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| @@ -1,12 +1,14 @@ | |
| 1 1 | {<<"app">>,<<"sorted_set">>}. |
| 2 | + {<<"build_tools">>,[<<"mix">>]}. |
| 2 3 | {<<"contributors">>,[<<"Seneca Systems">>]}. |
| 3 4 | {<<"description">>,<<"SortedSet implementation for Elixir">>}. |
| 4 5 | {<<"elixir">>,<<"~> 1.0">>}. |
| 5 6 | {<<"files">>, |
| 6 | - [<<"lib/sorted_set.ex">>,<<"mix.exs">>,<<"README.md">>,<<"LICENSE">>]}. |
| 7 | + [<<"lib/red_black_tree.ex">>,<<"lib/red_black_tree/node.ex">>, |
| 8 | + <<"lib/sorted_set.ex">>,<<"mix.exs">>,<<"README.md">>,<<"LICENSE">>]}. |
| 7 9 | {<<"licenses">>,[<<"MIT">>]}. |
| 8 10 | {<<"links">>, |
| 9 11 | [{<<"GitHub">>,<<"https://github.com/SenecaSystems/sorted_set">>}]}. |
| 10 12 | {<<"name">>,<<"sorted_set">>}. |
| 11 13 | {<<"requirements">>,[]}. |
| 12 | - {<<"version">>,<<"0.1.1">>}. |
| 14 | + {<<"version">>,<<"0.2.0">>}. |
| @@ -0,0 +1,606 @@ | |
| 1 | + defmodule RedBlackTree do |
| 2 | + @moduledoc """ |
| 3 | + Red-black trees are key-value stores. |
| 4 | + While not guaranteed to be perfectly balanced, they guarantee O(log(n)) search |
| 5 | + time. |
| 6 | + |
| 7 | + The RedBlackTree module contains an eponymous struct and various useful |
| 8 | + functions. |
| 9 | + |
| 10 | + Nodes know their depth (automatically updated on insert/delete) |
| 11 | + """ |
| 12 | + alias RedBlackTree.Node |
| 13 | + |
| 14 | + defstruct root: nil, size: 0 |
| 15 | + |
| 16 | + @key_hash_bucket 4294967296 |
| 17 | + |
| 18 | + # Inline key hashing |
| 19 | + @compile {:inline, key_less_than?: 2, hash_key: 1, fallback_key_hash: 1} |
| 20 | + |
| 21 | + def new() do |
| 22 | + %RedBlackTree{} |
| 23 | + end |
| 24 | + |
| 25 | + def new(values) when is_list(values) do |
| 26 | + new(%RedBlackTree{}, values) |
| 27 | + end |
| 28 | + |
| 29 | + defp new(tree, []) do |
| 30 | + tree |
| 31 | + end |
| 32 | + |
| 33 | + # Allow initialization with key/value tuples |
| 34 | + defp new(tree, [{key, value}|tail]) do |
| 35 | + new(RedBlackTree.insert(tree, key, value), tail) |
| 36 | + end |
| 37 | + |
| 38 | + # Allow initialization with individual values, in which case they will be both |
| 39 | + # the key and the value |
| 40 | + defp new(tree, [key|tail]) do |
| 41 | + new(RedBlackTree.insert(tree, key, key), tail) |
| 42 | + end |
| 43 | + |
| 44 | + def size(%RedBlackTree{size: size}) do |
| 45 | + size |
| 46 | + end |
| 47 | + |
| 48 | + def put(tree, key, value) do |
| 49 | + insert(tree, key, value) |
| 50 | + end |
| 51 | + |
| 52 | + def insert(%RedBlackTree{root: nil}, key, value) do |
| 53 | + %RedBlackTree{root: Node.new(key, value), size: 1} |
| 54 | + end |
| 55 | + |
| 56 | + def insert(%RedBlackTree{root: root, size: size}=tree, key, value) do |
| 57 | + {nodes_added, new_root} = do_insert(root, key, value, 1) |
| 58 | + %RedBlackTree{ |
| 59 | + tree | |
| 60 | + root: make_node_black(new_root), |
| 61 | + size: size + nodes_added |
| 62 | + } |
| 63 | + end |
| 64 | + |
| 65 | + def delete(%RedBlackTree{root: root, size: size}=tree, key) do |
| 66 | + {nodes_removed, new_root} = do_delete(root, key) |
| 67 | + %RedBlackTree{ |
| 68 | + tree | |
| 69 | + root: new_root, |
| 70 | + size: size - nodes_removed |
| 71 | + } |
| 72 | + end |
| 73 | + |
| 74 | + def fetch(tree, key) do |
| 75 | + search(tree, key) |
| 76 | + end |
| 77 | + |
