Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
How to Compute Cosine Similarity Between Two Vectors in Python
This code calculates the cosine similarity between two numeric vectors using the dot product and Euclidean norms, returning a value between -1 and 1.
import math
def cosine_similarity(vec_a, vec_b):
if len(vec_a) != len(vec_b):
raise ValueError("Vectors must have the same length")
dot_product = sum(a * b for a, b in zip(vec_a, vec_b))
norm_a = math.sqrt(sum(a * a for a in vec_a))
norm_b = math.sqrt(sum(b * b for b in vec_b))
i…How to Compute the Cartesian Product of Two Lists in Python
Generates all ordered pairs from two lists using itertools.product and prints each combination.
from itertools import product
# Two small input lists
list_a = [1, 2, 3]
list_b = ["x", "y"]
# Compute the Cartesian product
result = list(product(list_a, list_b))
# Display the result
print("Cartesian product of", list_a, "and", list_b, "is:")
for pair in result:
print(pair)How to Compute the Dot Product of Two Lists in Python
Compute the dot product of two equal-length numeric lists using a generator expression with zip and sum.
def dot_product(list1, list2):
"""
Compute the dot product of two numeric lists.
The lists must have the same length.
"""
if len(list1) != len(list2):
raise ValueError("Lists must have the same length")
return sum(a * b for a, b in zip(list1, list2))
if __name__ == "__main__":
…How to Count Distinct Elements in a List in Python
Count the number of unique items in a list by converting it to a set and returning its length.
def count_distinct_elements(items):
return len(set(items))
if __name__ == "__main__":
sample = [1, 2, 3, 2, 1, 4, 3, 5, 4, 6]
result = count_distinct_elements(sample)
print(result)How to Count Occurrences of Each Value in Python
Count how many times each value appears in a list using Python's Counter from the collections module.
from collections import Counter
def count_occurrences(values):
"""Return a dictionary mapping each value to its count."""
return dict(Counter(values))
if __name__ == "__main__":
sample_data = ["apple", "banana", "apple", "cherry", "banana", "apple"]
result = count_occurrences(sample_data)
print(r…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 Find the Nearest Value to a Target in a Sorted List in Python
Use bisect to binary-search a sorted list and return the element closest to a target value.
import bisect
def nearest_value(sorted_list, target):
if not sorted_list:
return None
pos = bisect.bisect_left(sorted_list, target)
if pos == 0:
return sorted_list[0]
if pos == len(sorted_list):
return sorted_list[-1]
before = sorted_list[pos - 1]
after = sorted_list[po…How to Generate a Geometric Progression List in Python
This Python function builds a list of n terms in a geometric progression, starting with a given first term and multiplying by a constant ratio at each step.
def geometric_progression(first_term, ratio, count):
"""
Generate a list of 'count' terms in a geometric progression
starting with 'first_term' and multiplied by 'ratio' each step.
"""
progression = []
current = first_term
for _ in range(count):
progression.append(current)
c…How to Generate an Arithmetic Progression List in Python
Generates a list of terms in an arithmetic progression using a list comprehension.
def generate_ap(start, difference, count):
"""Generate a list of n terms in an arithmetic progression."""
return [start + i * difference for i in range(count)]
if __name__ == "__main__":
ap = generate_ap(3, 5, 6)
print(ap)How to Get the Breadth-First Traversal Order of a Graph in Python
Performs a breadth-first search on an adjacency list and returns the order nodes are visited, using a deque for efficient queue operations.
from collections import deque
def bfs_order(adjacency, start=0):
"""Return the order nodes are visited in a breadth-first traversal."""
visited = set()
order = []
queue = deque([start])
visited.add(start)
while queue:
node = queue.popleft()
order.append(node)
for neig…How to Heapify a List into a Min Heap with heapq in Python
Convert any list into a valid min heap in-place using Python's heapq.heapify(), then pop the smallest element to verify heap order.
import heapq
data = [5, 3, 8, 1, 9, 2, 7, 4, 6]
print("Original list:", data)
heapq.heapify(data)
print("Min heap:", data)
popped = heapq.heappop(data)
print("Smallest element popped:", popped)
print("Heap after pop:", data)How to Implement a Moving Average from a Data Stream in Python
Implement a MovingAverage class using a deque and running sum to compute the average of the last k values from a continuous data stream.
from collections import deque
class MovingAverage:
def __init__(self, size):
self.size = size
self.queue = deque()
self.window_sum = 0
def next(self, val):
self.queue.append(val)
self.window_sum += val
if len(self.queue) > self.size:
self.window_su…How to Implement a Recent Counter with a Deque in Python
Implements a RecentCounter class that uses a deque to count ping requests within the last 3000 milliseconds.
