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Add testing and text to notebook
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‎source-code/functional-programming/persistent_binary_search_tree.ipynb

Lines changed: 108 additions & 74 deletions
Original file line numberDiff line numberDiff line change
@@ -291,6 +291,49 @@
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" return flatten(left(tree)) + (value(tree), ) + flatten(right(tree))"
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]
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},
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{
295+
"cell_type": "markdown",
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"id": "d93d4c6e-d88f-49b1-b189-17017c7de51c",
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"metadata": {},
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"source": [
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"The implementation of `flatten` would be much simpler if we would use Python `list` rather than `tuple`, but given the fact that we want to program in a functional style, we make sure the data structures are immutable."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "113acbc3-b18b-4ef5-b993-1ab5d8b3a043",
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"metadata": {},
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"outputs": [],
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"source": [
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"def visualize_tree(tree, indent=''):\n",
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" '''Print a visualization of a tree to standard output\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" tree: tuple[Any, tuple | None, tuple | None] | None\n",
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" binary search tree to visualize\n",
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" '''\n",
317+
" if is_empty(tree):\n",
318+
" print(f'{indent}empty tree')\n",
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" else:\n",
320+
" print(f'{indent}{value(tree)}')\n",
321+
" if not is_empty(left(tree)):\n",
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" print(f'{indent} left:')\n",
323+
" visualize_tree(left(tree), indent + ' ')\n",
324+
" if not is_empty(right(tree)):\n",
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" print(f'{indent} right:')\n",
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" visualize_tree(right(tree), indent + ' ')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fa4074a4-e15b-4388-958e-7497a11eba64",
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"metadata": {},
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"source": [
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"# Testing"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b86c0c7a-d2c2-4e3a-8b70-108868d83f85",
@@ -301,140 +344,131 @@
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},
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{
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"cell_type": "code",
304-
"execution_count": 9,
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"execution_count": 28,
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"id": "2c595c38-71e1-4df1-8016-99b632373817",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"is_empty(empty())"
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"assert is_empty(empty()), 'empty tree is not empty'"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ccd1eec7-7eea-4193-9323-053d1638d3d9",
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"metadata": {},
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"source": [
328-
"Store the successive trees in a list that are obtained by inserting values into it, flatten them and print the result."
360+
"Store the successive trees in a list that are obtained by inserting values into it, that illustrates that this implementation of binary search trees is indeed persistent, and hence purely functional."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": 23,
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"id": "9bf2469e-c918-450e-bae0-86afa77dd371",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
341-
"4 into None\n",
342-
"1 into (4, None, None)\n",
343-
"7 into (4, (1, None, None), None)\n",
344-
"-3 into (4, (1, None, None), (7, None, None))\n",
345-
"1 into (4, (1, (-3, None, None), None), (7, None, None))\n",
346-
"8 into (4, (1, (-3, None, None), None), (7, None, None))\n",
347-
"4 into (4, (1, (-3, None, None), None), (7, None, (8, None, None)))\n",
348-
"9 into (4, (1, (-3, None, None), None), (7, None, (8, None, None)))\n",
349-
"-3 into (4, (1, (-3, None, None), None), (7, None, (8, None, (9, None, None))))\n",
350373
"None\n",
351-
"(4,)\n",
352-
"(1, 4)\n",
353-
"(1, 4, 7)\n",
354-
"(-3, 1, 4, 7)\n",
355-
"(-3, 1, 4, 7)\n",
356-
"(-3, 1, 4, 7, 8)\n",
357-
"(-3, 1, 4, 7, 8)\n",
358-
"(-3, 1, 4, 7, 8, 9)\n",
359-
"(-3, 1, 4, 7, 8, 9)\n"
374+
"(4, None, None)\n",
375+
"(4, (1, None, None), None)\n",
376+
"(4, (1, None, None), (7, None, None))\n",
377+
"(4, (1, (-3, None, None), None), (7, None, None))\n",
378+
"(4, (1, (-3, None, None), None), (7, None, None))\n",
379+
"(4, (1, (-3, None, None), None), (7, None, (8, None, None)))\n",
380+
"(4, (1, (-3, None, None), None), (7, None, (8, None, None)))\n",
381+
"(4, (1, (-3, None, None), None), (7, None, (8, None, (9, None, None))))\n",
382+
"(4, (1, (-3, None, None), None), (7, None, (8, None, (9, None, None))))\n"
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]
361384
}
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],
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"source": [
364387
"new_values = (4, 1, 7, -3, 1, 8, 4, 9, -3)\n",
365388
"trees = [empty()]\n",
366389
"for new_value in new_values:\n",
367-
" print(f'{new_value} into {trees[-1]}')\n",
368390
" trees.append(insert(trees[-1], new_value))\n",
369391
"for tree in trees:\n",
370-
" print(flatten(tree))"
392+
" print(tree)"
393+
]
394+
},
395+
{
396+
"cell_type": "markdown",
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"id": "c88e781a-303e-4ac4-933c-f9b3d9c39255",
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"metadata": {},
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"source": [
400+
"In order to test the implementation, you should note that when a correct binary search tree is flattened, the resulting tuple ir ordered, i.e, its elements are in ascending order. To test this, we implement the function `is_ordered`."
