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[pre-commit.ci] auto fixes from pre-commit.com hooks
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"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
"""
Returns the smallest member when n = 1000000
>>> solution(1000000)
14316
>>> solution(5000)
220
"""

sum_of_div = [0] * (number + 1)
for i in range(1, number // 2 + 1):
for j in range(i * 2, number + 1, i):
sum_of_div[j] += i

checked = [False] * (number + 1)
max_len_of_chain = 0
result = 0
for i in range(2, number + 1):
possible_chain = []
j = i
while not checked[j]:
checked[j] = True
possible_chain.append(j)
j = sum_of_div[j]
if j > number:
break
if j in possible_chain:
len_of_chain = len(possible_chain) - possible_chain.index(j)
if len_of_chain > max_len_of_chain:
max_len_of_chain = len_of_chain
result = min(possible_chain[-len_of_chain:])
break
return result


if __name__ == "__main__":
import doctest

doctest.testmod()
print(f"{solution() = }")
, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
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59 changes: 59 additions & 0 deletions
project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")

, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
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[pre-commit.ci] auto fixes from pre-commit.com hooks


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59 changes: 59 additions & 0 deletions
project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")

, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
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#9998
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[pre-commit.ci] auto fixes from pre-commit.com hooks


pre-commit-ci[bot] Oct 7, 2023

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project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")

, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
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[pre-commit.ci] auto fixes from pre-commit.com hooks


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project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")

, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
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[pre-commit.ci] auto fixes from pre-commit.com hooks


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project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")

, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
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[pre-commit.ci] auto fixes from pre-commit.com hooks


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project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")

, '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 : to add the solution of PROJECT EULER - 95 by kosuri-indu · Pull Request #9998 · TheAlgorithms/Python · GitHub
Skip to content
add : to add the solution of PROJECT EULER - 95#9998

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 Closed

kosuri-indu
wants to merge
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commits into

from

 Closed


add : to add the solution of PROJECT EULER - 95
#9998
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1d93eb3

to add the program


kosuri-indu Oct 7, 2023
ea33d45

[pre-commit.ci] auto fixes from pre-commit.com hooks


pre-commit-ci[bot] Oct 7, 2023

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59 changes: 59 additions & 0 deletions
project_euler/problem_095/sol1.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,59 @@
"""
Problem 95
Url: https://projecteuler.net/problem=95
Statement:
The proper divisors of a number are all the divisors excluding the number itself.
For example, the proper divisors of 28 is 1,2,4,7 and 14.
As the sum of these divisors is equal to 28, we call it a perfect number.
Interestingly the sum of the proper divisors of 220 is 284.
The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
For this reason, 220 and 284 are called an amicable pair.
Perhaps less well known are longer chains.
For example, starting with 12496, we form a chain of five numbers:
12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
Since this chain returns to its starting point, it is called an amicable chain.
Find the smallest member of the longest amicable chain with ..
no element exceeding one million.
"""


def solution(number: int = 10**6) -> int:
 """
 Returns the smallest member when n = 1000000
 >>> solution(1000000)
 14316
 >>> solution(5000)
 220
 """

 sum_of_div = [0] * (number + 1)
 for i in range(1, number // 2 + 1):
 for j in range(i * 2, number + 1, i):
 sum_of_div[j] += i

 checked = [False] * (number + 1)
 max_len_of_chain = 0
 result = 0
 for i in range(2, number + 1):
 possible_chain = []
 j = i
 while not checked[j]:
 checked[j] = True
 possible_chain.append(j)
 j = sum_of_div[j]
 if j > number:
 break
 if j in possible_chain:
 len_of_chain = len(possible_chain) - possible_chain.index(j)
 if len_of_chain > max_len_of_chain:
 max_len_of_chain = len_of_chain
 result = min(possible_chain[-len_of_chain:])
 break
 return result


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"{solution() = }")