from collections import deque
import time
class RecentCounter:
def __init__(self):
self.hits = deque()
def ping(self, t: int) -> int:
self.hits.append(t)
while self.hits and self.hits[0] < t - 3000:
self.hits.popleft()
return len(self.hits)
if __name__ == "__mai…How to Remove Banned Values from a List in Python
Filters a list by removing elements present in a banned set, preserving the original order.
def remove_banned(values, banned):
banned_set = set(banned)
return [item for item in values if item not in banned_set]
if __name__ == "__main__":
values = [1, 2, 3, 4, 5, 2, 6, 3, 7]
banned = [2, 3]
result = remove_banned(values, banned)
print(result)How to Remove Duplicates in Python Preserving Order
Removes duplicate items from a list while keeping the first occurrence order intact using a set for fast membership checks.
def remove_duplicates_preserving_order(items):
seen = set()
result = []
for item in items:
if item not in seen:
seen.add(item)
result.append(item)
return result
if __name__ == "__main__":
sample = [3, 1, 2, 1, 3, 4, 2, 5]
unique_items = remove_duplicates_preserv…How to Replace Outliers Beyond Threshold with Cap in Python
Replace values that fall below a lower threshold or above an upper threshold by capping them to the threshold values using a simple Python function.
def replace_outliers_with_cap(data, lower_threshold=None, upper_threshold=None):
"""Replace values beyond given thresholds with the threshold values (capping)."""
if lower_threshold is None and upper_threshold is None:
raise ValueError("At least one threshold must be provided.")
capped_data = …How to Sample Random Items Without Replacement in Python
Select k random unique items from a sequence using random.sample for uniform, non-repeating selection.
import random
def sample_without_replacement(population, k):
"""Return k random items from population without replacement."""
if k > len(population):
raise ValueError("k cannot exceed population size")
# Use random.sample for O(k) time, no mutation of the original
return random.sample(populati…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…How to Split a List by a Predicate into Two Lists in Python
Partition any Python list into two lists based on a predicate: items that match go into one list, everything else into the other.
from typing import Callable, List, TypeVar
T = TypeVar("T")
def split_by_predicate(items: List[T], predicate: Callable[[T], bool]) -> tuple[List[T], List[T]]:
matching = []
non_matching = []
for item in items:
if predicate(item):
matching.append(item)
else:
non_mat…How to compress consecutive numbers into range strings in Python
Convert a sorted list of consecutive integers into compact range strings like '1-3', '5-6', and '15'.
def compress_ranges(nums):
"""Convert a list of sorted consecutive numbers into range strings."""
if not nums:
return []
ranges = []
start = prev = nums[0]
for num in nums[1:]:
if num == prev + 1:
prev = num
else:
if start == prev:
…How to partition a list into n nearly equal parts in Python
Divide a list into n contiguous chunks of nearly equal size using an average-length calculation that distributes the remainder evenly.
def partition(lst, n):
"""Partition a list into n nearly equal contiguous parts."""
if n <= 0:
raise ValueError("n must be positive")
if not lst:
return [[] for _ in range(n)]
parts = []
avg = len(lst) / n
last_idx = 0.0
while last_idx < len(lst):
end_idx =…Implement Queue Using Two Stacks in Python
Python class that implements a FIFO queue using two stacks, with enqueue, dequeue, peek, and emptiness checks.
class QueueUsingStacks:
def __init__(self):
self.stack_in = []
self.stack_out = []
def enqueue(self, value):
self.stack_in.append(value)
def dequeue(self):
if not self.stack_out:
while self.stack_in:
self.stack_out.append(self.stack_in.pop())
…Implement a Stack Using List Push Pop in Python
A minimal Stack class built on a Python list, with push, pop, peek, is_empty, and size methods, including empty-stack guards.
class Stack:
def __init__(self):
self.items = []
def push(self, item):
self.items.append(item)
def pop(self):
if self.is_empty():
raise IndexError("pop from empty stack")
return self.items.pop()
def peek(self):
if self.is_empty():
raise…Insert Multiple Values Into a Sorted List in Python
Insert multiple values into an already-sorted list while keeping it sorted using the bisect.insort function.
import bisect
def insert_sorted(sorted_list, values):
for value in values:
bisect.insort(sorted_list, value)
return sorted_list
if __name__ == "__main__":
original = [1, 3, 5, 7, 9]
new_values = [4, 6, 2, 8, 0]
result = insert_sorted(original, new_values)
print(f"Original: {original}"…Browse by section
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