From: Attractive Chaos <attractor@live.co.uk>
Date: Tue, 17 Dec 2019 04:27:05 +0000 (-0500)
Subject: prepare not add dynamic RMQ (unfinished)
X-Git-Url: http://www.kaiwu.me/postgresql/commit/static/gitweb.js?a=commitdiff_plain;h=702e598bc35cb4a9139bc65edfe1ed325b603af9;p=klib.git

prepare not add dynamic RMQ (unfinished)
---

diff --git a/krmq.h b/krmq.h
new file mode 100644
index 0000000..bbb2164
--- /dev/null
+++ b/krmq.h
@@ -0,0 +1,430 @@
+/* The MIT License
+
+   Copyright (c) 2019 by Attractive Chaos <attractor@live.co.uk>
+
+   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.
+*/
+
+/* An example:
+
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include "krmq.h"
+
+struct my_node {
+  char key;
+  KRMQ_HEAD(struct my_node) head;
+};
+#define my_cmp(p, q) (((q)->key < (p)->key) - ((p)->key < (q)->key))
+KRMQ_INIT(my, struct my_node, head, my_cmp)
+
+int main(void) {
+  const char *str = "MNOLKQOPHIA"; // from wiki, except a duplicate
+  struct my_node *root = 0;
+  int i, l = strlen(str);
+  for (i = 0; i < l; ++i) {        // insert in the input order
+    struct my_node *q, *p = malloc(sizeof(*p));
+    p->key = str[i];
+    q = krmq_insert(my, &root, p, 0);
+    if (p != q) free(p);           // if already present, free
+  }
+  krmq_itr_t(my) itr;
+  krmq_itr_first(my, root, &itr);  // place at first
+  do {                             // traverse
+    const struct my_node *p = krmq_at(&itr);
+    putchar(p->key);
+    free((void*)p);                // free node
+  } while (krmq_itr_next(my, &itr));
+  putchar('\n');
+  return 0;
+}
+*/
+
+#ifndef KRMQ_H
+#define KRMQ_H
+
+#ifdef __STRICT_ANSI__
+#define inline __inline__
+#endif
+
+#define KRMQ_MAX_DEPTH 64
+
+#define krmq_size(head, p) ((p)? (p)->head.size : 0)
+#define krmq_size_child(head, q, i) ((q)->head.p[(i)]? (q)->head.p[(i)]->head.size : 0)
+
+#define KRMQ_HEAD(__type) \
+	struct { \
+		__type *p[2], *s; \
+		signed char balance; /* balance factor */ \
+		unsigned size; /* #elements in subtree */ \
+	}
+
+#define __KRMQ_FIND(suf, __scope, __type, __head,  __cmp) \
+	__scope __type *krmq_find_##suf(const __type *root, const __type *x, unsigned *cnt_) { \
+		const __type *p = root; \
+		unsigned cnt = 0; \
+		while (p != 0) { \
+			int cmp; \
+			cmp = __cmp(x, p); \
+			if (cmp >= 0) cnt += krmq_size_child(__head, p, 0) + 1; \
+			if (cmp < 0) p = p->__head.p[0]; \
+			else if (cmp > 0) p = p->__head.p[1]; \
+			else break; \
+		} \
+		if (cnt_) *cnt_ = cnt; \
+		return (__type*)p; \
+	} \
+	__scope __type *krmq_interval_##suf(const __type *root, const __type *x, __type **lower, __type **upper) { \
+		const __type *p = root, *l = 0, *u = 0; \
+		while (p != 0) { \
+			int cmp; \
+			cmp = __cmp(x, p); \
+			if (cmp < 0) u = p, p = p->__head.p[0]; \
+			else if (cmp > 0) l = p, p = p->__head.p[1]; \
+			else { l = u = p; break; } \
+		} \
+		if (lower) *lower = (__type*)l; \
+		if (upper) *upper = (__type*)u; \
+		return (__type*)p; \
