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Reworked algorithm descriptions. Added notebook index. Minor cleanup.

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Donne Martin 2015-05-02 17:14:29 -04:00
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131
arrays-strings/unique_chars.ipynb
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@ -4,7 +4,16 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem: Implement an algorithm to determine if a string has all unique characters"
"## Problem: Implement an algorithm to determine if a string has all unique characters\n",
"\n",
"* [Clarifying Questions](#Clarifying-Questions)\n",
"* [Test Cases](#Test-Cases)\n",
"* [Algorithm 1: Sets and Length Comparison](#Algorithm-1:-Sets-and-Length-Comparison)\n",
"* [Code: Sets and Length Comparison](#Code:-Sets-and-Length-Comparison)\n",
"* [Algorithm 2: Hash Map Lookup](#Algorithm-2:-Hash-Map-Lookup)\n",
"* [Code: Hash Map Lookup](#Code:-Hash-Map-Lookup)\n",
"* [Algorithm 3: In-Place](#Algorithm-3:-In-Place)\n",
"* [Code: In-Place](#Code:-In-Place)"
]
},
{
@ -13,7 +22,7 @@
"source": [
"## Clarifying Questions\n",
"* Is the string in ASCII (extended?) or Unicode? \n",
" * ASCII extended, which is 256 characters.\n",
" * ASCII extended, which is 256 characters\n",
"* Can you use additional data structures? \n",
" * Yes"
]
@ -24,40 +33,34 @@
"source": [
"## Test Cases\n",
"\n",
"* \"\" -> True\n",
"* \"foo\" -> False\n",
"* \"bar\" -> True"
"* '' -> True\n",
"* 'foo' -> False\n",
"* 'bar' -> True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"## Algorithm 1: Sets and Length Comparison\n",
"\n",
"We'll keep a hash map (set) to keep track of unique characters we encounter. \n",
"\n",
"Note:\n",
"* We could also use a dictionary, but it seems more logical to use a set as it does not contain duplicate elements.\n",
"* Since the characters are in ASCII, we could potentially use an array of size 128 (or 256 for extended ASCII)\n",
"\n",
"Steps:\n",
"* Scan each character.\n",
"* For each character:\n",
" * If the character does not exist in a hash map, add the character to a hash map.\n",
" * Else, return False.\n",
"* Return True\n",
"A set is an unordered collection of unique elements. \n",
"\n",
"* If the length of the set(string) equals the length of the string\n",
" * Return True\n",
"* Else\n",
" * Return False\n",
" \n",
"Complexity:\n",
"* Time: O(n).\n",
"* Space: Additional O(m), where m is the number of unique characters in the hash map."
"* Time: O(n)\n",
"* Space: Additional O(m), where m is the number of unique characters in the set"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
"## Code: Sets and Length Comparison"
]
},
{
@ -69,13 +72,7 @@
"outputs": [],
"source": [
"def unique_chars(string):\n",
" chars_set = set()\n",
" for char in string:\n",
" if char in chars_set:\n",
" return False\n",
" else:\n",
" chars_set.add(char)\n",
" return True\n",
" return len(set(string)) == len(string)\n",
"\n",
"print(unique_chars(''))\n",
"print(unique_chars('foo'))\n",
@ -86,10 +83,59 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm: No Additional Data Structures\n",
"## Algorithm 2: Hash Map Lookup\n",
"\n",
"We'll keep a hash map (set) to keep track of unique characters we encounter. \n",
"\n",
"Steps:\n",
"* Scan each character\n",
"* For each character:\n",
" * If the character does not exist in a hash map, add the character to a hash map\n",
" * Else, return False\n",
"* Return True\n",
"\n",
"Notes:\n",
"* We could also use a dictionary, but it seems more logical to use a set as it does not contain duplicate elements\n",
"* Since the characters are in ASCII, we could potentially use an array of size 128 (or 256 for extended ASCII)\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: Additional O(m), where m is the number of unique characters in the hash map"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code: Hash Map Lookup"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def unique_chars_alt(string):\n",
" chars_set = set()\n",
" for char in string:\n",
" if char in chars_set:\n",
" return False\n",
" else:\n",
" chars_set.add(char)\n",
" return True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm 3: In-Place\n",
"\n",
"Since we cannot use additional data structures, this will eliminate the fast lookup O(1) time provided by our hash map.\n",
"* Scan each character.\n",
"* Scan each character\n",
"* For each character:\n",
" * Scan all [other] characters in the array\n",
" * Exluding the current character from the scan is rather tricky in Python and results in a non-Pythonic solution\n",
@ -97,15 +143,15 @@
"* Return True\n",
"\n",
"Algorithm Complexity:\n",
"* Time: O(n^2).\n",
"* Space: In-place."
"* Time: O(n^2)\n",
"* Space: In-place"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
"## Code: In-Place"
]
},
{
@ -122,25 +168,6 @@
" return False\n",
" return True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pythonic Solution(s)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def unique_chars_alt2(string):\n",
" return len(set(string)) == len(string)"
]
}
],
"metadata": {