| 78 | + def search(%RedBlackTree{root: root}, key) do |
| 79 | + do_search(root, key) |
| 80 | + end |
| 81 | + |
| 82 | + defp do_search(nil, _key) do |
| 83 | + nil |
| 84 | + end |
| 85 | + |
| 86 | + defp do_search(%Node{key: node_key, value: value}, search_key) when node_key === search_key do |
| 87 | + value |
| 88 | + end |
| 89 | + |
| 90 | + defp do_search(%Node{key: node_key, left: left}, search_key) when search_key < node_key do |
| 91 | + do_search(left, search_key) |
| 92 | + end |
| 93 | + |
| 94 | + defp do_search(%Node{key: node_key, right: right}, search_key) when search_key > node_key do |
| 95 | + do_search(right, search_key) |
| 96 | + end |
| 97 | + |
| 98 | + # For cases when `insert_key !== node_key` but `insert_key == node_key` (e.g. |
| 99 | + # `1` and `1.0`,) hash the keys to provide consistent ordering. |
| 100 | + defp do_search(%Node{key: node_key, left: left, right: right}, search_key) when search_key == node_key do |
| 101 | + if key_less_than?(search_key, node_key) do |
| 102 | + do_search(left, search_key) |
| 103 | + else |
| 104 | + do_search(right, search_key) |
| 105 | + end |
| 106 | + end |
| 107 | + |
| 108 | + def has_key?(%RedBlackTree{root: root}, key) do |
| 109 | + do_has_key?(root, key) |
| 110 | + end |
| 111 | + |
| 112 | + defp do_has_key?(nil, _key) do |
| 113 | + false |
| 114 | + end |
| 115 | + |
| 116 | + defp do_has_key?(%Node{key: node_key}, search_key) when node_key === search_key do |
| 117 | + true |
| 118 | + end |
| 119 | + |
| 120 | + defp do_has_key?(%Node{key: node_key, left: left}, search_key) when search_key < node_key do |
| 121 | + do_has_key?(left, search_key) |
| 122 | + end |
| 123 | + |
| 124 | + defp do_has_key?(%Node{key: node_key, right: right}, search_key) when search_key > node_key do |
| 125 | + do_has_key?(right, search_key) |
| 126 | + end |
| 127 | + |
| 128 | + # For cases when `insert_key !== node_key` but `insert_key == node_key` (e.g. |
| 129 | + # `1` and `1.0`,) hash the keys to provide consistent ordering. |
| 130 | + defp do_has_key?(%Node{key: node_key, left: left, right: right}, search_key) when search_key == node_key do |
| 131 | + if key_less_than?(search_key, node_key) do |
| 132 | + do_has_key?(left, search_key) |
| 133 | + else |
| 134 | + do_has_key?(right, search_key) |
| 135 | + end |
| 136 | + end |
| 137 | + |
| 138 | + |
| 139 | + def balance(%RedBlackTree{root: root}=tree) do |
| 140 | + %RedBlackTree{tree | root: do_balance(root)} |
| 141 | + end |
| 142 | + |
| 143 | + def to_list(%RedBlackTree{}=tree) do |
| 144 | + reduce(tree, [], fn (node, members) -> |
| 145 | + [{node.key, node.value} | members] |
| 146 | + end) |> Enum.reverse |
| 147 | + end |
| 148 | + |
| 149 | + @doc """ |
| 150 | + For each node, calls the provided function passing in (node, acc) |
| 151 | + Optionally takes an order as the first argument which can be one of |
| 152 | + `:in_order`, `:pre_order`, or `:post_order`. |
| 153 | + |
| 154 | + Defaults to `:in_order` if no order is given. |
| 155 | + """ |
| 156 | + def reduce(tree, acc, fun) do |
| 157 | + reduce(:in_order, tree, acc, fun) |
| 158 | + end |
| 159 | + |
| 160 | + def reduce(_order, %RedBlackTree{root: nil}, acc, _fun) do |
| 161 | + acc |
| 162 | + end |
| 163 | + |
| 164 | + def reduce(order, %RedBlackTree{root: root}, acc, fun) do |
