mp_pairheap_pop(mp_pairheap_lt_t lt, mp_pairheap_t *heap) {
+    return mp_pairheap_pairing(lt, heap->child);
+}
+
+#endif // MICROPY_INCLUDED_PY_PAIRHEAP_H
diff --git a/py/py.mk b/py/py.mk
index 09de1962d3..1a56dcce8f 100644
--- a/py/py.mk
+++ b/py/py.mk
@@ -94,6 +94,7 @@ PY_CORE_O_BASENAME = $(addprefix py/,\
 	runtime_utils.o \
 	scheduler.o \
 	nativeglue.o \
+	pairheap.o \
 	ringbuf.o \
 	stackctrl.o \
 	argcheck.o \