Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Bucket Numbers into Histogram Bin Counts in Python
Partition a list of numbers into equal-width histogram bins and count how many fall into each bin using only the Python standard library.
from collections import Counter
def histogram_bins(numbers, num_bins):
"""Bucket numbers into histogram bin counts."""
if not numbers:
return []
min_val = min(numbers)
max_val = max(numbers)
bin_width = (max_val - min_val) / num_bins
# Handle edge case where all values are id…Find Longest Consecutive Run in an Unsorted List in Python
Find the length of the longest sequence of consecutive integers in an unsorted list using a set and a linear scan.
def longest_run(nums):
if not nums:
return 0
num_set = set(nums)
longest = 0
for num in num_set:
# Only start counting from the smallest number in a sequence
if num - 1 not in num_set:
current = num
length = 1
while current + 1 in num_set:
…Find Longest Consecutive Sequence in Python
Find the length of the longest consecutive elements sequence in an unsorted array using a set for O(n) lookups.
def longest_consecutive_length(nums):
num_set = set(nums)
longest = 0
for num in num_set:
if num - 1 not in num_set:
current = num
current_streak = 1
while current + 1 in num_set:
current += 1
current_streak += 1
…Find Longest Increasing Subsequence Length in Python
Compute the length of the longest increasing subsequence in an array using dynamic programming.
def longest_increasing_subsequence(nums):
if not nums:
return 0
dp = [1] * len(nums)
for i in range(1, len(nums)):
for j in range(i):
if nums[i] > nums[j]:
dp[i] = max(dp[i], dp[j] + 1)
return max(dp)
if __name__ == "__main__":
# Demo with…Find Median of Two Sorted Arrays in Python
Merges two sorted arrays with a two-pointer walk and returns the median of the combined sorted sequence.
def median_of_two_sorted_arrays(nums1, nums2):
merged = []
i = j = 0
while i < len(nums1) and j < len(nums2):
if nums1[i] <= nums2[j]:
merged.append(nums1[i])
i += 1
else:
merged.append(nums2[j])
j += 1
merged.extend(nums1[i:])
merged.…Find Missing Number in Python Sequence 1 to N
Find the missing number from a list containing numbers 1 to N using the arithmetic sum formula.
def find_missing_number(nums, n):
expected_sum = n * (n + 1) // 2
actual_sum = sum(nums)
return expected_sum - actual_sum
if __name__ == "__main__":
n = 10
numbers = [1, 2, 3, 4, 5, 6, 7, 9, 10]
missing = find_missing_number(numbers, n)
print(f"The missing number is: {missing}")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 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 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_…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 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 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 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 Generate Fibonacci Sequence in Python
Generate the first n Fibonacci numbers as a list using a simple iterative loop.
def fibonacci(n):
"""Generate the first n terms of the Fibonacci sequence."""
if n <= 0:
return []
seq = [0, 1]
while len(seq) < n:
seq.append(seq[-1] + seq[-2])
return seq[:n]
if __name__ == "__main__":
n = 10
result = fibonacci(n)
print(result)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 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 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 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())
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