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213 lines
7.2 KiB
/*


An implementation of topdown splaying with sizes


D. Sleator <sleator@cs.cmu.edu>, January 1994.




This extends topdownsplay.c to maintain a size field in each node.


This is the number of nodes in the subtree rooted there. This makes


it possible to efficiently compute the rank of a key. (The rank is


the number of nodes to the left of the given key.) It it also


possible to quickly find the node of a given rank. Both of these


operations are illustrated in the code below. The remainder of this


introduction is taken from topdownsplay.c.




"Splay trees", or "selfadjusting search trees" are a simple and


efficient data structure for storing an ordered set. The data


structure consists of a binary tree, with no additional fields. It


allows searching, insertion, deletion, deletemin, deletemax,


splitting, joining, and many other operations, all with amortized


logarithmic performance. Since the trees adapt to the sequence of


requests, their performance on real access patterns is typically even


better. Splay trees are described in a number of texts and papers


[1,2,3,4].




The code here is adapted from simple topdown splay, at the bottom of


page 669 of [2]. It can be obtained via anonymous ftp from


spade.pc.cs.cmu.edu in directory /usr/sleator/public.




The chief modification here is that the splay operation works even if the


item being splayed is not in the tree, and even if the tree root of the


tree is NULL. So the line:




t = splay(i, t);




causes it to search for item with key i in the tree rooted at t. If it's


there, it is splayed to the root. If it isn't there, then the node put


at the root is the last one before NULL that would have been reached in a


normal binary search for i. (It's a neighbor of i in the tree.) This


allows many other operations to be easily implemented, as shown below.




[1] "Data Structures and Their Algorithms", Lewis and Denenberg,


Harper Collins, 1991, pp 243251.


[2] "Selfadjusting Binary Search Trees" Sleator and Tarjan,


JACM Volume 32, No 3, July 1985, pp 652686.


[3] "Data Structure and Algorithm Analysis", Mark Weiss,


Benjamin Cummins, 1992, pp 119130.


[4] "Data Structures, Algorithms, and Performance", Derick Wood,


AddisonWesley, 1993, pp 367375


*/




#include <stdlib.h>


#include <assert.h>


#include "splaytree.h"




#define compare(i,j) ((i)(j))


/* This is the comparison. */


/* Returns <0 if i<j, =0 if i=j, and >0 if i>j */




#define node_size(x) (((x)==NULL) ? 0 : ((x)>size))


/* This macro returns the size of a node. Unlike "x>size", */


/* it works even if x=NULL. The test could be avoided by using */


/* a special version of NULL which was a real node with size 0. */




/* Splay using the key i (which may or may not be in the tree.)


* The starting root is t, and the tree used is defined by rat


* size fields are maintained */


splay_tree * splaytree_splay (splay_tree *t, int i) {


splay_tree N, *l, *r, *y;


int comp, root_size, l_size, r_size;




if (t == NULL) return t;


N.left = N.right = NULL;


l = r = &N;


root_size = node_size(t);


l_size = r_size = 0;




for (;;) {


comp = compare(i, t>key);


if (comp < 0) {


if (t>left == NULL) break;


if (compare(i, t>left>key) < 0) {


y = t>left; /* rotate right */


t>left = y>right;


y>right = t;


t>size = node_size(t>left) + node_size(t>right) + 1;


t = y;


if (t>left == NULL) break;


}


r>left = t; /* link right */


r = t;


t = t>left;


r_size += 1+node_size(r>right);


} else if (comp > 0) {


if (t>right == NULL) break;


if (compare(i, t>right>key) > 0) {


y = t>right; /* rotate left */


t>right = y>left;


y>left = t;


t>size = node_size(t>left) + node_size(t>right) + 1;


t = y;


if (t>right == NULL) break;


}


l>right = t; /* link left */


l = t;


t = t>right;


l_size += 1+node_size(l>left);


} else {


break;


}


}


l_size += node_size(t>left); /* Now l_size and r_size are the sizes of */


r_size += node_size(t>right); /* the left and right trees we just built.*/


t>size = l_size + r_size + 1;




l>right = r>left = NULL;




/* The following two loops correct the size fields of the right path */


/* from the left child of the root and the right path from the left */


/* child of the root. */


for (y = N.right; y != NULL; y = y>right) {


y>size = l_size;


l_size = 1+node_size(y>left);


}


for (y = N.left; y != NULL; y = y>left) {


y>size = r_size;


r_size = 1+node_size(y>right);


}




l>right = t>left; /* assemble */


r>left = t>right;


t>left = N.right;


t>right = N.left;




return t;


}




splay_tree * splaytree_insert(splay_tree * t, int i, void *data) {


/* Insert key i into the tree t, if it is not already there. */


/* Return a pointer to the resulting tree. */


splay_tree * new;




if (t != NULL) {


t = splaytree_splay(t, i);


if (compare(i, t>key)==0) {


return t; /* it's already there */


}


}


new = (splay_tree *) malloc (sizeof (splay_tree));


assert(new);


if (t == NULL) {


new>left = new>right = NULL;


} else if (compare(i, t>key) < 0) {


new>left = t>left;


new>right = t;


t>left = NULL;


t>size = 1+node_size(t>right);


} else {


new>right = t>right;


new>left = t;


t>right = NULL;


t>size = 1+node_size(t>left);


}


new>key = i;


new>data = data;


new>size = 1 + node_size(new>left) + node_size(new>right);


return new;


}




splay_tree * splaytree_delete(splay_tree *t, int i) {


/* Deletes i from the tree if it's there. */


/* Return a pointer to the resulting tree. */


splay_tree * x;


int tsize;




if (t==NULL) return NULL;


tsize = t>size;


t = splaytree_splay(t, i);


if (compare(i, t>key) == 0) { /* found it */


if (t>left == NULL) {


x = t>right;


} else {


x = splaytree_splay(t>left, i);


x>right = t>right;


}


free(t);


if (x != NULL) {


x>size = tsize1;


}


return x;


} else {


return t; /* It wasn't there */


}


}




splay_tree *find_rank(int r, splay_tree *t) {


/* Returns a pointer to the node in the tree with the given rank. */


/* Returns NULL if there is no such node. */


/* Does not change the tree. To guarantee logarithmic behavior, */


/* the node found here should be splayed to the root. */


int lsize;


if ((r < 0)  (r >= node_size(t))) return NULL;


for (;;) {


lsize = node_size(t>left);


if (r < lsize) {


t = t>left;


} else if (r > lsize) {


r = r  lsize 1;


t = t>right;


} else {


return t;


}


}


}