| 165 | + do_reduce(order, root, acc, fun) |
| 166 | + end |
| 167 | + |
| 168 | + ## Helpers |
| 169 | + |
| 170 | + defp make_node_black(%Node{}=node) do |
| 171 | + %Node{node | color: :black} |
| 172 | + end |
| 173 | + |
| 174 | + # ¡This is only used as a tiebreaker! |
| 175 | + # For cases when `insert_key !== node_key` but `insert_key == node_key` (e.g. |
| 176 | + # `1` and `1.0`,) hash the keys to provide consistent ordering. |
| 177 | + defp hash_key(key) do |
| 178 | + :erlang.phash2(key, @key_hash_bucket) |
| 179 | + end |
| 180 | + |
| 181 | + # In the case that `hash_key(key1) == hash_key(key2)` we can fall back again |
| 182 | + # to the slower phash function distributed over @key_hash_bucket integers. |
| 183 | + # If these two collide, go home. |
| 184 | + defp fallback_key_hash(key) do |
| 185 | + :erlang.phash(key, @key_hash_bucket) |
| 186 | + end |
| 187 | + |
| 188 | + # Should only be used when `key1 !== key2 and key1 == key2`. In the case |
| 189 | + defp key_less_than?(key1, key2) do |
| 190 | + hashed_key1 = hash_key(key1) |
| 191 | + hashed_key2 = hash_key(key2) |
| 192 | + cond do |
| 193 | + hashed_key1 === hashed_key2 -> |
| 194 | + fallback_key_hash(key1) < fallback_key_hash(key2) |
| 195 | + hashed_key1 < hashed_key2 -> true |
| 196 | + true -> false |
| 197 | + end |
| 198 | + end |
| 199 | + |
| 200 | + ### Operations |
| 201 | + |
| 202 | + #### Insert |
| 203 | + |
| 204 | + defp do_insert(nil, insert_key, insert_value, depth) do |
| 205 | + { |
| 206 | + 1, |
| 207 | + %Node{ |
| 208 | + Node.new(insert_key, insert_value, depth) | |
| 209 | + color: :red |
| 210 | + } |
| 211 | + } |
| 212 | + |
| 213 | + end |
| 214 | + |
| 215 | + defp do_insert(%Node{key: node_key}=node, insert_key, insert_value, _depth) when node_key === insert_key do |
| 216 | + {0, %Node{node | value: insert_value}} |
| 217 | + end |
| 218 | + |
| 219 | + defp do_insert(%Node{key: node_key}=node, insert_key, insert_value, depth) when insert_key < node_key do |
| 220 | + do_insert_left(node, insert_key, insert_value, depth) |
| 221 | + end |
| 222 | + |
| 223 | + defp do_insert(%Node{key: node_key}=node, insert_key, insert_value, depth) when insert_key > node_key do |
| 224 | + do_insert_right(node, insert_key, insert_value, depth) |
| 225 | + end |
| 226 | + |
| 227 | + # For cases when `insert_key !== node_key` but `insert_key == node_key` (e.g. |
| 228 | + # `1` and `1.0`,) hash the keys to provide consistent ordering. |
| 229 | + defp do_insert(%Node{key: node_key}=node, insert_key, insert_value, depth) when insert_key == node_key do |
| 230 | + if key_less_than?(insert_key, node_key) do |
| 231 | + do_insert_left(node, insert_key, insert_value, depth) |
| 232 | + else |
| 233 | + do_insert_right(node, insert_key, insert_value, depth) |
| 234 | + end |
| 235 | + end |
| 236 | + |
| 237 | + defp do_insert_left(%Node{left: left}=node, insert_key, insert_value, depth) do |
| 238 | + {nodes_added, new_left} = do_insert(left, insert_key, insert_value, depth + 1) |
| 239 | + {nodes_added, %Node{node | left: do_balance(new_left)}} |
| 240 | + end |
| 241 | + |
| 242 | + defp do_insert_right(%Node{right: right}=node, insert_key, insert_value, depth) do |
| 243 | + {nodes_added, new_right} = do_insert(right, insert_key, insert_value, depth + 1) |
| 244 | + {nodes_added, %Node{node | right: do_balance(new_right)}} |