371401
]
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},
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{
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"cell_type": "code",
375-
"execution_count": 14,
376-
"id": "41b1e508-407c-4fb5-aa40-45943825a7dd",
405+
"execution_count": 26,
406+
"id": "d3da91e3-4658-43bc-a980-f611cf65bd35",
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"metadata": {},
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"outputs": [],
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"source": [
380-
"t = insert(insert(insert(insert(empty(), 3), 5), 1), 2)"
410+
"def is_ordered(elements):\n",
411+
" '''Check whether the elements of a tuple are orded\n",
412+
" \n",
413+
" Parameters\n",
414+
" ----------\n",
415+
" elements: tuple[Any] | None\n",
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" tuple to check\n",
417+
" \n",
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" Returns\n",
419+
" -------\n",
420+
" bool\n",
421+
" True if the tuple's elements are in order, False otherwise; None, that represents\n",
422+
" the elements of an empty tree is also consired ordered\n",
423+
" '''\n",
424+
" return (elements is None or len(elements) <= 1 or\n",
425+
" (elements[0] <= elements[1]) and is_ordered(elements[1:])) "
381426
]
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},
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{
384-
"cell_type": "code",
385-
"execution_count": 15,
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"id": "8b71169d-3660-4024-b23b-1a77037ea922",
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"cell_type": "markdown",
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"id": "e81e0471-68d8-440c-bf74-9d408fbd517d",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(1, 2, 3, 5)"
393-
]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"flatten(t)"
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"We can now test the implementation."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "d3da91e3-4658-43bc-a980-f611cf65bd35",
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"execution_count": 27,
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"id": "7ea1284c-8ca6-49b3-b051-263e3109d0f7",
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"metadata": {},
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"outputs": [],
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"source": [
411-
"def is_ordered(xs):\n",
412-
" return len(xs) <= 1 or (xs[0] <= xs[1]) and is_ordered(xs[1:]) "
443+
"new_values = (4, 1, 7, -3, 1, 8, 4, 9, -3)\n",
444+
"trees = [empty()]\n",
445+
"for new_value in new_values:\n",
446+
" trees.append(insert(trees[-1], new_value))\n",
447+
"for tree in trees:\n",
448+
" assert is_ordered(flatten(tree)), f'{tree} is not ordered'"
449+
]
450+
},
451+
{
452+
"cell_type": "markdown",
453+
"id": "36904405-5769-41db-9e8e-5314d50aa42b",
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"metadata": {},
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"source": [
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"Check whether the visualization works as expected."
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]
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},
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{
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"cell_type": "code",
417-
"execution_count": 10,
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"id": "113acbc3-b18b-4ef5-b993-1ab5d8b3a043",
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"execution_count": 16,
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"id": "41b1e508-407c-4fb5-aa40-45943825a7dd",
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"metadata": {},
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"outputs": [],
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"source": [
422-
"def visualize_tree(xs, indent=''):\n",
423-
" if is_empty(xs):\n",
424-
" print(f'{indent}empty tree')\n",
425-
" else:\n",
426-
" print(f'{indent}{value(xs)}')\n",
427-
" if not is_empty(left(xs)):\n",
428-
" print(f'{indent} left:')\n",
429-
" visualize_tree(left(xs), indent + ' ')\n",
430-
" if not is_empty(right(xs)):\n",
431-
" print(f'{indent} right:')\n",
432-
" visualize_tree(right(xs), indent + ' ')"
466+
"tree = insert(insert(insert(insert(empty(), 3), 5), 1), 2)"
433467
]
434468
},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": 22,
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"id": "df17e319-80d1-45c1-8fe9-bf81626ea48d",
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"metadata": {},
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"outputs": [
@@ -453,7 +487,7 @@
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}
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],
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"source": [
456-
"visualize_tree(t)"
490+
"visualize_tree(tree)"
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]
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}
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],

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