| 1 | /*****************************************************************************/ |
| 2 | /* AVL */ |
| 3 | /*****************************************************************************/ |
| 4 | |
| 5 | #include <stdio.h> |
| 6 | #include <stdlib.h> |
| 7 | |
| 8 | typedef int t_cle; |
| 9 | |
| 10 | typedef struct noeud { |
| 11 | t_cle cle; |
| 12 | int deseq; /* deseq = hauteur du ss-abre gauche - hauteur du ss-arbre droit */ |
| 13 | struct noeud *gauche, *droit; |
| 14 | } N_AVL, *AVL; |
| 15 | |
| 16 | /*****************************************************************************/ |
| 17 | AVL RG(AVL a) |
| 18 | { |
| 19 | AVL b; |
| 20 | |
| 21 | b = a->droit; |
| 22 | a->droit = b->gauche; |
| 23 | b->gauche = a; |
| 24 | return b; |
| 25 | } |
| 26 | |
| 27 | /*****************************************************************************/ |
| 28 | AVL RD(AVL a) |
| 29 | { |
| 30 | AVL b; |
| 31 | |
| 32 | b = a->gauche; |
| 33 | a->gauche = b->droit; |
| 34 | b->droit = a; |
| 35 | return b; |
| 36 | } |
| 37 | |
| 38 | /*****************************************************************************/ |
| 39 | AVL RGD(AVL a) |
| 40 | { |
| 41 | a->gauche = RG(a->gauche); |
| 42 | return (RD(a)); |
| 43 | } |
| 44 | |
| 45 | /*****************************************************************************/ |
| 46 | AVL RDG(AVL a) |
| 47 | { |
| 48 | a->droit = RD(a->droit); |
| 49 | return (RG(a)); |
| 50 | } |
| 51 | |
| 52 | /*****************************************************************************/ |
| 53 | AVL insere(AVL p, int x, int *verif) |
| 54 | { |
| 55 | if (p == NULL) { |
| 56 | p = (N_AVL *) malloc(sizeof(N_AVL)); |
| 57 | if (p == NULL) |
| 58 | exit(-1); |
| 59 | p->cle = x; |
| 60 | p->gauche = NULL; |
| 61 | p->droit = NULL; |
| 62 | p->deseq = 0; |
| 63 | *verif = 1; |
| 64 | } else if (x == p->cle) |
| 65 | printf("Insertion impossible ! %d est deja dans l'arbre\n", x); |
| 66 | |
| 67 | else if (x < p->cle) { |
| 68 | p->gauche = insere(p->gauche, x, verif); |
| 69 | if (*verif) { /* on a insere a gauche */ |
| 70 | switch (p->deseq) { |
| 71 | case -1: |
| 72 | p->deseq = 0; |
| 73 | *verif = 0; |
| 74 | break; |
| 75 | case 0: |
| 76 | p->deseq = 1; |
| 77 | break; |
| 78 | case 1: // reequilibrage |
| 79 | if (p->gauche->deseq == 1) { // rotation droite |
| 80 | printf("RD pour %6d\n", p->cle); |
| 81 | p = RD(p); |
| 82 | p->deseq = p->droit->deseq = 0; |
| 83 | *verif = 0; |
| 84 | } else { /* rotation gauche droite */ |
| 85 | printf("RGD pour %6d\n", p->cle); |
| 86 | p = RGD(p); |
| 87 | switch (p->deseq) { |
| 88 | case -1: |
| 89 | p->droit->deseq = 0; |
| 90 | p->gauche->deseq = 1; |
| 91 | break; |
| 92 | case 0: |
| 93 | p->droit->deseq = 0; |
| 94 | p->gauche->deseq = 0; |
| 95 | break; |
| 96 | case 1: |
| 97 | p->droit->deseq = -1; |
| 98 | p->gauche->deseq = 0; |
| 99 | } |
| 100 | p->deseq = 0; |
| 101 | *verif = 0; |
| 102 | } |
| 103 | break; |
| 104 | } |
| 105 | |
| 106 | } |
| 107 | } else { |
| 108 | p->droit = insere(p->droit, x, verif); |
| 109 | if (*verif) { /* on a insere a droite */ |
| 110 | switch (p->deseq) { |
| 111 | case 1: |
| 112 | p->deseq = 0; |
