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Beap

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find operation can be implemented if parent pointers at each node are maintained. You would start at the absolute bottom-most element of the top node (similar to the left-most child in a heap) and move either up or right to find the element of interest.
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in the worst case. Removal and insertion of new elements involves propagation of elements up or down (much like in a heap) in order to restore the beap invariant. An additional perk is that beap provides constant time access to the smallest element and
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time. In a beap, each element is stored in a node with up to two parents and up to two children, with the property that the value of a parent node is never greater than the value of either of its children.
121:, which are usually implemented that way as well. However, their performance characteristics are different from heaps; in particular, a beap enables sublinear retrieval of arbitrary elements. 330: 294: 231: 198: 174: 54: 260: 113:
containing only the values to be stored, with the parent-child relationships being determined implicitly by the array indices. (That is: beaps are an
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for a set (or map, or multiset or multimap) that enables elements (or mappings) to be located, inserted, or deleted in
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time on average. Find operations in the heap can be
324: 288: 254: 225: 192: 168: 46:but its sources remain unclear because it lacks 152:The height of the structure is approximately 8: 362: 312: 304: 276: 268: 238: 213: 205: 183: 181: 159: 157: 77:Learn how and when to remove this message 375:(Jun 1964). "Algorithm 232 - Heapsort". 138: 350:Journal of Computer and System Sciences 343:Munro, J. Ian; Suwanda, Hendra (1980). 117:.) In that respect they are similar to 7: 132:. A related data structure is the 14: 23: 109:Beaps are implemented using an 325:{\displaystyle O({\sqrt {n}})} 319: 309: 296:time for the maximum element. 289:{\displaystyle O({\sqrt {n}})} 283: 273: 249: 243: 226:{\displaystyle O({\sqrt {n}})} 220: 210: 1: 364:10.1016/0022-0000(80)90037-9 193:{\displaystyle {\sqrt {n}}} 169:{\displaystyle {\sqrt {n}}} 124:The beap was introduced by 424: 378:Communications of the ACM 32:This article includes a 408:Heaps (data structures) 115:implicit data structure 61:more precise citations. 326: 290: 256: 227: 194: 170: 144: 391:10.1145/512274.512284 327: 291: 257: 228: 195: 171: 142: 303: 267: 255:{\displaystyle O(n)} 237: 204: 180: 156: 373:Williams, J. W. J. 322: 286: 252: 223: 190: 166: 145: 34:list of references 317: 281: 218: 188: 164: 87: 86: 79: 415: 394: 368: 366: 331: 329: 328: 323: 318: 313: 295: 293: 292: 287: 282: 277: 261: 259: 258: 253: 232: 230: 229: 224: 219: 214: 199: 197: 196: 191: 189: 184: 175: 173: 172: 167: 165: 160: 95:bi-parental heap 82: 75: 71: 68: 62: 57:this article by 48:inline citations 27: 26: 19: 423: 422: 418: 417: 416: 414: 413: 412: 398: 397: 371: 342: 339: 301: 300: 265: 264: 235: 234: 202: 201: 178: 177: 154: 153: 150: 83: 72: 66: 63: 52: 38:related reading 28: 24: 17: 12: 11: 5: 421: 419: 411: 410: 400: 399: 396: 395: 385:(6): 347–348. 369: 357:(2): 236–250. 338: 335: 321: 316: 311: 308: 285: 280: 275: 272: 251: 248: 245: 242: 222: 217: 212: 209: 187: 163: 149: 146: 130:Hendra Suwanda 99:data structure 85: 84: 42:external links 31: 29: 22: 16:Data structure 15: 13: 10: 9: 6: 4: 3: 2: 420: 409: 406: 405: 403: 392: 388: 384: 380: 379: 374: 370: 365: 360: 356: 352: 351: 346: 341: 340: 336: 334: 314: 306: 297: 278: 270: 246: 240: 215: 207: 185: 161: 147: 141: 137: 135: 134:Young tableau 131: 127: 122: 120: 116: 112: 107: 104: 100: 96: 92: 81: 78: 70: 60: 56: 50: 49: 43: 39: 35: 30: 21: 20: 382: 376: 354: 348: 299:Actually, a 298: 151: 123: 119:binary heaps 108: 94: 90: 88: 73: 64: 53:Please help 45: 148:Performance 59:introducing 337:References 126:Ian Munro 103:sublinear 402:Category 67:May 2024 97:, is a 55:improve 111:array 93:, or 40:, or 143:Beap 128:and 91:beap 387:doi 359:doi 404:: 381:. 355:21 353:. 347:. 136:. 89:A 44:, 36:, 393:. 389:: 383:7 367:. 361:: 320:) 315:n 310:( 307:O 284:) 279:n 274:( 271:O 250:) 247:n 244:( 241:O 221:) 216:n 211:( 208:O 186:n 162:n 80:) 74:( 69:) 65:( 51:.

Index

list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
data structure
sublinear
array
implicit data structure
binary heaps
Ian Munro
Hendra Suwanda
Young tableau

"Implicit data structures for fast search and update"
Journal of Computer and System Sciences
doi
10.1016/0022-0000(80)90037-9
Williams, J. W. J.
Communications of the ACM
doi
10.1145/512274.512284
Category
Heaps (data structures)

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