/* avl.c - routines to implement an avl tree */ /* $OpenLDAP$ */ /* This work is part of OpenLDAP Software . * * Copyright 2005 The OpenLDAP Foundation. * Portions Copyright (c) 2005 by Howard Chu, Symas Corp. * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted only as authorized by the OpenLDAP * Public License. * * A copy of this license is available in the file LICENSE in the * top-level directory of the distribution or, alternatively, at * . */ /* ACKNOWLEDGEMENTS: * This work was initially developed by Howard Chu for inclusion * in OpenLDAP software. */ #include "portable.h" #include #include #ifdef CSRIMALLOC #define ber_memalloc malloc #define ber_memrealloc realloc #define ber_memfree free #else #include "lber.h" #endif #define AVL_INTERNAL #include "avl.h" static const int avl_bfs[] = {LH, RH}; /* * Threaded AVL trees - for fast in-order traversal of nodes. */ /* * tavl_insert -- insert a node containing data data into the avl tree * with root root. fcmp is a function to call to compare the data portion * of two nodes. it should take two arguments and return <, >, or == 0, * depending on whether its first argument is <, >, or == its second * argument (like strcmp, e.g.). fdup is a function to call when a duplicate * node is inserted. it should return 0, or -1 and its return value * will be the return value from avl_insert in the case of a duplicate node. * the function will be called with the original node's data as its first * argument and with the incoming duplicate node's data as its second * argument. this could be used, for example, to keep a count with each * node. * * NOTE: this routine may malloc memory */ int tavl_insert( Avlnode ** root, void *data, AVL_CMP fcmp, AVL_DUP fdup ) { Avlnode *t, *p, *s, *q, *r; int a, cmp, ncmp; if ( *root == NULL ) { if (( r = (Avlnode *) ber_memalloc( sizeof( Avlnode ))) == NULL ) { return( -1 ); } r->avl_link[0] = r->avl_link[1] = NULL; r->avl_data = data; r->avl_bf = EH; r->avl_bits[0] = r->avl_bits[1] = AVL_THREAD; *root = r; return( 0 ); } t = NULL; s = p = *root; /* find insertion point */ while (1) { cmp = fcmp( data, p->avl_data ); if ( cmp == 0 ) return (*fdup)( p->avl_data, data ); cmp = (cmp > 0); q = avl_child( p, cmp ); if (q == NULL) { /* insert */ if (( q = (Avlnode *) ber_memalloc( sizeof( Avlnode ))) == NULL ) { return( -1 ); } q->avl_link[cmp] = p->avl_link[cmp]; q->avl_link[!cmp] = p; q->avl_data = data; q->avl_bf = EH; q->avl_bits[0] = q->avl_bits[1] = AVL_THREAD; p->avl_link[cmp] = q; p->avl_bits[cmp] = AVL_CHILD; break; } else if ( q->avl_bf ) { t = p; s = q; } p = q; } /* adjust balance factors */ cmp = fcmp( data, s->avl_data ) > 0; r = p = s->avl_link[cmp]; a = avl_bfs[cmp]; while ( p != q ) { cmp = fcmp( data, p->avl_data ) > 0; p->avl_bf = avl_bfs[cmp]; p = p->avl_link[cmp]; } /* checks and balances */ if ( s->avl_bf == EH ) { s->avl_bf = a; return 0; } else if ( s->avl_bf == -a ) { s->avl_bf = EH; return 0; } else if ( s->avl_bf == a ) { cmp = (a > 0); ncmp = !cmp; if ( r->avl_bf == a ) { /* single rotation */ p = r; if ( r->avl_bits[ncmp] == AVL_THREAD ) { r->avl_bits[ncmp] = AVL_CHILD; s->avl_bits[cmp] = AVL_THREAD; } else { s->avl_link[cmp] = r->avl_link[ncmp]; r->avl_link[ncmp] = s; } s->avl_bf = 0; r->avl_bf = 0; } else if ( r->avl_bf == -a ) { /* double rotation */ p = r->avl_link[ncmp]; if ( p->avl_bits[cmp] == AVL_THREAD ) { p->avl_bits[cmp] = AVL_CHILD; r->avl_bits[ncmp] = AVL_THREAD; } else { r->avl_link[ncmp] = p->avl_link[cmp]; p->avl_link[cmp] = r; } if ( p->avl_bits[ncmp] == AVL_THREAD ) { p->avl_bits[ncmp] = AVL_CHILD; s->avl_link[cmp] = p; s->avl_bits[cmp] = AVL_THREAD; } else { s->avl_link[cmp] = p->avl_link[ncmp]; p->avl_link[ncmp] = s; } if ( p->avl_bf == a ) { s->avl_bf = -a; r->avl_bf = 0; } else if ( p->avl_bf == -a ) { s->avl_bf = 0; r->avl_bf = a; } else { s->avl_bf = 0; r->avl_bf = 0; } p->avl_bf = 0; } /* Update parent */ if ( t == NULL ) *root = p; else if ( s == t->avl_right ) t->avl_right = p; else t->avl_left = p; } return 0; } void* tavl_delete( Avlnode **root, void* data, AVL_CMP fcmp ) { Avlnode *p, *q, *r, *s, *top; int side, side_bf, shorter, nside; /* parent stack */ Avlnode *pptr[sizeof(void *)*8]; unsigned char pdir[sizeof(void *)*8]; int depth = 0; if ( *root == NULL ) return NULL; p = *root; while (1) { side = fcmp( data, p->avl_data ); if ( !side ) break; side = ( side > 0 ); pdir[depth] = side; pptr[depth++] = p; if ( p->avl_bits[side] == AVL_THREAD ) return NULL; p = p->avl_link[side]; } data = p->avl_data; /* If this node has two children, swap so we are deleting a node with * at most one child. */ if ( p->avl_bits[0] == AVL_CHILD && p->avl_bits[1] == AVL_CHILD && p->avl_link[0] && p->avl_link[1] ) { /* find the immediate predecessor */ q = p->avl_link[0]; side = depth; pdir[depth++] = 0; while (q->avl_bits[1] == AVL_CHILD && q->avl_link[1]) { pdir[depth] = 1; pptr[depth++] = q; q = q->avl_link[1]; } /* swap links */ r = p->avl_link[0]; p->avl_link[0] = q->avl_link[0]; q->avl_link[0] = r; q->avl_link[1] = p->avl_link[1]; p->avl_link[1] = q; p->avl_bits[0] = q->avl_bits[0]; p->avl_bits[1] = q->avl_bits[1]; q->avl_bits[0] = q->avl_bits[1] = AVL_CHILD; q->avl_bf = p->avl_bf; /* fix stack positions: old parent of p points to q */ pptr[side] = q; if ( side ) { --side; r = pptr[side]; r->avl_link[pdir[side]] = q; } else { *root = q; } /* new parent of p points to p */ if ( depth > 2 ) { r = pptr[depth-2]; r->avl_link[1] = p; pptr[depth-1] = p; } else { q->avl_link[0] = p; } /* fix right subtree: successor of p points to q */ r = q->avl_link[1]; while ( r->avl_bits[0] == AVL_CHILD && r->avl_link[0] ) r = r->avl_link[0]; r->avl_link[0] = q; } /* now

has at most one child, get it */ if ( p->avl_link[0] && p->avl_bits[0] == AVL_CHILD ) { q = p->avl_link[0]; /* Preserve thread continuity */ r = p->avl_link[1]; nside = 1; } else if ( p->avl_link[1] && p->avl_bits[1] == AVL_CHILD ) { q = p->avl_link[1]; r = p->avl_link[0]; nside = 0; } else { q = NULL; if ( depth > 0 ) r = p->avl_link[pdir[depth-1]]; else r = NULL; } ber_memfree( p ); if ( !depth ) { *root = q; return data; } /* set the child into p's parent */ depth--; p = pptr[depth]; side = pdir[depth]; p->avl_link[side] = q; /* Update child thread */ if ( q ) { for ( ; q->avl_bits[nside] == AVL_CHILD && q->avl_link[nside]; q = q->avl_link[nside] ) ; q->avl_link[nside] = r; } else { p->avl_bits[side] = AVL_THREAD; p->avl_link[side] = r; } top = NULL; shorter = 1; while ( shorter ) { p = pptr[depth]; side = pdir[depth]; nside = !side; side_bf = avl_bfs[side]; /* case 1: height unchanged */ if ( p->avl_bf == EH ) { /* Tree is now heavier on opposite side */ p->avl_bf = avl_bfs[nside]; shorter = 0; } else if ( p->avl_bf == side_bf ) { /* case 2: taller subtree shortened, height reduced */ p->avl_bf = EH; } else { /* case 3: shorter subtree shortened */ if ( depth ) top = pptr[depth-1]; /* p->parent; */ else top = NULL; /* set to the taller of the two subtrees of