| 245 | + end |
| 246 | + |
| 247 | + #### Delete |
| 248 | + |
| 249 | + # If we reach a leaf and the key never matched, do nothing |
| 250 | + defp do_delete(nil, _key) do |
| 251 | + {0, nil} |
| 252 | + end |
| 253 | + |
| 254 | + # If both the right and left are nil, the new tree is nil. For example, |
| 255 | + # deleting A in the following tree results in B having no left |
| 256 | + # |
| 257 | + # B |
| 258 | + # / \ |
| 259 | + # A C |
| 260 | + # |
| 261 | + defp do_delete(%Node{key: node_key, left: nil, right: nil}, delete_key) when node_key === delete_key do |
| 262 | + {1, nil} |
| 263 | + end |
| 264 | + |
| 265 | + # If left is nil and there is a right, promote the right. For example, |
| 266 | + # deleting C in the following tree results in B's right becoming D |
| 267 | + # |
| 268 | + # B |
| 269 | + # / \ |
| 270 | + # A C |
| 271 | + # \ |
| 272 | + # D |
| 273 | + # |
| 274 | + defp do_delete(%Node{key: node_key, left: nil, right: right}, delete_key) when node_key === delete_key do |
| 275 | + {1, %Node{right | depth: right.depth - 1}} |
| 276 | + end |
| 277 | + |
| 278 | + # If there is a left promote it. For example, |
| 279 | + # deleting B in the following tree results in C's left becoming A |
| 280 | + # |
| 281 | + # C |
| 282 | + # / \ |
| 283 | + # B D |
| 284 | + # / |
| 285 | + # A |
| 286 | + # |
| 287 | + defp do_delete(%Node{key: node_key, left: left, right: nil}, delete_key) when node_key === delete_key do |
| 288 | + {1, %Node{left | depth: left.depth - 1}} |
| 289 | + end |
| 290 | + |
| 291 | + # If there are both left and right nodes, recursively promote the left-most |
| 292 | + # nodes. For example, deleting E below results in the following: |
| 293 | + # |
| 294 | + # G => G |
| 295 | + # / \ / \ |
| 296 | + # E H => C H |
| 297 | + # / \ / \ |
| 298 | + # C F => B D |
| 299 | + # / \ / \ |
| 300 | + # A D => A F |
| 301 | + # \ |
| 302 | + # B |
| 303 | + # |
| 304 | + # |
| 305 | + defp do_delete(%Node{key: node_key, left: left, right: right}, delete_key) when node_key === delete_key do |
| 306 | + { |
| 307 | + 1, |
| 308 | + do_balance(%Node{ |
| 309 | + left | |
| 310 | + depth: left.depth - 1, |
| 311 | + left: do_balance(promote(left)), |
| 312 | + right: right |
| 313 | + }) |
| 314 | + } |
| 315 | + end |
| 316 | + |
| 317 | + defp do_delete(%Node{key: node_key}=node, delete_key) when delete_key < node_key do |
| 318 | + do_delete_left(node, delete_key) |
| 319 | + end |
| 320 | + |
| 321 | + defp do_delete(%Node{key: node_key}=node, delete_key) when delete_key > node_key do |
| 322 | + do_delete_right(node, delete_key) |
| 323 | + end |
| 324 | + |
| 325 | + # For cases when `delete_key !== node_key` but `delete_key == node_key` (e.g. |
| 326 | + # `1` and `1.0`,) hash the keys to provide consistent ordering. |
| 327 | + defp do_delete(%Node{key: node_key}=node, delete_key) when delete_key == node_key do |
| 328 | + if key_less_than?(delete_key, node_key) do |
| 329 | + do_delete_left(node, delete_key) |
| 330 | + else |
| 331 | + do_delete_right(node, delete_key) |
| 332 | + end |
| 333 | + end |
| 334 | + |
| 335 | + defp do_delete_left(%Node{left: left}=node, delete_key) do |
| 336 | + {nodes_removed, new_left} = do_delete(left, delete_key) |
| 337 | + { |
| 338 | + nodes_removed, |
| 339 | + %Node{ |
| 340 | + node | |
