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Update max_sub_array.py #8642

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Update max_sub_array.py
snehanjaligvs Apr 11, 2023
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75 changes: 13 additions & 62 deletions dynamic_programming/max_sub_array.py
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Open in desktop
Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
if low == high:
return low, high, a[low]
else:
mid = (low + high) // 2
left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
left_sum, max_left = -999999999, -1
right_sum, max_right = -999999999, -1
summ = 0
for i in range(mid, low - 1, -1):
summ += a[i]
if summ > left_sum:
left_sum = summ
max_left = i
summ = 0
for i in range(mid + 1, high + 1):
summ += a[i]
if summ > right_sum:
right_sum = summ
max_right = i
return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
"""
Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
>>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
187
"""
best = 0
current = 0
for i in nums:
current += i
current = max(current, 0)
best = max(best, current)
return best
sol = [0] * (len(a) + 1)
for i in range(1, len(sol)):
sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

answer = sol[0]
for i in range(1, len(sol)):
if answer < sol[i]:
answer = sol[i]
return answer


if __name__ == "__main__":
"""
A random simulation of this algorithm.
"""
import time
from random import randint

from matplotlib import pyplot as plt

inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
tim = []
for i in inputs:
li = [randint(1, i) for j in range(i)]
strt = time.time()
(find_max_sub_array(li, 0, len(li) - 1))
end = time.time()
tim.append(end - strt)
print("No of Inputs Time Taken")
for i in range(len(inputs)):
print(inputs[i], "\t\t", tim[i])
plt.plot(inputs, tim)
plt.xlabel("Number of Inputs")
plt.ylabel("Time taken in seconds ")
plt.show()
inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
print(max_sub_array(inputs))
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(function() {
function addCopyButtons() {
document.querySelectorAll('pre code').forEach(function(codeBlock) {
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codeBlock.parentElement.setAttribute('data-copy-added', 'true');
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btn.textContent = 'Copy';
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btn.onmouseover = function() { this.style.opacity = '1'; };
btn.onmouseout = function() { this.style.opacity = '0.7'; };
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btn.textContent = 'Copied!';
setTimeout(function() { btn.textContent = 'Copy'; }, 1500);
});
};
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codeBlock.parentElement.appendChild(btn);
});
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observer.observe(document.body, { childList: true, subtree: true });
})();
}
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})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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Update max_sub_array.py#8642

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#8642
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9f1b577

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319e88c

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


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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))

, '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('^' + ".*" + '
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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Update max_sub_array.py#8642

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Update max_sub_array.py
#8642
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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

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Open in desktop

Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))

, '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
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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('^' + ".*" + '
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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Update max_sub_array.py#8642

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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))

, '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" + '
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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Update max_sub_array.py#8642

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9f1b577

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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

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Open in desktop

Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))

, '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('^' + ".*" + '
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

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Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))

, '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('^' + ".*" + '
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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Update max_sub_array.py#8642

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Update max_sub_array.py
#8642
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9f1b577

Update max_sub_array.py


snehanjaligvs Apr 11, 2023
319e88c

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


pre-commit-ci[bot] Apr 11, 2023

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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))

, '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); }
})();
})();
Update max_sub_array.py by snehanjaligvs · Pull Request #8642 · TheAlgorithms/Python · GitHub
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Update max_sub_array.py#8642

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#8642
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9f1b577

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319e88c

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


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75 changes: 13 additions & 62 deletions
dynamic_programming/max_sub_array.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
@@ -1,44 +1,11 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


def find_max_sub_array(a, low, high):
 if low == high:
 return low, high, a[low]
 else:
 mid = (low + high) // 2
 left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
 right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
 cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
 if left_sum >= right_sum and left_sum >= cross_sum:
 return left_low, left_high, left_sum
 elif right_sum >= left_sum and right_sum >= cross_sum:
 return right_low, right_high, right_sum
 else:
 return cross_left, cross_right, cross_sum


def find_max_cross_sum(a, low, mid, high):
 left_sum, max_left = -999999999, -1
 right_sum, max_right = -999999999, -1
 summ = 0
 for i in range(mid, low - 1, -1):
 summ += a[i]
 if summ > left_sum:
 left_sum = summ
 max_left = i
 summ = 0
 for i in range(mid + 1, high + 1):
 summ += a[i]
 if summ > right_sum:
 right_sum = summ
 max_right = i
 return max_left, max_right, (left_sum + right_sum)


def max_sub_array(nums: list[int]) -> int:
def max_sub_array(a: list[int]) -> int:
 """
 Finds the contiguous subarray which has the largest sum and return its sum.

Expand All@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
 >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
 187
 """
 best = 0
 current = 0
 for i in nums:
 current += i
 current = max(current, 0)
 best = max(best, current)
 return best
 sol = [0] * (len(a) + 1)
 for i in range(1, len(sol)):
 sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

 answer = sol[0]
 for i in range(1, len(sol)):
 if answer < sol[i]:
 answer = sol[i]
 return answer


if __name__ == "__main__":
 """
 A random simulation of this algorithm.
 """
 import time
 from random import randint

 from matplotlib import pyplot as plt

 inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
 tim = []
 for i in inputs:
 li = [randint(1, i) for j in range(i)]
 strt = time.time()
 (find_max_sub_array(li, 0, len(li) - 1))
 end = time.time()
 tim.append(end - strt)
 print("No of Inputs Time Taken")
 for i in range(len(inputs)):
 print(inputs[i], "\t\t", tim[i])
 plt.plot(inputs, tim)
 plt.xlabel("Number of Inputs")
 plt.ylabel("Time taken in seconds ")
 plt.show()
 inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 print(max_sub_array(inputs))