+	}
+
+#define __KRMQ_ROTATE(suf, __type, __head, __lt2) \
+	/* */ \
+	static inline void krmq_update_min_##suf(__type *p, const __type *q, const __type *r) { \
+		p->__head.s = !q || __lt2(p, q->__head.s)? p : q->__head.s; \
+		p->__head.s = !r || __lt2(p->__head.s, r->__head.s)? p->__head.s : r->__head.s; \
+	} \
+	/* one rotation: (a,(b,c)q)p => ((a,b)p,c)q */ \
+	static inline __type *krmq_rotate1_##suf(__type *p, int dir) { /* dir=0 to left; dir=1 to right */ \
+		int opp = 1 - dir; /* opposite direction */ \
+		__type *q = p->__head.p[opp], *s = p->__head.s; \
+		unsigned size_p = p->__head.size; \
+		p->__head.size -= q->__head.size - krmq_size_child(__head, q, dir); \
+		q->__head.size = size_p; \
+		krmq_update_min_##suf(p, p->__head.p[dir], q->__head.p[dir]); \
+		q->__head.s = s; \
+		p->__head.p[opp] = q->__head.p[dir]; \
+		q->__head.p[dir] = p; \
+		return q; \
+	} \
+	/* two consecutive rotations: (a,((b,c)r,d)q)p => ((a,b)p,(c,d)q)r */ \
+	static inline __type *krmq_rotate2_##suf(__type *p, int dir) { \
+		int b1, opp = 1 - dir; \
+		__type *q = p->__head.p[opp], *r = q->__head.p[dir], *s = p->__head.s; \
+		unsigned size_x_dir = krmq_size_child(__head, r, dir); \
+		r->__head.size = p->__head.size; \
+		p->__head.size -= q->__head.size - size_x_dir; \
+		q->__head.size -= size_x_dir + 1; \
+		krmq_update_min_##suf(p, p->__head.p[dir], r->__head.p[dir]); \
+		krmq_update_min_##suf(q, q->__head.p[opp], r->__head.p[opp]); \
+		r->__head.s = s; \
+		p->__head.p[opp] = r->__head.p[dir]; \
+		r->__head.p[dir] = p; \
+		q->__head.p[dir] = r->__head.p[opp]; \
+		r->__head.p[opp] = q; \
+		b1 = dir == 0? +1 : -1; \
+		if (r->__head.balance == b1) q->__head.balance = 0, p->__head.balance = -b1; \
+		else if (r->__head.balance == 0) q->__head.balance = p->__head.balance = 0; \
+		else q->__head.balance = b1, p->__head.balance = 0; \
+		r->__head.balance = 0; \
+		return r; \
+	}
+
+#define __KRMQ_INSERT(suf, __scope, __type, __head, __cmp, __lt2) \
+	__scope __type *krmq_insert_##suf(__type **root_, __type *x, unsigned *cnt_) { \
+		unsigned char stack[KRMQ_MAX_DEPTH]; \
+		__type *path[KRMQ_MAX_DEPTH]; \
+		__type *bp, *bq; \
+		__type *p, *q, *r = 0; /* _r_ is potentially the new root */ \
+		int i, which = 0, top, b1, path_len; \
+		unsigned cnt = 0; \
+		bp = *root_, bq = 0; \
+		/* find the insertion location */ \
+		for (p = bp, q = bq, top = path_len = 0; p; q = p, p = p->__head.p[which]) { \
+			int cmp; \
+			cmp = __cmp(x, p); \
+			if (cmp >= 0) cnt += krmq_size_child(__head, p, 0) + 1; \
+			if (cmp == 0) { \
+				if (cnt_) *cnt_ = cnt; \
+				return p; \
+			} \
+			if (p->__head.balance != 0) \
+				bq = q, bp = p, top = 0; \
+			stack[top++] = which = (cmp > 0); \
+			path[path_len++] = p; \
+		} \
+		if (cnt_) *cnt_ = cnt; \
+		x->__head.balance = 0, x->__head.size = 1, x->__head.p[0] = x->__head.p[1] = 0, x->__head.s = x; \
+		if (q == 0) *root_ = x; \
+		else q->__head.p[which] = x; \