| 113 | *verif = 0; |
| 114 | break; |
| 115 | case 0: |
| 116 | p->deseq = -1; |
| 117 | break; |
| 118 | case -1: // reequilibrage |
| 119 | if (p->droit->deseq == -1) { /* rotation gauche */ |
| 120 | printf("RG pour %6d\n", p->cle); |
| 121 | p = RG(p); |
| 122 | p->deseq = p->gauche->deseq = 0; |
| 123 | *verif = 0; |
| 124 | } else { /* rotation droite gauche */ |
| 125 | printf("RDG pour %6d\n", p->cle); |
| 126 | p = RDG(p); |
| 127 | switch (p->deseq) { |
| 128 | case 1: |
| 129 | p->droit->deseq = -1; |
| 130 | p->gauche->deseq = 0; |
| 131 | break; |
| 132 | case 0: |
| 133 | p->droit->deseq = 0; |
| 134 | p->gauche->deseq = 0; |
| 135 | break; |
| 136 | case -1: |
| 137 | p->droit->deseq = 0; |
| 138 | p->gauche->deseq = 1; |
| 139 | } |
| 140 | p->deseq = 0; |
| 141 | *verif = 0; |
| 142 | } |
| 143 | break; |
| 144 | } |
| 145 | } |
| 146 | } |
| 147 | return (p); |
| 148 | } |
| 149 | |
| 150 | /*****************************************************************************/ |
| 151 | AVL equigauche(AVL p, int *verif) |
| 152 | /* quand on entre dans la fonction, *verif = 1 */ |
| 153 | { |
| 154 | switch (p->deseq) { |
| 155 | case 1: |
| 156 | p->deseq = 0; |
| 157 | break; |
| 158 | case 0: |
| 159 | p->deseq = -1; |
| 160 | *verif = 0; |
| 161 | break; |
| 162 | case -1: /* reequilibrage */ |
| 163 | if (p->droit->deseq <= 0) { /* rotation gauche */ |
| 164 | printf("RG pour %6d\n", p->cle); |
| 165 | p = RG(p); |
| 166 | if (p->deseq == 0) { |
| 167 | p->gauche->deseq = -1; |
| 168 | p->deseq = 1; |
| 169 | *verif = 0; |
| 170 | } else { // forcement p->deseq = -1 |
| 171 | p->deseq = p->gauche->deseq = 0; |
| 172 | } |
| 173 | } else { /* rotation droite gauche */ |
| 174 | printf("RDG pour %6d\n", p->cle); |
| 175 | p = RDG(p); |
| 176 | switch (p->deseq) { |
| 177 | case 0: |
| 178 | p->droit->deseq = p->gauche->deseq = 0; |
| 179 | break; |
| 180 | case 1: |
| 181 | p->droit->deseq = -1; |
| 182 | p->gauche->deseq = 0; |
| 183 | break; |
| 184 | case -1: |
| 185 | p->droit->deseq = 0; |
| 186 | p->gauche->deseq = 1; |
| 187 | } |
| 188 | p->deseq = 0; |
| 189 | } |
| 190 | } |
| 191 | return p; |
| 192 | } |
| 193 | |
| 194 | /*****************************************************************************/ |
| 195 | AVL equidroit(AVL p, int *verif) // quand on entre dans la fonction, verif = 1 |
| 196 | { |
| 197 | switch (p->deseq) { |
| 198 | case -1: |
| 199 | p->deseq = 0; |
| 200 | break; |
| 201 | case 0: |
| 202 | p->deseq = 1; |
| 203 | *verif = 0; |
| 204 | break; |
| 205 | case 1: /* reequilibrage */ |
| 206 | if (p->gauche->deseq >= 0) { /* rotation droite */ |
| 207 | printf("RD pour %6d\n", p->cle); |
| 208 | p = RD(p); |
| 209 | if (p->deseq == 0) { |
| 210 | p->droit->deseq = 1; |
| 211 | p->deseq = -1; |
| 212 | *verif = 0; |
| 213 | } else { /* forcement p->deseq = 1 */ |
| 214 | p->deseq = p->droit->deseq = 0; |
| 215 | } |
| 216 | } else { /* rotation gauche droite */ |
| 217 | printf("RGD pour %6d\n", p->cle); |
| 218 | p = RGD(p); |
| 219 | switch (p->deseq) { |
| 220 | case 0: |
| 221 | p->gauche->deseq = p->droit->deseq = 0; |
| 222 | break; |
| 223 | case 1: |
| 224 | p->gauche->deseq = 0; |
