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cclauss merged 3 commits into from
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Add Integer Square Root Algorithm #10949

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Add Integer Square Root Algorithm
aqib-m31 Oct 25, 2023
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Update integer_square_root.py
cclauss Oct 29, 2023
e0dc27f
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73 changes: 73 additions & 0 deletions maths/integer_square_root.py
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@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
- This algorithm is designed for non-negative integers only.
- The result is rounded down to the nearest integer.
- The algorithm has a time complexity of O(log(x)).
- Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
"""
Returns the integer square root of a non-negative integer num.
Args:
num: A non-negative integer.
Returns:
The integer square root of num.
Raises:
ValueError: If num is not an integer or is negative.
>>> [integer_square_root(i) for i in range(18)]
[0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
>>> integer_square_root(625)
25
>>> integer_square_root(2_147_483_647)
46340
>>> from math import isqrt
>>> all(integer_square_root(i) == isqrt(i) for i in range(20))
True
>>> integer_square_root(-1)
Traceback (most recent call last):
...
ValueError: num must be non-negative integer
>>> integer_square_root(1.5)
Traceback (most recent call last):
...
ValueError: num must be non-negative integer
>>> integer_square_root("0")
Traceback (most recent call last):
...
ValueError: num must be non-negative integer
"""
if not isinstance(num, int) or num < 0:
raise ValueError("num must be non-negative integer")

if num < 2:
return num

left_bound = 0
right_bound = num // 2

while left_bound <= right_bound:
mid = left_bound + (right_bound - left_bound) // 2
mid_squared = mid * mid
if mid_squared == num:
return mid

if mid_squared < num:
left_bound = mid + 1
else:
right_bound = mid - 1

return right_bound


if __name__ == "__main__":
import doctest

doctest.testmod()
, 'i'); if (__m === '*' || __re.test(location.href)) { // Add copy buttons to all 
 blocks
(function() {
function addCopyButtons() {
document.querySelectorAll('pre code').forEach(function(codeBlock) {
if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;
codeBlock.parentElement.setAttribute('data-copy-added', 'true');
var btn = document.createElement('button');
btn.textContent = 'Copy';
btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';
btn.onmouseover = function() { this.style.opacity = '1'; };
btn.onmouseout = function() { this.style.opacity = '0.7'; };
btn.onclick = function() {
navigator.clipboard.writeText(codeBlock.textContent).then(function() {
btn.textContent = 'Copied!';
setTimeout(function() { btn.textContent = 'Copy'; }, 1500);
});
};
codeBlock.parentElement.style.position = 'relative';
codeBlock.parentElement.appendChild(btn);
});
}
addCopyButtons();
// Re-run on dynamic content
var observer = new MutationObserver(addCopyButtons);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
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Oct 29, 2023
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53a10df

Update integer_square_root.py


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e0dc27f

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maths/integer_square_root.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Force GitHub README to respect dark mode
(function() {
var style = document.createElement('style');
style.textContent = '
.markdown-body {
color-scheme: dark light;
}
.markdown-body pre { background: #161b22 !important; }
.markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }
.markdown-body table th, .markdown-body table td { border-color: #30363d !important; }
.markdown-body img { background: #0d1117; }
.markdown-body blockquote { border-left-color: #8b949e; }
.markdown-body hr { border-color: #30363d; }
';
document.head.appendChild(style);
})();
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
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Add Integer Square Root Algorithm#10949

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 Merged

cclauss
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Oct 29, 2023
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#10949
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5cfbc2e

Add Integer Square Root Algorithm


aqib-m31 Oct 25, 2023
53a10df

Update integer_square_root.py


cclauss Oct 29, 2023
e0dc27f

Update integer_square_root.py


cclauss Oct 29, 2023

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maths/integer_square_root.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Highlight search terms from Google/DuckDuckGo/Bing referrer
(function() {
var ref = document.referrer;
var terms = [];
if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {
var url = new URL(ref);
var q = url.searchParams.get('q') || url.searchParams.get('p');
if (q) {
terms = q.split(/\s+/).filter(function(t) { return t.length > 2; });
}
}
if (terms.length === 0) return;
var style = document.createElement('style');
style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';
document.head.appendChild(style);
function highlight(node) {
if (node.nodeType === 3) { // text node
var text = node.textContent;
var found = false;
terms.forEach(function(term) {
var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\]\\]/g, '\\') + ')', 'gi');
if (regex.test(text)) {
found = true;
var frag = document.createDocumentFragment();
var parts = text.split(regex);
parts.forEach(function(part, i) {
if (i % 2 === 0) {
frag.appendChild(document.createTextNode(part));
} else {
var span = document.createElement('span');
span.className = 'userscript-highlight';
span.textContent = part;
frag.appendChild(span);
}
});
node.parentNode.replaceChild(frag, node);
}
});
} else if (node.nodeType === 1 && node.childNodes) { // element
var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];
if (!skipTags.includes(node.tagName)) {
Array.from(node.childNodes).forEach(highlight);
}
}
}
highlight(document.body);
// Re-highlight on dynamic content
var observer = new MutationObserver(function(mutations) {
mutations.forEach(function(m) {
m.addedNodes.forEach(function(node) {
if (node.nodeType === 1 || node.nodeType === 3) highlight(node);
});
});
});
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
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Add Integer Square Root Algorithm#10949