| 341 | + left: do_balance(new_left) |
| 342 | + } |
| 343 | + } |
| 344 | + end |
| 345 | + |
| 346 | + defp do_delete_right(%Node{right: right}=node, delete_key) do |
| 347 | + {nodes_removed, new_right} = do_delete(right, delete_key) |
| 348 | + { |
| 349 | + nodes_removed, |
| 350 | + %Node{ |
| 351 | + node | |
| 352 | + right: do_balance(new_right) |
| 353 | + } |
| 354 | + } |
| 355 | + end |
| 356 | + |
| 357 | + defp promote(nil) do |
| 358 | + nil |
| 359 | + end |
| 360 | + |
| 361 | + defp promote(%Node{left: nil, right: nil, depth: depth}=node) do |
| 362 | + %Node{ node | color: :red, depth: depth - 1 } |
| 363 | + end |
| 364 | + |
| 365 | + defp promote(%Node{left: left, right: nil, depth: depth}) do |
| 366 | + %Node{ left | color: :red, depth: depth - 1} |
| 367 | + end |
| 368 | + |
| 369 | + defp promote(%Node{left: nil, right: right, depth: depth}) do |
| 370 | + %Node{ right | color: :red, depth: depth - 1} |
| 371 | + end |
| 372 | + |
| 373 | + defp promote(%Node{left: left, right: right, depth: depth}) do |
| 374 | + balance(%Node{ |
| 375 | + left | |
| 376 | + depth: depth - 1, |
| 377 | + left: do_balance(promote(left)), |
| 378 | + right: right |
| 379 | + }) |
| 380 | + end |
| 381 | + |
| 382 | + #### Balance |
| 383 | + |
| 384 | + # If we have a tree that looks like this: |
| 385 | + # B (Black) |
| 386 | + # / \ |
| 387 | + # A D (Red) |
| 388 | + # / \ |
| 389 | + # C F (Red) |
| 390 | + # / \ |
| 391 | + # E G |
| 392 | + # |
| 393 | + # |
| 394 | + # Rotate to balance and look like this: |
| 395 | + # |
| 396 | + # D (Red) |
| 397 | + # / \ |
| 398 | + # B (Black) F (Black) |
| 399 | + # / \ / \ |
| 400 | + # A C E G |
| 401 | + # |
| 402 | + # |
| 403 | + defp do_balance( |
| 404 | + %Node{ |
| 405 | + color: :black, |
| 406 | + left: a_node, |
| 407 | + right: %Node{ |
| 408 | + color: :red, |
| 409 | + left: c_node, |
| 410 | + right: %Node{ |
| 411 | + color: :red, |
| 412 | + left: e_node, |
| 413 | + right: g_node |
| 414 | + }=f_node |
| 415 | + }=d_node |
| 416 | + }=b_node) do |
| 417 | + |
| 418 | + balanced_tree(a_node, b_node, c_node, d_node, e_node, f_node, g_node) |
| 419 | + end |
| 420 | + |
| 421 | + # If we have a tree that looks like this: |
| 422 | + # |
| 423 | + # B (Black) |
| 424 | + # / \ |
| 425 | + # A F (Red) |
| 426 | + # / \ |
| 427 | + # D (Red) G |
| 428 | + # / \ |
| 429 | + # C E |
| 430 | + # |
| 431 | + # Rotate to balance like so: |
| 432 | + # |
| 433 | + # D (Red) |
| 434 | + # / \ |
| 435 | + # B (Black) F (Black) |
| 436 | + # / \ / \ |
| 437 | + # A C E G |
| 438 | + # |
| 439 | + # |
| 440 | + # |
| 441 | + defp do_balance( |
| 442 | + %Node{ |
| 443 | + color: :black, |
| 444 | + left: a_node, |
| 445 | + right: %Node{ |
| 446 | + color: :red, |
| 447 | + left: %Node{ |
| 448 | + color: :red, |
| 449 | + left: c_node, |
| 450 | + right: e_node |
| 451 | + }=d_node, |
| 452 | + right: g_node |
| 453 | + }=f_node |
| 454 | + }=b_node) do |
| 455 | + |
| 456 | + balanced_tree(a_node, b_node, c_node, d_node, e_node, f_node, g_node) |
| 457 | + end |
| 458 | + |
| 459 | + # If we have a tree that looks like this: |
| 460 | + # |
| 461 | + # |
| 462 | + # F (Black) |
| 463 | + # / \ |
| 464 | + # D (Red) G |
| 465 | + # / \ |
| 466 | + # B (Red) E |
| 467 | + # / \ |
| 468 | + # A C |
| 469 | + # |
| 470 | + # |