+		if (bp == 0) return x; \
+		for (i = 0; i < path_len; ++i) ++path[i]->__head.size; \
+		for (i = path_len - 1; i >= 0; --i) { \
+			krmq_update_min_##suf(path[i], path[i]->__head.p[0], path[i]->__head.p[1]); \
+			if (path[i]->__head.s != x) break; \
+		} \
+		for (p = bp, top = 0; p != x; p = p->__head.p[stack[top]], ++top) /* update balance factors */ \
+			if (stack[top] == 0) --p->__head.balance; \
+			else ++p->__head.balance; \
+		if (bp->__head.balance > -2 && bp->__head.balance < 2) return x; /* no re-balance needed */ \
+		/* re-balance */ \
+		which = (bp->__head.balance < 0); \
+		b1 = which == 0? +1 : -1; \
+		q = bp->__head.p[1 - which]; \
+		if (q->__head.balance == b1) { \
+			r = krmq_rotate1_##suf(bp, which); \
+			q->__head.balance = bp->__head.balance = 0; \
+		} else r = krmq_rotate2_##suf(bp, which); \
+		if (bq == 0) *root_ = r; \
+		else bq->__head.p[bp != bq->__head.p[0]] = r; \
+		return x; \
+	}
+
+#define __KRMQ_ERASE(suf, __scope, __type, __head, __cmp, __lt2) \
+	__scope __type *krmq_erase_##suf(__type **root_, const __type *x, unsigned *cnt_) { \
+		__type *p, *path[KRMQ_MAX_DEPTH], fake; \
+		unsigned char dir[KRMQ_MAX_DEPTH]; \
+		int i, d = 0, cmp; \
+		unsigned cnt = 0; \
+		fake.__head.p[0] = *root_, fake.__head.p[1] = 0; \
+		if (cnt_) *cnt_ = 0; \
+		if (x) { \
+			for (cmp = -1, p = &fake; cmp; cmp = __cmp(x, p)) { \
+				int which = (cmp > 0); \
+				if (cmp > 0) cnt += krmq_size_child(__head, p, 0) + 1; \
+				dir[d] = which; \
+				path[d++] = p; \
+				p = p->__head.p[which]; \
+				if (p == 0) { \
+					if (cnt_) *cnt_ = 0; \
+					return 0; \
+				} \
+			} \
+			cnt += krmq_size_child(__head, p, 0) + 1; /* because p==x is not counted */ \
+		} else { \
+			for (p = &fake, cnt = 1; p; p = p->__head.p[0]) \
+				dir[d] = 0, path[d++] = p; \
+			p = path[--d]; \
+		} \
+		if (cnt_) *cnt_ = cnt; \
+		for (i = 1; i < d; ++i) --path[i]->__head.size; \
+		if (p->__head.p[1] == 0) { /* ((1,.)2,3)4 => (1,3)4; p=2 */ \
+			path[d-1]->__head.p[dir[d-1]] = p->__head.p[0]; \
+		} else { \
+			__type *q = p->__head.p[1]; \
+			if (q->__head.p[0] == 0) { /* ((1,2)3,4)5 => ((1)2,4)5; p=3,q=2 */ \
+				q->__head.p[0] = p->__head.p[0]; \
+				q->__head.balance = p->__head.balance; \
+				path[d-1]->__head.p[dir[d-1]] = q; \
+				path[d] = q, dir[d++] = 1; \
+				q->__head.size = p->__head.size - 1; \
+			} else { /* ((1,((.,2)3,4)5)6,7)8 => ((1,(2,4)5)3,7)8; p=6 */ \
+				__type *r; \
+				int e = d++; /* backup _d_ */\
+				for (;;) { \
+					dir[d] = 0; \
+					path[d++] = q; \
+					r = q->__head.p[0]; \
+					if (r->__head.p[0] == 0) break; \
+					q = r; \
+				} \
+				r->__head.p[0] = p->__head.p[0]; \
+				q->__head.p[0] = r->__head.p[1]; \
+				r->__head.p[1] = p->__head.p[1]; \
+				r->__head.balance = p->__head.balance; \
+				path[e-1]->__head.p[dir[e-1]] = r; \
+				path[e] = r, dir[e] = 1; \
+				for (i = e + 1; i < d; ++i) --path[i]->__head.size; \