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 Merged

cclauss
merged 3 commits into

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Oct 29, 2023
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Add Integer Square Root Algorithm
#10949
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5cfbc2e

Add Integer Square Root Algorithm


aqib-m31 Oct 25, 2023
53a10df

Update integer_square_root.py


cclauss Oct 29, 2023
e0dc27f

Update integer_square_root.py


cclauss Oct 29, 2023

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maths/integer_square_root.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Strip utm_, fbclid, gclid, etc. from all links on page
(function() {
var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',
'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
'ref', 'ref_src', 'source', 'medium', 'campaign'];
function cleanUrl(url) {
try {
var u = new URL(url, window.location.origin);
var changed = false;
trackingParams.forEach(function(p) {
if (u.searchParams.has(p)) {
u.searchParams.delete(p);
changed = true;
}
});
return changed ? u.toString() : url;
} catch (e) {
return url;
}
}
function cleanLinks() {
document.querySelectorAll('a[href]').forEach(function(a) {
var clean = cleanUrl(a.href);
if (clean !== a.href) a.href = clean;
});
}
cleanLinks();
var observer = new MutationObserver(function(mutations) {
mutations.forEach(function(m) {
m.addedNodes.forEach(function(node) {
if (node.nodeType === 1) {
if (node.tagName === 'A') cleanLinks();
node.querySelectorAll('a[href]').forEach(function(a) {
var clean = cleanUrl(a.href);
if (clean !== a.href) a.href = clean;
});
}
});
});
});
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
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Add Integer Square Root Algorithm#10949

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 Merged

cclauss
merged 3 commits into

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Oct 29, 2023
 Merged


Add Integer Square Root Algorithm
#10949
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5cfbc2e

Add Integer Square Root Algorithm


aqib-m31 Oct 25, 2023
53a10df

Update integer_square_root.py


cclauss Oct 29, 2023
e0dc27f

Update integer_square_root.py


cclauss Oct 29, 2023

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73 changes: 73 additions & 0 deletions
maths/integer_square_root.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Auto-enable theater mode on YouTube
(function() {
function tryTheater() {
var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]');
if (btn && !btn.classList.contains('activated')) {
btn.click();
}
}
// Try immediately
tryTheater();
// Try after navigation (SPA)
var lastUrl = location.href;
setInterval(function() {
if (location.href !== lastUrl) {
lastUrl = location.href;
setTimeout(tryTheater, 500);
}
}, 1000);
// Also try on player load
var observer = new MutationObserver(tryTheater);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
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Add Integer Square Root Algorithm#10949

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 Merged

cclauss
merged 3 commits into

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Oct 29, 2023
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Add Integer Square Root Algorithm
#10949
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5cfbc2e

Add Integer Square Root Algorithm


aqib-m31 Oct 25, 2023
53a10df

Update integer_square_root.py


cclauss Oct 29, 2023
e0dc27f

Update integer_square_root.py


cclauss Oct 29, 2023

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maths/integer_square_root.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Remove or un-stick sticky/fixed headers that block content
(function() {
function unstick() {
document.querySelectorAll('header, nav, [role="banner"], .header, .navbar, .sticky, .fixed-top, [style*="position: fixed"], [style*="position:sticky"]').forEach(function(el) {
if (el.style.position === 'fixed' || el.style.position === 'sticky' || getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {
el.style.position = 'static';
el.style.top = 'auto';
el.style.zIndex = 'auto';
}
});
}
unstick();
var observer = new MutationObserver(unstick);
observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });
})();
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
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Add Integer Square Root Algorithm#10949

