Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Find Pivot Index in Python
Locate the index where the sum of elements to the left equals the sum to the right, using a single pass with prefix sums.
def find_pivot_index(nums):
total = sum(nums)
left_sum = 0
for i, num in enumerate(nums):
if left_sum == total - left_sum - num:
return i
left_sum += num
return -1
if __name__ == "__main__":
test_cases = [
[1, 7, 3, 6, 5, 6],
[1, 2, 3],
[2, 1, -…Find Single Number Appearing Once in Python
Count frequency of each number in a list and return the one that appears exactly once when all others appear twice.
from collections import Counter
def find_single_number(nums):
counts = Counter(nums)
for num, count in counts.items():
if count == 1:
return num
return None
if __name__ == "__main__":
nums = [4, 1, 2, 1, 2]
result = find_single_number(nums)
print(f"Single number in {nums} …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…Find the Duplicate Number in Python Using Floyd's Cycle Detection
Detects the duplicate integer in an array of n+1 numbers (values 1 to n) in O(n) time and O(1) space using Floyd's cycle detection algorithm applied to a linked-list model.
def find_duplicate(nums):
slow = nums[0]
fast = nums[0]
# Phase 1: Find intersection point of the cycle
while True:
slow = nums[slow]
fast = nums[nums[fast]]
if slow == fast:
break
# Phase 2: Find the start of the cycle (the duplicate)
slow = nums[0…Find the Equilibrium Index of a List in Python
Find every index in a list where the sum of elements to its left equals the sum to its right, using a single pass.
def find_equilibrium_indexes(arr):
total = sum(arr)
left_sum = 0
indexes = []
for i, num in enumerate(arr):
total -= num
if left_sum == total:
indexes.append(i)
left_sum += num
return indexes
if __name__ == "__main__":
test = [1, 2, 3, -1, 2, 3]
result =…Find the First Index Where a Condition Is True in Python
Search any iterable for the first element matching a predicate and return its index, or -1 if none match.
def first_true_index(items, condition):
"""Return the first index where condition(item) is True, or -1 if none match."""
for i, item in enumerate(items):
if condition(item):
return i
return -1
if __name__ == "__main__":
numbers = [1, 3, 5, 8, 10, 12]
# Find first number greate…Find the Last Index Where a Condition Is True in Python
This code scans a sequence from the end and returns the index of the last element that satisfies a given condition, or -1 if none do.
def last_index_where(sequence, condition):
"""Return the index of the last element in sequence that satisfies condition."""
for i in range(len(sequence) - 1, -1, -1):
if condition(sequence[i]):
return i
return -1
if __name__ == "__main__":
numbers = [1, 4, 7, 2, 9, 5, 8, 3]
is_…Find the Majority Element in Python with Boyer-Moore Vote
Use Boyer-Moore majority vote to find the element appearing more than n/2 times in an array in O(n) time and O(1) space.
def majority_element(nums):
candidate = None
count = 0
for num in nums:
if count == 0:
candidate = num
count += 1 if num == candidate else -1
return candidate
if __name__ == "__main__":
nums = [2, 2, 1, 1, 1, 2, 2]
result = majority_element(nums)
print(f"Major…Find the Second Largest Unique Number in a Python List
This Python function finds the second largest unique number from a list by converting it to a set, removing the maximum, and returning the new maximum.
def second_largest_unique(numbers):
unique_numbers = set(numbers)
if len(unique_numbers) < 2:
return None
unique_numbers.remove(max(unique_numbers))
return max(unique_numbers)
if __name__ == "__main__":
test_list = [4, 2, 9, 5, 2, 9, 1, 5]
result = second_largest_unique(test_list)
…Find two unique numbers in an array with Python
Returns the two numbers that appear exactly once in a list where every other number appears twice, using XOR bit manipulation.
def find_two_odd(arr):
"""Return the two numbers that appear exactly once, while all others appear twice."""
xor_all = 0
for num in arr:
xor_all ^= num
# xor_all now equals the XOR of the two unique numbers.
# Find a set bit (any bit where they differ).
diff_bit = xor_all & (-xor_all)
…Game of Life Next State Grid in Python
Compute the next generation of Conway's Game of Life from a 2D grid using the standard three rules with neighbor counting.