| 471 | + # Rebalance to look like so: |
| 472 | + # |
| 473 | + # D (Red) |
| 474 | + # / \ |
| 475 | + # B (Black) F (Black) |
| 476 | + # / \ / \ |
| 477 | + # A C E G |
| 478 | + # |
| 479 | + defp do_balance(%Node{ |
| 480 | + color: :black, |
| 481 | + left: %Node{ |
| 482 | + color: :red, |
| 483 | + left: %Node{ |
| 484 | + color: :red, |
| 485 | + left: a_node, |
| 486 | + right: c_node |
| 487 | + }=b_node, |
| 488 | + right: e_node |
| 489 | + }=d_node, |
| 490 | + right: g_node |
| 491 | + }=f_node) do |
| 492 | + |
| 493 | + balanced_tree(a_node, b_node, c_node, d_node, e_node, f_node, g_node) |
| 494 | + end |
| 495 | + |
| 496 | + # If we have a tree that looks like this: |
| 497 | + # |
| 498 | + # F (Black) |
| 499 | + # / \ |
| 500 | + # B (Red) G |
| 501 | + # / \ |
| 502 | + # A D (Red) |
| 503 | + # / \ |
| 504 | + # C E |
| 505 | + # |
| 506 | + # Rebalance to look like this: |
| 507 | + # |
| 508 | + # D (Red) |
| 509 | + # / \ |
| 510 | + # B (Black) F (Black) |
| 511 | + # / \ / \ |
| 512 | + # A C E G |
| 513 | + # |
| 514 | + defp do_balance(%Node{ |
| 515 | + color: :black, |
| 516 | + left: %Node{ |
| 517 | + color: :red, |
| 518 | + left: a_node, |
| 519 | + right: %Node{ |
| 520 | + color: :red, |
| 521 | + left: c_node, |
| 522 | + right: e_node |
| 523 | + }=d_node |
| 524 | + }=b_node, |
| 525 | + right: g_node |
| 526 | + }=f_node) do |
| 527 | + |
| 528 | + balanced_tree(a_node, b_node, c_node, d_node, e_node, f_node, g_node) |
| 529 | + end |
| 530 | + |
| 531 | + |
| 532 | + defp do_balance(node) do |
| 533 | + node |
| 534 | + end |
| 535 | + |
| 536 | + defp balanced_tree(a_node, b_node, c_node, d_node, e_node, f_node, g_node) do |
| 537 | + min_depth = min_depth([a_node, b_node, c_node, d_node, e_node, f_node, g_node]) |
| 538 | + %Node { |
| 539 | + d_node | |
| 540 | + color: :red, |
| 541 | + depth: min_depth, |
| 542 | + left: %Node{b_node | color: :black, depth: min_depth + 1, |
| 543 | + left: %Node{a_node | depth: min_depth + 2}, |
| 544 | + right: %Node{c_node | depth: min_depth + 2}}, |
| 545 | + right: %Node{f_node | color: :black, depth: min_depth + 1, |
| 546 | + left: %Node{e_node | depth: min_depth + 2}, |
| 547 | + right: %Node{g_node | depth: min_depth + 2},} |
| 548 | + } |
| 549 | + end |
| 550 | + |
| 551 | + defp min_depth(list_of_nodes) do |
| 552 | + Enum.reduce(list_of_nodes, -1, fn (node, acc) -> |
| 553 | + if acc == -1 || node.depth < acc do |
| 554 | + node.depth |
| 555 | + else |
| 556 | + acc |
| 557 | + end |
| 558 | + end) |
| 559 | + end |
| 560 | + |
| 561 | + defp do_reduce(_order, nil, acc, _fun) do |
| 562 | + acc |
| 563 | + end |
| 564 | + |
| 565 | + # self, left, right |
| 566 | + defp do_reduce(:pre_order, %Node{left: left, right: right}=node, acc, fun) do |
| 567 | + acc_after_self = fun.(node, acc) |
| 568 | + acc_after_left = do_reduce(:pre_order, left, acc_after_self, fun) |
| 569 | + do_reduce(:pre_order, right, acc_after_left, fun) |
| 570 | + end |
| 571 | + |
| 572 | + # left, self, right |
| 573 | + defp do_reduce(:in_order, %Node{left: left, right: right}=node, acc, fun) do |
| 574 | + acc_after_left = do_reduce(:in_order, left, acc, fun) |
| 575 | + acc_after_self = fun.(node, acc_after_left) |
| 576 | + do_reduce(:in_order, right, acc_after_self, fun) |
| 577 | + end |
| 578 | + |
| 579 | + # left, right, self |
