Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Find k Closest Points to Origin in Python
Sorts a list of (x, y) point tuples by their Euclidean distance from the origin and returns the k nearest points.
import math
def k_closest(points, k):
points.sort(key=lambda p: math.sqrt(p[0]**2 + p[1]**2))
return points[:k]
if __name__ == "__main__":
points = [(1, 2), (3, 4), (-1, 0), (5, 5), (0, 1)]
k = 3
result = k_closest(points, k)
print(f"Original points: {points}")
print(f"K closest points (k…How to Find Gaps Between Sorted Intervals in Python
This code finds gap ranges between sorted intervals using pairwise iteration, returning ranges where no interval covers.
from itertools import pairwise
def find_gaps(intervals):
intervals = sorted(intervals)
gaps = []
for prev, curr in pairwise(intervals):
if prev[1] < curr[0]:
gaps.append((prev[1] + 1, curr[0] - 1))
return gaps
if __name__ == "__main__":
intervals = [(1, 3), (5, 7), (10, 12), (…How to Sort Array by Parity (Even Before Odd) in Python
Rearrange an array so all even numbers appear before all odd numbers using a simple two-list partition approach.
def sort_array_by_parity(nums):
"""
Rearrange the array so that all even integers come first,
followed by all odd integers. The order within even and odd
groups is not required to be sorted.
"""
even = []
odd = []
for num in nums:
if num % 2 == 0:
even.append(nu…Merge Two Sorted Arrays Without Extra Space in Python
Merge two sorted arrays in-place from the end, using the trailing zeros in the first array to avoid extra space.
def merge_sorted(arr1, arr2):
m, n = len(arr1), len(arr2)
i, j = m - 1, n - 1
while j >= 0:
if i >= 0 and arr1[i] > arr2[j]:
arr1[i + j + 1] = arr1[i]
i -= 1
else:
arr1[i + j + 1] = arr2[j]
j -= 1
return arr1
if __name__ == "__main__":
…Rearrange array alternately max min in Python
Rearranges a sorted list so its elements alternate between the current maximum and current minimum using two pointers in O(n) time.
def rearrange_alternately(arr):
"""
Rearrange sorted array so elements alternate: max, min, next max, next min...
Returns a new list in O(n) time using O(n) space.
"""
n = len(arr)
result = []
left, right = 0, n - 1
while left <= right:
if left == right:
result.appen…Sort Unique Values by Frequency in Python
Count element frequencies with Counter and sort unique values by descending frequency, breaking ties alphabetically.
from collections import Counter
def sort_unique_by_frequency(values):
counts = Counter(values)
return sorted(counts.keys(), key=lambda x: (-counts[x], x))
if __name__ == "__main__":
data = [4, 2, 2, 8, 3, 3, 1, 3, 5, 5, 5, 5, 1]
result = sort_unique_by_frequency(data)
print(f"Sorted unique values…Sort list by multiple keys with tuple ordering in Python
Sort a list of dictionaries by multiple criteria — surname, age, then score descending — using a tuple key and negation.
def sort_multi_key(data):
# Sorts by surname, then age, then score descending
return sorted(
data,
key=lambda person: (
person['surname'].lower(),
person['age'],
-person['score'] # negative to reverse sort by score
)
)
if __name__ == "__main__"…Stable sort preserving equal order demo in Python
Demonstrates Python's stable sort, showing that elements with equal sort keys retain their original relative order.
from operator import itemgetter
def stable_sort_demo():
data = [(3, "first"), (1, "second"), (3, "third"), (1, "fourth"), (2, "fifth")]
print("Original:", data)
# Sort by first element (the tuple's first value), keeping relative order of equal items
sorted_data = sorted(data, key=itemgetter(0))
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