+				r->__head.size = p->__head.size - 1; \
+			} \
+		} \
+		for (i = d - 1; i >= 0; --i) /* not sure why adding condition "path[i]==p" doesn't work */ \
+			krmq_update_min_##suf(path[i], path[i]->__head.p[0], path[i]->__head.p[1]); \
+		while (--d > 0) { \
+			__type *q = path[d]; \
+			int which, other, b1 = 1, b2 = 2; \
+			which = dir[d], other = 1 - which; \
+			if (which) b1 = -b1, b2 = -b2; \
+			q->__head.balance += b1; \
+			if (q->__head.balance == b1) break; \
+			else if (q->__head.balance == b2) { \
+				__type *r = q->__head.p[other]; \
+				if (r->__head.balance == -b1) { \
+					path[d-1]->__head.p[dir[d-1]] = krmq_rotate2_##suf(q, which); \
+				} else { \
+					path[d-1]->__head.p[dir[d-1]] = krmq_rotate1_##suf(q, which); \
+					if (r->__head.balance == 0) { \
+						r->__head.balance = -b1; \
+						q->__head.balance = b1; \
+						break; \
+					} else r->__head.balance = q->__head.balance = 0; \
+				} \
+			} \
+		} \
+		*root_ = fake.__head.p[0]; \
+		return p; \
+	}
+
+#define krmq_free(__type, __head, __root, __free) do { \
+		__type *_p, *_q; \
+		for (_p = __root; _p; _p = _q) { \
+			if (_p->__head.p[0] == 0) { \
+				_q = _p->__head.p[1]; \
+				__free(_p); \
+			} else { \
+				_q = _p->__head.p[0]; \
+				_p->__head.p[0] = _q->__head.p[1]; \
+				_q->__head.p[1] = _p; \
+			} \
+		} \
+	} while (0)
+
+#define __KRMQ_ITR(suf, __scope, __type, __head, __cmp) \
+	struct krmq_itr_##suf { \
+		const __type *stack[KRMQ_MAX_DEPTH], **top; \
+	}; \
+	__scope void krmq_itr_first_##suf(const __type *root, struct krmq_itr_##suf *itr) { \
+		const __type *p; \
+		for (itr->top = itr->stack - 1, p = root; p; p = p->__head.p[0]) \
+			*++itr->top = p; \
+	} \
+	__scope int krmq_itr_find_##suf(const __type *root, const __type *x, struct krmq_itr_##suf *itr) { \
+		const __type *p = root; \
+		itr->top = itr->stack - 1; \
+		while (p != 0) { \
+			int cmp; \
+			*++itr->top = p; \
+			cmp = __cmp(x, p); \
+			if (cmp < 0) p = p->__head.p[0]; \
+			else if (cmp > 0) p = p->__head.p[1]; \
+			else break; \
+		} \
+		return p? 1 : 0; \
+	} \
+	__scope int krmq_itr_next_bidir_##suf(struct krmq_itr_##suf *itr, int dir) { \
+		const __type *p; \
+		if (itr->top < itr->stack) return 0; \
+		dir = !!dir; \
+		p = (*itr->top)->__head.p[dir]; \
+		if (p) { /* go down */ \
+			for (; p; p = p->__head.p[!dir]) \
+				*++itr->top = p; \
+			return 1; \
+		} else { /* go up */ \
+			do { \
+				p = *itr->top--; \
+			} while (itr->top >= itr->stack && p == (*itr->top)->__head.p[dir]); \
+			return itr->top < itr->stack? 0 : 1; \
+		} \
+	} \
+
+/**
+ * Insert a node to the tree
+ *
+ * @param suf     name suffix used in KRMQ_INIT()
+ * @param proot   pointer to the root of the tree (in/out: root may change)
+ * @param x       node to insert (in)
+ * @param cnt     number of nodes smaller than or equal to _x_; can be NULL (out)
+ *
+ * @return _x_ if not present in the tree, or the node equal to x.
