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implement exercise binary-search-tree #412
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# Binary Search Tree | ||
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Insert and search for numbers in a binary tree. | ||
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When we need to represent sorted data, an array does not make a good | ||
data structure. | ||
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Say we have the array `[1, 3, 4, 5]`, and we add 2 to it so it becomes | ||
`[1, 3, 4, 5, 2]` now we must sort the entire array again! We can | ||
improve on this by realizing that we only need to make space for the new | ||
item `[1, nil, 3, 4, 5]`, and then adding the item in the space we | ||
added. But this still requires us to shift many elements down by one. | ||
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Binary Search Trees, however, can operate on sorted data much more | ||
efficiently. | ||
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A binary search tree consists of a series of connected nodes. Each node | ||
contains a piece of data (e.g. the number 3), a variable named `left`, | ||
and a variable named `right`. The `left` and `right` variables point at | ||
`nil`, or other nodes. Since these other nodes in turn have other nodes | ||
beneath them, we say that the left and right variables are pointing at | ||
subtrees. All data in the left subtree is less than or equal to the | ||
current node's data, and all data in the right subtree is greater than | ||
the current node's data. | ||
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For example, if we had a node containing the data 4, and we added the | ||
data 2, our tree would look like this: | ||
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4 | ||
/ | ||
2 | ||
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If we then added 6, it would look like this: | ||
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4 | ||
/ \ | ||
2 6 | ||
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If we then added 3, it would look like this | ||
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4 | ||
/ \ | ||
2 6 | ||
\ | ||
3 | ||
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And if we then added 1, 5, and 7, it would look like this | ||
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4 | ||
/ \ | ||
/ \ | ||
2 6 | ||
/ \ / \ | ||
1 3 5 7 | ||
## Source | ||
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Josh Cheek [https://twitter.com/josh_cheek](https://twitter.com/josh_cheek) | ||
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## Submitting Incomplete Solutions | ||
It's possible to submit an incomplete solution so you can see how others have completed the exercise. |
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%% Erlang compiler options | ||
{erl_opts, [debug_info, warnings_as_errors]}. | ||
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{deps, [{erl_exercism, "0.1.2"}]}. | ||
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{dialyzer, [ | ||
{warnings, [underspecs, no_return]}, | ||
{get_warnings, true}, | ||
{plt_apps, top_level_deps}, % top_level_deps | all_deps | ||
{plt_extra_apps, []}, | ||
{plt_location, local}, % local | "/my/file/name" | ||
{plt_prefix, "rebar3"}, | ||
{base_plt_apps, [stdlib, kernel, crypto]}, | ||
{base_plt_location, global}, % global | "/my/file/name" | ||
{base_plt_prefix, "rebar3"} | ||
]}. | ||
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%% eunit:test(Tests) | ||
{eunit_tests, []}. | ||
%% Options for eunit:test(Tests, Opts) | ||
{eunit_opts, [verbose]}. | ||
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%% == xref == | ||
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{xref_warnings, true}. | ||
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%% xref checks to run | ||
{xref_checks, [undefined_function_calls, undefined_functions, | ||
locals_not_used, exports_not_used, | ||
deprecated_function_calls, deprecated_functions]}. |
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{application, binary_search_tree, | ||
[{description, "exercism.io - binary-search-tree"}, | ||
{vsn, "0.0.1"}, | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Canonical data is at version 1.0.0. |
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{modules, []}, | ||
{registered, []}, | ||
{applications, [kernel, | ||
stdlib]}, | ||
{env, []} | ||
]}. | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Newline please. |
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-module(binary_search_tree). | ||
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-export([empty/0, value/1, left/1, right/1, insert/2, to_list/1]). | ||
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%% empty tree | ||
empty() -> undefined. | ||
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%% value at the top of _BST | ||
value(_BST) -> undefined. | ||
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%% left subtree | ||
left(_BST) -> undefined. | ||
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%% right subtree | ||
right(_BST) -> undefined. | ||
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%% insert _Value into _BST | ||
insert(_BST, _Value) -> undefined. | ||
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%% convert _BST to a sorted list | ||
to_list(_BST) -> undefined. | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Newline please. Also this should really be |