| 225 | p->droit->deseq = -1; |
| 226 | break; |
| 227 | case -1: |
| 228 | p->gauche->deseq = 1; |
| 229 | p->droit->deseq = 0; |
| 230 | } |
| 231 | p->deseq = 0; |
| 232 | } |
| 233 | } |
| 234 | return p; |
| 235 | } |
| 236 | |
| 237 | /*****************************************************************************/ |
| 238 | AVL supmax(AVL p, AVL r, int *verif) |
| 239 | { |
| 240 | AVL q; |
| 241 | |
| 242 | if (r->droit == NULL) { |
| 243 | p->cle = r->cle; |
| 244 | q = r; /* q : l'element a supprimer par free */ |
| 245 | r = r->gauche; |
| 246 | free(q); |
| 247 | *verif = 1; |
| 248 | } else { |
| 249 | r->droit = supmax(p, r->droit, verif); |
| 250 | if (*verif) |
| 251 | r = equidroit(r, verif); |
| 252 | } |
| 253 | return r; |
| 254 | } |
| 255 | |
| 256 | /*****************************************************************************/ |
| 257 | AVL supprime(AVL p, int x, int *verif) |
| 258 | { |
| 259 | AVL q; |
| 260 | |
| 261 | if (p == NULL) |
| 262 | printf("Suppression impossible ! %d n'est pas dans l'arbre\n", x); |
| 263 | else if (x == p->cle) { /* Suppression de p */ |
| 264 | if (p->droit == NULL) { |
| 265 | q = p; |
| 266 | p = p->gauche; |
| 267 | free(q); |
| 268 | *verif = 1; |
| 269 | } else if (p->gauche == NULL) { |
| 270 | q = p; |
| 271 | p = p->droit; |
| 272 | free(q); |
| 273 | *verif = 1; |
| 274 | } else { |
| 275 | p->gauche = supmax(p, p->gauche, verif); |
| 276 | if (*verif) |
| 277 | p = equigauche(p, verif); |
| 278 | } |
| 279 | } else if (x < p->cle) { |
| 280 | p->gauche = supprime(p->gauche, x, verif); |
| 281 | if (*verif) |
| 282 | p = equigauche(p, verif); |
| 283 | } else { |
| 284 | p->droit = supprime(p->droit, x, verif); |
| 285 | if (*verif) |
| 286 | p = equidroit(p, verif); |
| 287 | } |
| 288 | return p; |
| 289 | } |
| 290 | |
| 291 | /*****************************************************************************/ |
| 292 | void affiche_arbre(AVL p, int col) |
| 293 | { |
| 294 | int i; |
| 295 | char esp = ' '; |
| 296 | |
| 297 | if (p) { |
| 298 | affiche_arbre(p->droit, col + 6); |
| 299 | for (i = 0; i < col; i++) |
| 300 | printf("%c", esp); |
| 301 | printf("%6d(%2d)\n", p->cle, p->deseq); |
| 302 | affiche_arbre(p->gauche, col + 6); |
| 303 | }; |
| 304 | } |
| 305 | |
| 306 | /*****************************************************************************/ |
| 307 | main() |
| 308 | { |
| 309 | AVL rac = NULL; |
| 310 | int x; |
| 311 | int verif; |
| 312 | |
| 313 | do { |
| 314 | printf("Entrez une cle: "); |
| 315 | scanf("%d", &x); |
| 316 | if (x) { |
| 317 | printf("Insertion de la cle %6d\n", x); |
| 318 | verif = 0; |
| 319 | rac = insere(rac, x, &verif); |
| 320 | affiche_arbre(rac, 0); |
| 321 | } |
| 322 | } |
| 323 | while (x); |
| 324 | |
| 325 | do { |
| 326 | printf("Entrez une cle: "); |
| 327 | scanf("%d", &x); |
| 328 | if (x) { |
| 329 | printf("Suppression de la cle %6d\n", x); |
| 330 | verif = 0; |
| 331 | rac = supprime(rac, x, &verif); |
| 332 | affiche_arbre(rac, 0); |
| 333 | } |
| 334 | } |
| 335 | while (x); |
| 336 | } |
| 337 | |
| 338 | /*****************************************************************************/ |