| 580 | + defp do_reduce(:post_order, %Node{left: left, right: right}=node, acc, fun) do |
| 581 | + acc_after_left = do_reduce(:post_order, left, acc, fun) |
| 582 | + acc_after_right = do_reduce(:post_order, right, acc_after_left, fun) |
| 583 | + fun.(node, acc_after_right) |
| 584 | + end |
| 585 | + end |
| 586 | + |
| 587 | + defimpl Access, for: RedBlackTree do |
| 588 | + def get(tree, key) do |
| 589 | + RedBlackTree.search(tree, key) |
| 590 | + end |
| 591 | + |
| 592 | + def get_and_update(tree, key, fun) do |
| 593 | + {get, update} = fun.(RedBlackTree.search(tree, key)) |
| 594 | + {get, RedBlackTree.insert(tree, key, update)} |
| 595 | + end |
| 596 | + end |
| 597 | + |
| 598 | + defimpl Collectable, for: RedBlackTree do |
| 599 | + def into(original) do |
| 600 | + {original, fn |
| 601 | + tree, {:cont, {key, value}} -> RedBlackTree.insert(tree, key, value) |
| 602 | + tree, :done -> tree |
| 603 | + _, :halt -> :ok |
| 604 | + end} |
| 605 | + end |
| 606 | + end |
| @@ -0,0 +1,14 @@ | |
| 1 | + defmodule RedBlackTree.Node do |
| 2 | + defstruct( |
| 3 | + color: :black, |
| 4 | + depth: 1, |
| 5 | + key: nil, |
| 6 | + value: nil, |
| 7 | + left: nil, |
| 8 | + right: nil |
| 9 | + ) |
| 10 | + |
| 11 | + def new(key, value, depth \\ 1) do |
| 12 | + %__MODULE__{key: key, value: value, depth: depth} |
| 13 | + end |
| 14 | + end |
| @@ -1,4 +1,5 @@ | |
| 1 1 | defmodule SortedSet do |
| 2 | + alias RedBlackTree |
| 2 3 | @moduledoc """ |
| 3 4 | A Set implementation that always remains sorted. |
| 4 5 | |
| @@ -10,9 +11,9 @@ defmodule SortedSet do | |
| 10 11 | |
| 11 12 | # Define the type as opaque |
| 12 13 | |
| 13 | - @opaque t :: %__MODULE__{members: list, size: non_neg_integer} |
| 14 | + @opaque t :: %__MODULE__{members: RedBlackTree, size: non_neg_integer} |
| 14 15 | @doc false |
| 15 | - defstruct size: 0, members: [] |
| 16 | + defstruct members: RedBlackTree.new, size: 0 |
| 16 17 | |
| 17 18 | @doc ~S""" |
| 18 19 | Returns a new `SortedSet`, initialized with the unique, sorted values of |
| @@ -53,7 +54,8 @@ defmodule SortedSet do | |
| 53 54 | [1,3,5] |
| 54 55 | """ |
| 55 56 | def to_list(%SortedSet{members: members}) do |
| 56 | - members |
| 57 | + RedBlackTree.to_list(members) |
| 58 | + |> Enum.map(fn ({key, _value}) -> key end) |
| 57 59 | end |
| 58 60 | |
| 59 61 | @doc ~S""" |
| @@ -69,9 +71,9 @@ defmodule SortedSet do | |
| 69 71 | iex> SortedSet.to_list SortedSet.put(set, 2) |
| 70 72 | [1,2,3,5] |
| 71 73 | """ |
| 72 | - def put(%SortedSet{members: members, size: size}, element) do |
| 73 | - {new_members, members_added} = do_put(members, element) |
| 74 | - %SortedSet{members: new_members, size: size + members_added} |
| 74 | + def put(%SortedSet{members: members}, element) do |
| 75 | + new_tree = RedBlackTree.insert members, element, element |
| 76 | + %SortedSet{members: new_tree, size: new_tree.size} |
| 75 77 | end |
| 76 78 | |
| 77 79 | @doc ~S""" |
| @@ -91,9 +93,9 @@ defmodule SortedSet do | |
| 91 93 | iex> SortedSet.to_list SortedSet.delete(set, 2) |
| 92 94 | [] |
| 93 95 | """ |
| 94 | - def delete(%SortedSet{members: members, size: size}, element) do |
| 95 | - {new_members, members_removed} = do_delete(members, element) |
| 96 | - %SortedSet{members: new_members, size: size - members_removed} |