def next_state(grid):
m, n = len(grid), len(grid[0])
new = [[0] * n for _ in range(m)]
for r in range(m):
for c in range(n):
total = 0
for dr in (-1, 0, 1):
for dc in (-1, 0, 1):
if dr == 0 and dc == 0:
continue
…Generate Pascal's Triangle Rows in Python
Builds Pascal's triangle as a list of rows, where each inner value is the sum of the two values above it.
def generate_pascals_triangle(rows):
triangle = []
for row_num in range(rows):
row = [1] * (row_num + 1)
for col in range(1, row_num):
row[col] = triangle[row_num - 1][col - 1] + triangle[row_num - 1][col]
triangle.append(row)
return triangle
if __name__ == "__main__":
…How to Add Two Lists Elementwise in Python
Add two equal-length lists element by element using a list comprehension with zip, returning a new list of summed values.
def elementwise_add(list1, list2):
return [a + b for a, b in zip(list1, list2)]
if __name__ == "__main__":
list_a = [1, 2, 3, 4]
list_b = [10, 20, 30, 40]
result = elementwise_add(list_a, list_b)
print(result)How to Apply a Function to Sliding Window Slices in Python
This Python code applies a given function to every contiguous window of a specified size in a list, returning a list of results.
def apply_to_sliding_windows(data, window_size, func):
return [func(data[i:i + window_size]) for i in range(len(data) - window_size + 1)]
if __name__ == "__main__":
numbers = [1, 2, 3, 4, 5, 6]
window_size = 3
results = apply_to_sliding_windows(numbers, window_size, sum)
print(results)
results…How to Build a Coordinate Grid with Nested Loops in Python
Generate a 2D list of (row, col) coordinate pairs using nested loops and return the grid structure.
def build_coordinate_grid(rows, cols):
"""Build a 2D grid of (row, col) coordinates using nested loops."""
grid = []
for r in range(rows):
row = []
for c in range(cols):
row.append((r, c))
grid.append(row)
return grid
if __name__ == "__main__":
grid = build_coo…How to Combine filter and map with a List Comprehension in Python
This Python code demonstrates how to combine filtering and mapping in a single list comprehension and shows the equivalent filter() and map() approach.
def square(x):
return x * x
def is_even(x):
return x % 2 == 0
numbers = [1, 2, 3, 4, 5, 6, 7, 8]
result = [square(x) for x in numbers if is_even(x)]
print(f"Original numbers: {numbers}")
print(f"Squares of even numbers: {result}")
# Combined filter + map equivalent
filtered = filter(is_even, numbers)
mapp…How to Compare Two Lists Elementwise for Greater Flags in Python
Compare two equal-length lists element by element and return a list of booleans marking where list_a values are greater than list_b values.
def compare_lists_greater(list_a, list_b):
"""
Compare two lists elementwise and return a list of booleans
indicating whether each element in list_a is greater than the
corresponding element in list_b.
"""
if len(list_a) != len(list_b):
raise ValueError("Lists must have the same length"…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 Jaccard Similarity in Python
Compute the Jaccard similarity between two lists by converting them to sets and dividing the intersection size by the union size.
def jaccard_similarity(list1, list2):
set1 = set(list1)
set2 = set(list2)
intersection = set1 & set2
union = set1 | set2
if not union:
return 0.0
return len(intersection) / len(union)
if __name__ == "__main__":
a = [1, 2, 3, 4, 5]
b = [3, 4, 5, 6, 7]
pri…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 Decode a String with Repeated Brackets in Python
Decodes strings with patterns like '3[a]2[bc]' by using a stack to handle nested and repeated bracket groups.
def decode_string(s: str) -> str:
stack = []
current_num = 0
current_str = ""
for ch in s:
if ch.isdigit():
current_num = current_num * 10 + int(ch)
elif ch == "[":
stack.append((current_str, current_num))
current_str = ""
current_num = 0…Browse by section
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