+ */
+#define krmq_insert(suf, proot, x, cnt) krmq_insert_##suf(proot, x, cnt)
+
+/**
+ * Find a node in the tree
+ *
+ * @param suf     name suffix used in KRMQ_INIT()
+ * @param root    root of the tree
+ * @param x       node value to find (in)
+ * @param cnt     number of nodes smaller than or equal to _x_; can be NULL (out)
+ *
+ * @return node equal to _x_ if present, or NULL if absent
+ */
+#define krmq_find(suf, root, x, cnt) krmq_find_##suf(root, x, cnt)
+#define krmq_interval(suf, root, x, lower, upper) krmq_interval_##suf(root, x, lower, upper)
+
+/**
+ * Delete a node from the tree
+ *
+ * @param suf     name suffix used in KRMQ_INIT()
+ * @param proot   pointer to the root of the tree (in/out: root may change)
+ * @param x       node value to delete; if NULL, delete the first node (in)
+ *
+ * @return node removed from the tree if present, or NULL if absent
+ */
+#define krmq_erase(suf, proot, x, cnt) krmq_erase_##suf(proot, x, cnt)
+#define krmq_erase_first(suf, proot) krmq_erase_##suf(proot, 0, 0)
+
+#define krmq_itr_t(suf) struct krmq_itr_##suf
+
+/**
+ * Place the iterator at the smallest object
+ *
+ * @param suf     name suffix used in KRMQ_INIT()
+ * @param root    root of the tree
+ * @param itr     iterator
+ */
+#define krmq_itr_first(suf, root, itr) krmq_itr_first_##suf(root, itr)
+
+/**
+ * Place the iterator at the object equal to or greater than the query
+ *
+ * @param suf     name suffix used in KRMQ_INIT()
+ * @param root    root of the tree
+ * @param x       query (in)
+ * @param itr     iterator (out)
+ *
+ * @return 1 if find; 0 otherwise. krmq_at(itr) is NULL if and only if query is
+ *         larger than all objects in the tree
+ */
+#define krmq_itr_find(suf, root, x, itr) krmq_itr_find_##suf(root, x, itr)
+
+/**
+ * Move to the next object in order
+ *
+ * @param itr     iterator (modified)
+ *
+ * @return 1 if there is a next object; 0 otherwise
+ */
+#define krmq_itr_next(suf, itr) krmq_itr_next_bidir_##suf(itr, 1)
+#define krmq_itr_prev(suf, itr) krmq_itr_next_bidir_##suf(itr, 0)
+
+/**
+ * Return the pointer at the iterator
+ *
+ * @param itr     iterator
+ *
+ * @return pointer if present; NULL otherwise
+ */
+#define krmq_at(itr) ((itr)->top < (itr)->stack? 0 : *(itr)->top)
+
+#define KRMQ_INIT2(suf, __scope, __type, __head, __cmp, __lt2) \
+	__KRMQ_FIND(suf, __scope, __type, __head,  __cmp) \
+	__KRMQ_ROTATE(suf, __type, __head, __lt2) \
+	__KRMQ_INSERT(suf, __scope, __type, __head, __cmp, __lt2) \
+	__KRMQ_ERASE(suf, __scope, __type, __head, __cmp, __lt2) \
+	__KRMQ_ITR(suf, __scope, __type, __head, __cmp)
+
+#define KRMQ_INIT(suf, __type, __head, __cmp, __lt2) \
+	KRMQ_INIT2(suf,, __type, __head, __cmp, __lt2)
+
+#endif
diff --git a/test/krmq_test.c b/test/krmq_test.c
new file mode 100644
index 0000000..32b48ba
--- /dev/null