*/ q = p->avl_link[nside]; if ( q->avl_bf == EH ) { /* case 3a: height unchanged, single rotate */ if ( q->avl_bits[side] == AVL_THREAD ) { q->avl_bits[side] = AVL_CHILD; p->avl_bits[nside] = AVL_THREAD; } else { p->avl_link[nside] = q->avl_link[side]; q->avl_link[side] = p; } shorter = 0; q->avl_bf = side_bf; p->avl_bf = (- side_bf); } else if ( q->avl_bf == p->avl_bf ) { /* case 3b: height reduced, single rotate */ if ( q->avl_bits[side] == AVL_THREAD ) { q->avl_bits[side] = AVL_CHILD; p->avl_bits[nside] = AVL_THREAD; } else { p->avl_link[nside] = q->avl_link[side]; q->avl_link[side] = p; } shorter = 1; q->avl_bf = EH; p->avl_bf = EH; } else { /* case 3c: height reduced, balance factors opposite */ r = q->avl_link[side]; if ( r->avl_bits[nside] == AVL_THREAD ) { r->avl_bits[nside] = AVL_CHILD; q->avl_bits[side] = AVL_THREAD; } else { q->avl_link[side] = r->avl_link[nside]; r->avl_link[nside] = q; } if ( r->avl_bits[side] == AVL_THREAD ) { r->avl_bits[side] = AVL_CHILD; p->avl_bits[nside] = AVL_THREAD; p->avl_link[nside] = r; } else { p->avl_link[nside] = r->avl_link[side]; r->avl_link[side] = p; } if ( r->avl_bf == side_bf ) { q->avl_bf = (- side_bf); p->avl_bf = EH; } else if ( r->avl_bf == (- side_bf)) { q->avl_bf = EH; p->avl_bf = side_bf; } else { q->avl_bf = EH; p->avl_bf = EH; } r->avl_bf = EH; q = r; } /* a rotation has caused (or in case 3c) to become * the root. let

's former parent know this. */ if ( top == NULL ) { *root = q; } else if (top->avl_link[0] == p) { top->avl_link[0] = q; } else { top->avl_link[1] = q; } /* end case 3 */ p = q; } if ( !depth ) break; depth--; } /* end while(shorter) */ return data; } /* * tavl_free -- traverse avltree root, freeing the memory it is using. * the dfree() is called to free the data portion of each node. The * number of items actually freed is returned. */ int tavl_free( Avlnode *root, AVL_FREE dfree ) { int nleft, nright; if ( root == 0 ) return( 0 ); nleft = tavl_free( avl_lchild( root ), dfree ); nright = tavl_free( avl_rchild( root ), dfree ); if ( dfree ) (*dfree)( root->avl_data ); ber_memfree( root ); return( nleft + nright + 1 ); } /* * tavl_find -- search avltree root for a node with data data. the function * cmp is used to compare things. it is called with data as its first arg * and the current node data as its second. it should return 0 if they match, * < 0 if arg1 is less than arg2 and > 0 if arg1 is greater than arg2. */ Avlnode * tavl_find2( Avlnode *root, const void *data, AVL_CMP fcmp ) { int cmp; while ( root != 0 && (cmp = (*fcmp)( data, root->avl_data )) != 0 ) { cmp = cmp > 0; root = avl_child( root, cmp ); } return root; } void* tavl_find( Avlnode *root, const void* data, AVL_CMP fcmp ) { int cmp; while ( root != 0 && (cmp = (*fcmp)( data, root->avl_data )) != 0 ) { cmp = cmp > 0; root = avl_child( root, cmp ); } return( root ? root->avl_data : 0 ); } /* Return the leftmost or rightmost node in the tree */ Avlnode * tavl_end( Avlnode *root, int dir ) { if ( root ) { while ( root->avl_bits[dir] == AVL_CHILD ) root = root->avl_link[dir]; } return root; } /* Return the next node in the given direction */ Avlnode * tavl_next( Avlnode *root, int dir ) { if ( root ) { int c = root->avl_bits[dir]; root = root->avl_link[dir]; if ( c == AVL_CHILD ) { dir ^= 1; while ( root->avl_bits[dir] == AVL_CHILD ) root = root->avl_link[dir]; } } return root; }