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5cfbc2e

Add Integer Square Root Algorithm


aqib-m31 Oct 25, 2023
53a10df

Update integer_square_root.py


cclauss Oct 29, 2023
e0dc27f

Update integer_square_root.py


cclauss Oct 29, 2023

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maths/integer_square_root.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Universal Dark Mode - works on any site
(function() {
var enabled = true;
function applyDarkMode() {
if (!enabled) return;
// Create style element if it doesn't exist
var style = document.getElementById('universal-dark-mode-style');
if (!style) {
style = document.createElement('style');
style.id = 'universal-dark-mode-style';
document.head.appendChild(style);
}
// Dark mode CSS - inverts colors but preserves images/video
style.textContent = '
/* Invert everything except media */
html {
filter: invert(1) hue-rotate(180deg) !important;
background: #1a1a2e !important;
}
/* Restore images, videos, iframes, canvas */
img, video, iframe, canvas, svg, picture, [style*="background-image"] {
filter: invert(1) hue-rotate(180deg) !important;
}
/* Preserve specific elements that should not be inverted */
.no-dark-mode, .no-dark-mode *,
[data-theme="light"], [data-theme="light"],
.ace_editor, .ace_editor *,
.CodeMirror, .CodeMirror *,
.monaco-editor, .monaco-editor *,
.markdown-body pre, .markdown-body pre *,
.highlight, .highlight *,
pre code, pre code * {
filter: none !important;
}
/* Fix common UI elements */
.modal, .popup, .dropdown-menu, .tooltip, .popover {
filter: invert(1) hue-rotate(180deg) !important;
background: #2d2d44 !important;
border-color: #444 !important;
}
/* Scrollbars */
::-webkit-scrollbar { background: #1a1a2e !important; }
::-webkit-scrollbar-thumb { background: #444 !important; }
::-webkit-scrollbar-thumb:hover { background: #555 !important; }
/* Selection */
::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
';
}
function removeDarkMode() {
var style = document.getElementById('universal-dark-mode-style');
if (style) style.remove();
}
// Toggle with Alt+Shift+D
document.addEventListener('keydown', function(e) {
if (e.altKey && e.shiftKey && e.key === 'D') {
e.preventDefault();
enabled = !enabled;
if (enabled) {
applyDarkMode();
console.log('[Universal Dark Mode] Enabled');
} else {
removeDarkMode();
console.log('[Universal Dark Mode] Disabled');
}
}
});
// Apply on load
applyDarkMode();
// Re-apply on dynamic content
var observer = new MutationObserver(function(mutations) {
if (enabled && !document.getElementById('universal-dark-mode-style')) {
applyDarkMode();
}
});
observer.observe(document.head, { childList: true });
console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');
})();
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();
Add Integer Square Root Algorithm by aqib-m31 · Pull Request #10949 · TheAlgorithms/Python · GitHub
Skip to content
Add Integer Square Root Algorithm#10949

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Merged

cclauss
merged 3 commits into

from

Oct 29, 2023
 Merged


Add Integer Square Root Algorithm
#10949
 Changes from all commits
Commits

Show all changes


3 commits


Select commit
Hold shift + click to select a range
5cfbc2e

Add Integer Square Root Algorithm


aqib-m31 Oct 25, 2023
53a10df

Update integer_square_root.py


cclauss Oct 29, 2023
e0dc27f

Update integer_square_root.py


cclauss Oct 29, 2023

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73 changes: 73 additions & 0 deletions
maths/integer_square_root.py

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Open in desktop

Original file line numberDiff line numberDiff line change
@@ -0,0 +1,73 @@
"""
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_square_root
* https://docs.python.org/3/library/math.html#math.isqrt
Note:
 - This algorithm is designed for non-negative integers only.
 - The result is rounded down to the nearest integer.
 - The algorithm has a time complexity of O(log(x)).
 - Original algorithm idea based on binary search.
"""


def integer_square_root(num: int) -> int:
 """
 Returns the integer square root of a non-negative integer num.
 Args:
 num: A non-negative integer.
 Returns:
 The integer square root of num.
 Raises:
 ValueError: If num is not an integer or is negative.
 >>> [integer_square_root(i) for i in range(18)]
 [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
 >>> integer_square_root(625)
 25
 >>> integer_square_root(2_147_483_647)
 46340
 >>> from math import isqrt
 >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
 True
 >>> integer_square_root(-1)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root(1.5)
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 >>> integer_square_root("0")
 Traceback (most recent call last):
 ...
 ValueError: num must be non-negative integer
 """
 if not isinstance(num, int) or num < 0:
 raise ValueError("num must be non-negative integer")

 if num < 2:
 return num

 left_bound = 0
 right_bound = num // 2

 while left_bound <= right_bound:
 mid = left_bound + (right_bound - left_bound) // 2
 mid_squared = mid * mid
 if mid_squared == num:
 return mid

 if mid_squared < num:
 left_bound = mid + 1
 else:
 right_bound = mid - 1

 return right_bound


if __name__ == "__main__":
 import doctest

 doctest.testmod()