+++ b/test/krmq_test.c
@@ -0,0 +1,116 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <limits.h>
+#include "krmq.h"
+
+#define CALLOC(type, num) ((type*)calloc(num, sizeof(type)))
+
+struct my_node {
+	int key;
+	int val;
+	KRMQ_HEAD(struct my_node) head;
+};
+
+#define my_cmp(p, q) (((p)->key > (q)->key) - ((p)->key < (q)->key))
+#define my_lt2(p, q) ((p)->val < (q)->val)
+KRMQ_INIT(my, struct my_node, head, my_cmp, my_lt2)
+
+int check(struct my_node *p, int *hh, int *min)
+{
+	*hh = 0, *min = INT_MAX;
+	if (p) {
+		int c = 1, h[2] = {0, 0}, m[2] = {INT_MAX, INT_MAX};
+		*min = p->val;
+		if (p->head.p[0]) c += check(p->head.p[0], &h[0], &m[0]);
+		if (p->head.p[1]) c += check(p->head.p[1], &h[1], &m[1]);
+		*min = *min < m[0]? *min : m[0];
+		*min = *min < m[1]? *min : m[1];
+		*hh = (h[0] > h[1]? h[0] : h[1]) + 1;
+		if (*min != p->head.s->val)
+			fprintf(stderr, "min %d != %d at %c\n", *min, p->head.s->val, p->key);
+		if (h[1] - h[0] != (int)p->head.balance)
+			fprintf(stderr, "%d - %d != %d at %c\n", h[1], h[0], p->head.balance, p->key);
+		if (c != (int)p->head.size)
+			fprintf(stderr, "%d != %d at %c\n", p->head.size, c, p->key);
+		return c;
+	} else return 0;
+}
+
+int print_tree(const struct my_node *p)
+{
+	int c = 1;
+	if (p == 0) return 0;
+	if (p->head.p[0] || p->head.p[1]) {
+		putchar('(');
+		if (p->head.p[0]) c += print_tree(p->head.p[0]);
+		else putchar('.');
+		putchar(',');
+		if (p->head.p[1]) c += print_tree(p->head.p[1]);
+		else putchar('.');
+		putchar(')');
+	}
+	printf("%c:%d/%d", p->key, p->val, p->head.s->val);
+	return c;
+}
+
+void check_and_print(struct my_node *root)
+{
+	int h, min;
+	check(root, &h, &min);
+	print_tree(root);
+	putchar('\n');
+}
+
+void shuffle(int n, char a[])
+{
+	int i, j;
+	for (i = n; i > 1; --i) {
+		char tmp;
+		j = (int)(drand48() * i);
+		tmp = a[j]; a[j] = a[i-1]; a[i-1] = tmp;
+	}
+}
+
+int main(void)
+{
+	char buf[256];
+	int i, n, h, min;
+	struct my_node *root = 0;
+	struct my_node *p, *q, t;
+	krmq_itr_t(my) itr;
+	unsigned cnt;
+
+	srand48(123);
+	for (i = 33, n = 0; i <= 126; ++i)
+		if (i != '(' && i != ')' && i != '.' && i != ';')
+			buf[n++] = i;
+	shuffle(n, buf);
+	for (i = 0; i < n; ++i) {
+		p = CALLOC(struct my_node, 1);
+		p->key = buf[i];
+		p->val = i;
+		q = krmq_insert(my, &root, p, &cnt);
+		if (p != q) free(p);
+		check(root, &h, &min);
+	}
+	shuffle(n, buf);
+	for (i = 0; i < n/2; ++i) {
+		t.key = buf[i];
+		//fprintf(stderr, "i=%d, key=%c, n/2=%d\n", i, t.key, n/2);
+		q = krmq_erase(my, &root, &t, 0);
+		if (q) free(q);
+		check(root, &h, &min);
+	}
+	check_and_print(root);
+
+	krmq_itr_first(my, root, &itr);
+	do {
+		const struct my_node *r = krmq_at(&itr);
+		putchar(r->key);
+	} while (krmq_itr_next(my, &itr));
+	putchar('\n');
+	krmq_free(struct my_node, head, root, free);
+	return 0;
+}