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-module(example). | ||
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-export([empty/0, value/1, left/1, right/1, insert/2, to_list/1]). | ||
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empty() -> empty. | ||
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value({V,_,_}) -> V. | ||
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left({_, L,_}) -> L. | ||
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right({_, _, R}) -> R. | ||
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insert(empty, V) -> {V, empty, empty}; | ||
insert({V1, L, R}, V2) when V1 < V2 -> {V1, L, insert(R, V2)}; | ||
insert({V1, L, R}, V2) when V1 >= V2 -> {V1, insert(L, V2), R}. | ||
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to_list(empty) -> []; | ||
to_list({V, L, R}) -> to_list(L) ++ [V] ++ to_list(R). | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Newline please |
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%% Based on canonical data version 1.4.0 | ||
%% https://github.com/exercism/problem-specifications/raw/master/exercises/bob/canonical-data.json | ||
%% This file is automatically generated from the exercises canonical data. | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. If the test suite is created manually (ie, there is no test generator), this line is wrong... There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. It were even wrong if it were from the generator, as it claims to be generated from |
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-module(binary_search_tree_tests). | ||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Please provide a comment, explaining that this was manually created from canonical data version 1.0.0 and a link to the specific commit (https://github.com/exercism/problem-specifications/blob/d5a4db7d282b16110e376f0ccfa91c80967b8b40/exercises/binary-search-tree/canonical-data.json) |
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-include_lib("erl_exercism/include/exercism.hrl"). | ||
-include_lib("eunit/include/eunit.hrl"). | ||
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'1_data_is_retained_test'() -> | ||
T = binary_search_tree:insert(binary_search_tree:empty(), 4), | ||
?assertMatch(4, binary_search_tree:value(T)). | ||
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'2_smaller_number_at_left_node_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), 4), | ||
2), | ||
?assertMatch(4, binary_search_tree:value(T)), | ||
?assertMatch(2, binary_search_tree:value(binary_search_tree:left(T))). | ||
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'3_same number_at_left_node_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), 4), | ||
4), | ||
?assertMatch(4, binary_search_tree:value(T)), | ||
?assertMatch(4, binary_search_tree:value(binary_search_tree:left(T))). | ||
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'4_greater_number_at_right_node_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), 4), | ||
5), | ||
?assertMatch(4, binary_search_tree:value(T)), | ||
?assertMatch(5, binary_search_tree:value(binary_search_tree:right(T))). | ||
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'5_can_create_complex_tree_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), | ||
4), | ||
2), | ||
6), | ||
1), | ||
3), | ||
5), | ||
7), | ||
?assertMatch(4, binary_search_tree:value(T)), | ||
?assertMatch(2, binary_search_tree:value(binary_search_tree:left(T))), | ||
?assertMatch(1, binary_search_tree:value( | ||
binary_search_tree:left( | ||
binary_search_tree:left(T)))), | ||
?assertMatch(3, binary_search_tree:value( | ||
binary_search_tree:right( | ||
binary_search_tree:left(T)))), | ||
?assertMatch(6, binary_search_tree:value(binary_search_tree:right(T))), | ||
?assertMatch(5, binary_search_tree:value( | ||
binary_search_tree:left( | ||
binary_search_tree:right(T)))), | ||
?assertMatch(7, binary_search_tree:value( | ||
binary_search_tree:right( | ||
binary_search_tree:right(T)))). | ||
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'6_can_sort_single_number_test'() -> | ||
T = binary_search_tree:insert(binary_search_tree:empty(), 2), | ||
?assertMatch([2], binary_search_tree:to_list(T)). | ||
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'7_can_sort_if_second_number_is_smaller_than_first_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), | ||
2), | ||
1), | ||
?assertMatch([1, 2], binary_search_tree:to_list(T)). | ||
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'8_can_sort_if_second_number_is_same_as_first_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), | ||
2), | ||
2), | ||
?assertMatch([2, 2], binary_search_tree:to_list(T)). | ||
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'9_can_sort_if_second_number_is_greater_than_first_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), | ||
2), | ||
3), | ||
?assertMatch([2, 3], binary_search_tree:to_list(T)). | ||
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'10_can_sort_complex_tree_test'() -> | ||
T = binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:insert( | ||
binary_search_tree:empty(), | ||
2), | ||
1), | ||
3), | ||
6), | ||
7), | ||
5), | ||
?assertMatch([1, 2, 3, 5, 6, 7], binary_search_tree:to_list(T)). |
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Choose a reason for hiding this comment
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Sections "Running tests" and "Questions?" are missing, please use
confliglet generate
to generate theREADME.md
.