| 96 | + def delete(%SortedSet{members: members}, element) do |
| 97 | + new_tree = RedBlackTree.delete members, element |
| 98 | + %SortedSet{members: new_tree, size: new_tree.size} |
| 97 99 | end |
| 98 100 | |
| 99 101 | ## SortedSet predicate methods |
| @@ -111,8 +113,8 @@ defmodule SortedSet do | |
| 111 113 | iex> SortedSet.member?(set, 0) |
| 112 114 | false |
| 113 115 | """ |
| 114 | - def member?(%SortedSet{}=set, element) do |
| 115 | - do_member?(to_list(set), element) |
| 116 | + def member?(%SortedSet{members: tree}, element) do |
| 117 | + RedBlackTree.has_key? tree, element |
| 116 118 | end |
| 117 119 | |
| 118 120 | # If the sizes are not equal, no need to check members |
| @@ -280,65 +282,6 @@ defmodule SortedSet do | |
| 280 282 | def difference(%SortedSet{}=set1, %SortedSet{size: 0}) do |
| 281 283 | set1 |
| 282 284 | end |
| 283 | - |
| 284 | - ## Private helper functions |
| 285 | - |
| 286 | - # SortedSet put |
| 287 | - |
| 288 | - defp do_put([head|tail], element) when element > head do |
| 289 | - {tail_members, members_added} = do_put(tail, element) |
| 290 | - {[head | tail_members], members_added} |
| 291 | - end |
| 292 | - |
| 293 | - defp do_put([head|_tail]=sorted_set, element) when element < head do |
| 294 | - {[element | sorted_set], 1} |
| 295 | - end |
| 296 | - |
| 297 | - defp do_put([head|_tail]=sorted_set, element) when element == head do |
| 298 | - {sorted_set, 0} |
| 299 | - end |
| 300 | - |
| 301 | - defp do_put([], element), do: {[element], 1} |
| 302 | - |
| 303 | - # SortedSet delete |
| 304 | - |
| 305 | - # If the element is less than the one we are looking at, we can safely |
| 306 | - # know it was never in the set |
| 307 | - defp do_delete([head|_tail]=members, element) when element < head do |
| 308 | - {members, 0} |
| 309 | - end |
| 310 | - |
| 311 | - # If the element is greater than the current head, we haven't reached where it |
| 312 | - # might exist in the set. Recur again on the tail. |
| 313 | - defp do_delete([head|tail], element) when element > head do |
| 314 | - {tail_members, members_removed} = do_delete(tail, element) |
| 315 | - {[head | tail_members], members_removed} |
| 316 | - end |
| 317 | - |
| 318 | - # If the element matches the head, drop it |
| 319 | - defp do_delete([head|tail], element) when element == head do |
| 320 | - {tail, 1} |
| 321 | - end |
| 322 | - |
| 323 | - defp do_delete([], _element) do |
| 324 | - {[], 0} |
| 325 | - end |
| 326 | - |
| 327 | - # SortedSet member? |
| 328 | - |
| 329 | - defp do_member?([head|_tail], element) when element < head do |
| 330 | - false |
| 331 | - end |
| 332 | - |
| 333 | - defp do_member?([head|tail], element) when element > head do |
| 334 | - do_member?(tail, element) |
| 335 | - end |
| 336 | - |
| 337 | - defp do_member?([head|_tail], element) when element == head do |
| 338 | - true |
| 339 | - end |
| 340 | - |
| 341 | - defp do_member?([], _element), do: false |
| 342 285 | end |
| 343 286 | |
| 344 287 | defimpl Enumerable, for: SortedSet do |
| @@ -3,7 +3,7 @@ defmodule SortedSet.Mixfile do | |
| 3 3 | |
| 4 4 | def project do |
| 5 5 | [app: :sorted_set, |
| 6 | - version: "0.1.1", |
| 6 | + version: "0.2.0", |
| 7 7 | source_url: "https://github.com/SenecaSystems/sorted_set", |
| 8 8 | elixir: "~> 1.0", |
| 9 9 | description: "SortedSet implementation for Elixir", |